GENERAL PHYSICS
1.1 INTRODUCTION
PHYSICS can be defined as the study of the physical properties of matter and the concepts of energy
MATTER refers to any material that can occupy some space and can be measured, weighed or examined by
experimental testing.
1.2 MEASUREMENT
1.2.1 Physical quantities
Any measurable physical feature or property of an object is called its PHYSICAL QUANTITY, e.g. temperature
of a body, an area of a field, speed of a car, etc.
In Physics length, mass and time are known as Basic or Fundamental physical quantities.
Many other physical quantities (e.g. force, speed, velocity, voltage, etc) are related to these fundamental physical
quantities, therefore they are known as DERIVED PHYSICAL QUANTITIES. (Even their units can be derived
from those of fundamental quantities and hence are called derived units) e.g.
SI unit of speed
Then SI unit of speed = SI unit of distance/SI unit of time
= m/s (read as metre per second)
1.2.2 INTERNATIONAL SYSTEM OF UNITS (Systĕme International d’Unitĕs- SI UNITS)
This is an internationally agreed system of units used to measure physical quantities. (Originally known as MKS
system; M- metre, K- kilogram and S- second). Each quantity has its own SI unit.
FUNDAMENTAL PHYSICAL QUANTITIES AND THEIR SI UNITS
Physical quantity
length
mass
time
symbol
L, l
m
t
SI unit
metre
kilogram
second
Symbol
m
kg
s
SOME DERIVED QUANTITIES AND THEIR SI UNITS
Quantity
symbol
SI unit
Symbol
area
acceleration
energy
force
density
power
velocity
pressure
frequency
period
A
a
E
F
D, ρ
P
u, v
P
f
T
square metre
metre per second squared
joule
newton
kilogram per cubic metre
watt
metre per second
pascal
hertz
second
m2
m/s2, m s-2
J
N
kg/m3
W
m/s, m s-1
Pa
Hz
s
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1.2.3 Submultiples and multiples of a base unit
These are bigger or smaller units obtained by putting certain prefixes (with scientific meanings) in front of a base
unit.
Examples
SUBMULTIPLES
Centimetre (cm), decisecond (ds), microvolt(μV), etc.
MULTIPLES
kilometre (km), gigawatt (GW), megahertz (MHz), etc.
PREFEXES USED IN SUBMULTIPLES AND MULTIPLES
Prefix
symbol
meaning
value
Conversion factor
nanomicromillicentideci-
n
μ
m
c
d
One thousand millionth
One millionth
One thousandth
One hundredth
One tenth
0.000 000 001
0.000 001
0.001
0.01
0.1
10-9
10-6
10-3
10-2
10-1
kilomegagiga-
k
M
G
One thousand
One million
One thousand million
1000
1 000 000
1 000 000 000
103
106
1012
1.2.4
CONVERSION OF UNITS:
Rule 1: When you convert from a larger to smaller unit, you multiply (by an appropriate conversion factor) ; e.g.
km -------> m; multiply by 1000.
Rule 2: When you convert from a smaller to larger unit, you divide (by an appropriate conversion factor); e.g.
seconds ----------> hours; divide by 3600
1.2.5
LENGTH
Definition: is the distance between two points
SI unit: metre (m)
Other units: centimetre (cm); 1 m = 100 cm
millimetre (mm); 1 m = 1000 mm
micrometre (μm); 1 m = 106 μm
nanometre (nm); 1 m = 109 nm
MEASURING INSTRUMENTS
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Ruler
Measuring tape
Vernier calliper
Micrometre screwgauge
Mileometer
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1) RULER ( metre rule)
Many length measurements are made using rulers. Owing to the thickness of the ruler, it is essential that the
reader’s eye must always be right above the mark to be read i.e. line of sight should make an angle of 90° with
the ruler, in order to avoid parallax error.
*Avoid start measuring from the dead end of a ruler since some parts of that end may be worn out and so the
end will not coincide with the zero mark of the ruler. The reader may start at, let say 10 cm mark, and then
subtract 10 cm from the obtained reading to get the actual length measured.
*A ruler can be read up to 1 decimal place in cm scale i.e. it is accurate to 0.1 cm.
2) VERNIER CALLIPER
A vernier calliper is used to measure length where an ordinary ruler cannot be used, e.g. measuring the inside
and outside diameter of a cylinder (test-tube).
Vernier calliper has two scales; a) main scale, b) vernier scale and is accurate to 0.1 mm or 0.01 cm.
HOW TO READ A VERNIER CALLIPER
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-First read the main scale
 Read the main scale mark on the immediate left of the zero mark of the vernier scale and record it as
main scale reading (M.S).
-Then read the vernier scale
 Look along the vernier scale until you find a mark exactly in line with (or closest to) one of the marks on
the main scale. Multiply the number of this mark by 0.01 cm for cm scale (or 0.1 mm for mm scale).
Record the product as vernier scale reading (V.S).
-Finally, to obtain the actual length of the object (vernier caliper’s reading), add the vernier scale reading to the
main scale reading
i.e.
Final reading = M.S + V.S
EXAMPLE
M.S = 5.3 cm
V. S = 8 x 0.01 cm
= 0.08
Final reading = 5.3 + 0.08
= 5.38 cm
3) MICROMETER SCREWGAUGE
This instrument measures very small lengths such as the diameter of a wire, thickness of a coin, thickness of a
sheet of paper.
HOW TO TAKE A READING FROM A MICROMETER
 Put the object between the spindle and anvil. Turn the thimble until the object is gripped very gently.
Fine adjustment can be obtained by turning the ratchet until a click sound is heard.
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To read the micrometer, first read the main scale on the sleeve. Sleeve reading (S) is given by the value
of the last visible mark on sleeve before the edge of the thimble. Note that sleeve marks above the
central horizontal line on the sleeve are full millimetre marks but those below are half-millimetre marks.
Then read the thimble scale. Thimble reading (T) is equal to the number of the thimble division level
with the sleeve scale central line multiplied by 0.01 mm.
Final reading = sleeve reading + thimble reading
EXAMPLE
S = 18.00 mm
T = 42 x 0.01 mm
= 0.42 mm
Final reading = 18.00 + 0.42
= 18.42 cm
POSSIBLE SOURCES OF ERRORS IN LENGTH MEASUREMENTS
1) Wrong calibration of instrument – where scale is wrongly marked or adjusted
2) Zero error - instrument fails to read exactly zero before any measurement is made or when nothing is
measured.
3) Parallax error - Failure to position the eye correctly.
PRECAUTIONS TO BE TAKEN TO AVOID ERRORS WHEN MEASURING LENGTH
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Zero the instrument before use (re-set the instrument to read zero), if necessary take the appropriate
measures to correct any zero error detected by either adding or subtracting its value from the obtained
reading.
Place your eye right above the mark to be read in order to avoid parallax error.
Before using a micrometer screwgauge, wipe clean the faces of the anvil and spindle to remove any
dust on them.
Take several readings from different positions on the object and then find the average.
1.2.6 TIME
Time can be defined as is the interval between two events.
SI unit: second (s)
Other units: microsecond (μs), millisecond (ms), decisecond (ds), minute (min), hour (h), day, year, etc.
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time
24 hours (86 400s)
60 minutes (3600 s)
60 seconds
10-3 seconds
name
day
hour
minute
millisecond
symbol
d
h
min
ms
Time can be measured with stopwatches or clocks. The electronic stopwatch can measure time precisely up to
1/100 of a second (0.01 s)
Time = 1 min + 48 s + 5/100 s
= 1 min 48.05 s
time = 0 min + 15 s
= 15.00 s
THE SIMPLE PENDULUM
A pendulum is a piece of a thread which is fixed at one end and tied to a metal ball (called a bob) on the other
end.
The bob of a pendulum is free to swing from one side to another.
The amplitude (a) of a pendulum is the angle between the rest position and position of maximum displacement.
The length (l) of pendulum is measured from the fixed position to the centre of the bob.
The period (T) of the pendulum is the time taken by the bob to complete one swing or oscillation, i.e. the time
taken by the bob to move from point A to C and back to A in the diagram below. Period is measured in seconds
(s)
Period = total time taken/number complete swings(oscillations)
Frequency (f) is the number of completed oscillations generated in 1 second. The SI unit is hertz (Hz)
frequency = number of swings/total time taken
Therefore;
f = 1/T
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or T = 1/f
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then 1 Hz = 1/s
EXPERIMENT:- To determine the period (T) of a simple pendulum
Procedure
 Set up a pendulum as shown in the diagram above with l = 10 cm.
 Pull the bob slightly to one and then release it and then let the pendulum make few oscillations until they
are periodic and start the stopwatch.
 Using the stopwatch, find the time t1 for 20 oscillations. Find time t2 for another 20 oscillations.
 Find the average time <t> for 20 oscillations using the equation <t> = (t1 + t2)/2.
 Calculate the period of the pendulum using the formula T = <t>/20.
 Repeat the experiment for different values of l; l = 20 cm, l = 30 cm, l = 40 cm, l = 50 and l = 60 cm.
 Record the observations appropriately in a table
 Plot a graph of T2 against l
Table of Results
Length l/cm
70.0
60.0
50.0
40.0
30.0
Time for 20
oscillations t
t1/s
t2/s
32.28
32.06
29.37
29.69
26.78
26.82
24.93
23.29
24.12
22.15
Average time <t>/s
Period T/s
T2/s2
32.17
29.53
26.80
24.11
23.14
1.61
1.48
1.34
1.21
1.16
2.6
2.2
1.8
1.5
1.3
Plot a graph of T2 against L
T2/s2
L/cm
From the experiment we found that
 The period of pendulum is affected by the length of the pendulum. (NB:- The size of the bob and
amplitude of the pendulum [for small angles] do not affect the period).
 The graph is a straight line which means T2 is directly proportional to l, this means if l is doubled, T
quadruples.
SOURCES OF ERROR IN TIME MEASUREMENT
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1.2.7
Human reaction time- a time lag between seeing an event and starting the watch. For people the lag is
normally 0.2 s.
The watch/clock may move faster or slower that the normal time/rate. This introduces a systematic
error in every reading taken using that watch.
Instrumental error /zero error – failure to re-set the watch to zero before starting to time the event.
ACCURACY OF A MEASURING INSTRUMENT
A more accurate instrument measures any quantity with least approximation. The accuracy of any given
instrument is represented numerically by the value of smallest unit an instrument can measure without
approximation. This is usually given by the value of the smallest division in any scale.
Examples
The accuracy of a: metre rule is 0.1 cm (0.01 mm)
 vernier calliper is 0.01 cm (0.1 mm)
 micrometer is 0.01 mm (0.001 cm)
 stopwatch is 0.01 s
 clock is 1 s
 lab thermometer is 1° C.
Accurancy = 1- 0/10 = 0.1 A
1.3
QUESTIONS
1. Complete the table below to show what property is measured by the instrument or what the instrument can be
used to measure the property stated. State the correct unit in each case.
instrument
Micrometer
Stopwatch
Property measured
Unit
length
centimetre
2. What are lengths of the objects in the diagrams below?
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3. What are the readings shown by the micrometers below?
(a)
(b)
4. What is time shown by the each of the stopwatches below?
(a)
(b)
5. (a) The diagram below shows a simple pendulum.
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The bob of the pendulum was pulled to position A and then was released. The period of the pendulum was
found to be 0.64 s.
(i) Describe, in terms of positions A, B or C, what is meant by one complete swing.
(ii) How long did it take the pendulum bob to swing from A to B?
(iii) Explain briefly how the period could be accurately measured.
(b) A student performs an experiment to determine the period of a simple pendulum. She uses a stopwatch to
record the time taken to produce 20 oscillations. The diagram below shows the face of the stopwatch
used.
(i) What is the time recorded by the stopwatch?
(ii) Calculate the period of the pendulum.
(iii) State two factors that affect the period of the pendulum.
6. A piece of metal pipe is 3 m long, and its internal and external diameters are 20.0 mm and 24.0 mm
respectively. Describe how you would obtain experimentally accurate values of these (i) the internal and (ii)
external diameters of the pipe.
7. Fig. 7.1 shows the face of an ammeter. The ammeter reads 0.2 A with no current passing through.
Fig. 7.1
(a) What is the value of the accuracy of the ammeter?
(b) What error does the ammeter show?
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c. Fig. 7.1 shows the same ammeter with current passing through.
Fig. 7.2
(i) What is the reading shown?
(ii) What is the correct value of the current passing through the ammeter?
8. In each of the following pairs, which quantity is larger?
(a) 2 km or 2500 m?
(b) 2 m or 1500 mm?
(c) 2 tonnes or 3000 kg?
(d) 2 litres or 300 cm3?
2.0 MOTION
*Scalar quantity:- quantity with magnitude only, e.g. mass, distance, temperature, speed, etc.
*Vector quantity:- quantity with both magnitude and direction, e.g. velocity, acceleration, force,
displacement,etc.
2.1.1
DISTANCE AND DISPLACEMENT
Distance travelled : distance covered by an object measured along the path of motion.
Displacement:- distance travelled in a specified direction and should be measured along a direct route from the
starting point to the finishing point.
SI unit of distance and displacement : metre (m)
Other unit commonly used: kilometre (km)
Note: Distance is a scalar as it has only the size while displacement is a vector as it has both the size and
direction.
Illustration:- A boy starts from point A and walks 3 km northwards to point B and then turns eastwards and walks
4 km to point C. Find a) his total distance travelled b) and displacement during the journey.
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a) total distance travelled ABC = 2 km + 2 km = 4 km
b) total displacement S; AC2 = AB2 + BC2
= 3 2 + 42
AC = 5 km, 54° east of north
c) The boy continues with the journey and walks back to point A. Calculate the total distance travelled and
displacement for the whole journey.
c. i) total distance travelled ACA’ = 3 km + 4 km + 5 km = 12 km
ii) total displacement AA’ = 0 km
2.1.2 SPEED AND VELOCITY
a). SPEED
-is the distance travelled per unit time. Speed tells us how fast or slow an object is moving. Its SI unit is metre per
second (m/s) or (m s-1).
Other units: cm/s, km/h, m/min, etc.
Conversions between m/s and km/h
3600/1000
-------------------------------->
m/s
km/h
<--------------------------------1000/3600
Mathematically speed is:
Speed = distance/time
*Average speed = total distance travelled/ total time taken
b). VELOCITY
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-is the distance travelled in a unit time in a stated direction, e.g. 60 km/h due north. Velocity is, in fact, the speed
in a specified direction. It tells us how fast or slow an object is moving and in what direction.
Velocity = displacement/time
And
Average velocity = total displacement/total time taken
*NB: - Velocity and speed are not the same. Speed is a scalar whereas velocity is vector.
2.1.3 ACCELERATION
It is the rate of change of velocity with time. Acceleration is also a vector quantity. Its SI unit is metre per second
squared (m/s2) or (m s-2).
Acceleration = change in velocity/time taken
a = final velocity – initial velocity/total time taken
a = (v – u)/t
DECELERATION
When a body slows down its speed decreases and the acceleration becomes negative. Negative acceleration is
called DECELERATION or RETARDATION.
2.2
STATES OF MOTION
2.2.1
UNIFORM/STEADY/CONSTANT SPEED
Distance travelled in equal intervals of time is the same i.e. distance travelled every second is the same.
e.g.
time/s
distance/m
0
0
1
5
2
10
3
15
4
20
5
25
The body covers 5 m every second, this represents a constant speed of 5 m/s.
2.2.2 NON-UNIFORM SPEED
Distance travelled per unit time varies.
i) non-uniform increasing speed
time/s
0
1
2
3
distance/m
0
5
10 30
The body moves a little further than the previous second every second.
4
50
ii) decreasing speed
time/s
distance/m
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0
0
1
5
2
9
3
12
4
14
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Every second the object covers a little less distance than in the previous second.
2.2.3 UNIFORM VELOCITY
Both speed and the direction don’t change i.e. the body travels with uniform speed and in the same
direction (in a straight line).
2.2.4
NON-UNIFORM VELOCITY
Either speed or direction changes (or both of them)
2.2.5
UNIFORM ACCELERATION
The rate of change of velocity with time is constant i.e. speed increases by the same amount every second and
the body is also travelling in one direction.
e.g.
time/s
speed (m/s)
0
0
1
4
2
8
3
12
4
16
5
20
Acceleration is constant and is 4 m/s2.
2.2.6
NON-UNIFORM INCREASING ACCELERATION
time/s
speed (m/s)
0
0
1
10
2
25
3
45
4
70
5
100
*Acceleration is zero for body travelling with steady speed in the same direction (uniform velocity).However,
acceleration is non-zero if the body travels with constant speed in a circular path.
-Even though the speed is constant (e.g. 5 m/s), the direction changes now and then. Therefore the velocity is
non-uniform and hence the acceleration is not zero.
2.2.7
NON-UNIFORM ACCELERATION
a) increasing acceleration
time/s
0
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1
2
3
4
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velocity(m/s)
0
10
30
60
100
b) decreasing acceleration
time/s
0
1
2
3
4
velocity (m/s)
0
20
30
35
37
2.3 QUESTIONS
1 Explain the difference between:
a) distance travelled and displacement
b) speed and velocity
2 Use the words in the list below to complete the paragraphs that follow. Each word may be used once, more
than once or not at all.
acceleration
vector
average
displacement
distance
instantaneous
scalar
speed
velocity
Quantities which have magnitude but no direction are called ................................ quantities. Speed is a
........................... quantity. Velocity is a ............................ quantity.
If an object moves in unspecified direction, it has moved through a certain ............................................. If
the direction is specified, it has undergone a ....................................................
The rate of change of ......................... of an object is called its acceleration. Acceleration is a ......................
quantity. The formula: (final speed – initial speed) / time gives the ..................................... of an object.
3 a) A millipede moves a distance of 3.0 m in 1.5 s. What is its average speed?
b) A car travels 600 m in 30 s. What is its average speed?
4 A car has a steady speed of 8m/s.
a) How far does the car travel in the 8 s?
b) How long does the car take to travel 160 m?
5 a) A cyclist, rides 2 km east then 2 km north. The trip takes two hours in all.
Find : i) the average speed and ii) the average velocity.
b) A racing car completes a 5 km lap in 100 s. After this lap what is its i) displacement
speed and iii) average velocity?
6 Express a) speed of 130 km/h and
ii) average
b) speed of sound in air (which is about 330 m/s) in km/h.
7 What is meant by:
a) a speed of 100 km/h
b) an acceleration of +10 m/s2
c) an acceleration of -5 m/s2
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8 A car takes 8 s to increase its velocity from 10 m/s to 30 m/s. What is its acceleration?
9 A motor cycle, travelling at 20 m/s, takes 5 s to stop. What is its average retardation?
10 An aircraft on its take-off run has a steady acceleration of 3 m/s2.
a) What velocity does the aircraft gain 4 s?
b) If the aircraft passes one post on the runaway at a velocity of 20 m/s, what is its 8 s later?
2.4
MOTION GRAPHS
2.4.1
Distance-time graph
A distance-time graph shows how the distance travelled varies with time. The gradient of the graph represents
the speed of the body
a) Uniform speed
The distance-time graph above is a straight line showing that the body is travelling with uniform speed.
The gradient of the graph;
Grad = ∆s/∆t = y2 – y1 / x2 – x1
=60 - 20/ 6 - 2
= 10
Then speed = 10 m/s
b) i) Non-uniform increasing speed
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In graph above the body is travelling with non uniform increasing speed since the graph is not a straight line but
instead is a curve. The gradient of the graph varies. The speed at any particular time is found by calculating the
gradient of the tangent to the curve at that time
ii) Non- uniform decreasing speed
2.4.2
Speed- time graph (Velocity-time graph)
The speed- time graph shows how speed varies with time.
Note; 1) the gradient of the speed- time represents the acceleration of the body
2). The area under the graph is equal to the distance travelled by the body.
a). Uniform acceleration
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In the speed- time graph above the body is moving with a uniform acceleration since the graph is a straight line.
Acceleration = grad = ∆Y/∆X
b). Constant speed
acceleration = gradient = 0
c). Non- uniform acceleration
ii) decreasing acceleration
Speed(m/s)
i) increasing acceleration
time/s
d). Uniform deceleration
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e). Non- uniform deceleration
Distance travelled in a speed-time graph
Distance travelled = area of rectangle OPRS + area of triangle PQR
= (L x W) + (½ bh)
= (5 s x 20 m/s) + (½ x 5 s x (40 m/s – 20 m/s))
= 100 m + 50 m
= 150 m
2.5
EQUATIONS OF MOTION
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The equations used to solve problems on motion when the acceleration of the body is uniform.
SUMMARY OF THE EQUATIONS OF MOTION
v = u + at (does not include s)
s = ut + ½ at2 (does not include v)
v2 = u2 + 2as (does not include t)
s = ½ (u + v)t (does not include a)
Note:
s = displacement/distance travelled
u = initial velocity/speed
v = final velocity/speed
a = acceleration
t = time taken
2.6
QUESTIONS
(For the questions below, assume that the motion is in a straight line and that the acceleration is uniform)
1 A motor cycle travelling at 10 m/s accelerates at 4 m/s2 for 8 s.
a) What is its final velocity?
b) How far does it travel during the 8 s?
2 A car accelerates from 8 m/s to 20 m/s in 10 s.
a) What is its acceleration?
b) How far does it travel during the 10 s?
3 A train is travelling at 40 m/s when its brakes are applied. This produces a deceleration of 2 m/s2.
a) How long does the train take to come to rest?
b) How far does the train travel before stopping?
4 An aircraft accelerates at 25 m/s2. Its take-off speed is 60 m/s.
a) What length of runway does it need to take off?
b) How long does it take to reach its take-off speed?
5 a) Use the values in the table to plot a distance-time graph for a car over a 10 s period
time/s
0
1
2
3
4
5
6
7
8
9
10
distance/m
0
20
40
60
80
100
100
100
100
130
160
b) Describe the motion as fully as you can.
c) What was the average speed over the 10 s?
6 The approximate velocity-time graph for a car on a 5 hour journey is shown below. (There is a very quick
driver change midway to prevent driving fatigue).
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a) State in which of the regions OA, AB, BC, CD, DE the car is i) accelerating
iii) travelling with uniform velocity.
b)
c)
d)
e)
ii) decelerating
Calculate the value of the acceleration, deceleration or constant velocity in each region.
What is the distance travelled over each region?
What is the total distance travelled?
Calculate the average velocity for the whole journey.
7 The distance-time graph for a motor cyclist riding off from rest follows.
a) Describe the motion.
b) How far does the motorbike move in 30 seconds?
c) Calculate the speed.
8 A car runs at a constant speed of 15 m/s for 300 s and then accelerates uniformly to a speed of 25 m/s over a
period of 20 s. This speed is maintained for 300 s before the car is brought to rest with uniform deceleration in
30 s.
a) Draw a speed-time graph to represent the journey described above.
b) From the graph find:
i) the acceleration while the speed changes from 15 m/s to 25 m/s.
ii) the total distance travelled in time described,
iii) the average speed over the time described
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2.7 FREE FALLING OBJECTS
2.7.1
ACCELERATION DUE TO GRAVITY (ACCELERATION OF A FREE FALL)
An object falling freely in vacuum under gravitational force of the earth only moves with uniform acceleration
known as acceleration due to gravity (or acceleration of free fall). The acceleration due to gravity is denoted by
letter g.
The value of g: is the same for all bodies irrespective of their masses. For this reason, a small body and a large one
both dropped from the same height would move at the same speed and reach the ground at the same
time moving at the same speed if there are no forces opposing their motions.
 varies over the surfaces of the earth, the maximum being at the poles and the minimum at the centre.
However the value of g is taken to be 10 m/s2 on Earth.
 is considered to be constant for a body near the surface of the Earth, however, it decreases with
increase in the altitude.
Equations of motion for free falls
For vertical motion a is replaced with g in the equations of motion studied previously.
i)
for a dropping object
g = +10 m/s2
v = u + at becomes v = u +gt if the body drops from rest i.e. u =o, v = gt --------------> (1)
s = ut + ½ at2 becomes s = ut + ½ gt2 if u = 0, s = ½ gt2 (note s = height) ------>(2)
v2 = u2 + 2as becomes v2 = u2 + 2gs if u = 0, v2 = 2gs ---------------------> (3)
* Same equations can be used for bodies thrown/moving vertically upwards but with g as -10 m/s2
NB:- i) velocity at the highest point is zero for any object.
ii) time for upward journey = time for downward journey to the same level
iii) a falling body would pass every point at same speed it did on its way up.
2.7.2 MOTION OF A BODY FREE FALLING IN AIR
a. At the start
(FR =0, a = 10 m/s2)
b. gaining speed, FR < W)
(FR increasing, a < 10 m/s2)
c. At the terminal velocity
(FR = W, a = 0)
When a body falls in air, initially its acceleration is about 10 m/s2. As its speed increases so does the air
resistance (fluid friction) opposing its motion and this causes the acceleration of the body to decrease. Eventually
the air resistance acting upwards equals the force of gravity (weight of the body) acting downwards and the
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acceleration becomes zero. Then the body falls with a constant velocity/ speed called its terminal velocity, which
is the maximum speed of falling body.
The value of the terminal velocity depends on the size, shape and weight of the object.
The effect of air resistance is greater for light object, e.g. raindrop and for bodies with large surface area like a
parachute and is less for heavy bodies.
Small dense object has high terminal velocity. It accelerates over a considerable distance before air resistance
equals its weight. Light object has a low terminal velocity since it only accelerates over a comparatively short
distance before air resistance balances its weight.
2.7.3
MOTION OF FALLING BODIES IN LIQUIDS
Same as that one for an object falling in air except that the resistive force here is called upthrust
The sketch of the velocity-time graph for body falling in air or liquid is as shown below;
3.0
MASS, INERTIA, WEIGHT AND CENTRE OF MASS.
3.1
Mass
-
is a measure of the amount of a substance (matter) in a body or an object.
SI unit: kilogram (kg)
Other units: gram (g), milligram (mg), tonnes (t)
Measuring instruments:- tripple-beam balance, bathroom balance, lever-arm scale, electronic scale,
top-pan balance.
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3.2
INERTIA
-is the tendency of a body to resist any change in its state of motion i.e. to remain at rest if it is at rest or to
continue moving (with uniform velocity in a straight line) if already in motion. The larger the mass of a body the
larger its inertia and the more difficult to change its state of rest or uniform motion or change the direction of its
travel. Mass is therefore defined as the measure of the object’s inertia.
Examples of some effects of inertia in everyday life
a. If a car stops suddenly the occupants are thrown forward because they tend to want to continue moving due
to inertia or if the car starts abruptly the upper part of the occupant is moved back because it seems to want
to remain at rest because of inertia.
b. It is more difficult to move a bigger stone as compared to a small one because of inertia
c.
When card is pulled away very quickly the coin will not move along with it but instead it drops into the glass due
to inertia.
3.3
WEIGHT
Definition: is the amount of force gravity acting on object.
Measuring instrument: spring balance/forcemeter
SI unit: newton (N).
Unlike mass, the weight of an object is not always constant, it depends on the gravitational pull on a unit mass
(gravitational field strength) at a particular place. On Earth the gravitational pull on a unit mass is 10 N i.e. g = 10
N/kg
On the moon the gravitational pull on a unit mass is 1.6 N i.e. g = 1.6 N/kg.
Mathematically, weight is expressed as:
W = mg
where W = weight in newtons (N)
m = mass in kilograms (kg)
g = gravitational field strength in N/kg.
3.4
QUESTIONS
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1) Calculate the weight of a body of mass:
i) 2 kg
ii) 700 g
Take g to be 10 N/kg.
2) A bag of coal has a mass of 10 kg on Earth. The acceleration due to gravity is 10 m/s2 on Earth and on
the moon is 1.6 m/s2.
a) What is its mass on the moon?
b) What is its weight on Earth?
c) What is its weight on the moon?
3) A bag of sugar has a weight of 125 N on Earth. Calculate its mass. Take g to be 10 N/kg.
4) State at least three differences between mass and weight.
3.5 CENTRE OF MASS
3.5.1
Definition: is a point on a body at which the whole mass of the body seems to be concentrated.
*Centre of gravity: is a point where the whole weight of the body seems to be concentrated.
The centre of (C.M) of an object:
 Coincides wits centre of gravity (c.g).
 Lies at the centre (middle point) if the body has uniform thickness (density) and regular shape, e.g.
the C.M of a metre rule is considered to be at a 50 cm mark.
 Can be either within or outside the body of the object.
3.5.2
C.M of some regular shaped object
*For some objects, (e.g. a ring, retort stand, etc), the C.M lies outside the body of the object, instead it lies in the
air around the object.
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3.5.3 C.M of irregular shaped object
Experiment: to determine the C.M of a irregular shaped lamina (a thin sheet of cardboard)
Procedure
 Make three holes A, C and E on the cardboard.
 Suspend the cardboard through hole A from a nail clamped on a stand such that it swings freely. When
it comes to rest, its centre of mass will be exactly below point A.
 To identify the point, hang the plumbline from the same nail very close to the cardboard.
 Draw a line AB along the plumbline
 Hang the cardboard from another hole C and repeat the experiment and draw the line CD.
 The C.M lies at the intersection of the two lines.
 To check if the position of C.M is correct, one can hang the cardboard from the third hole E and then
draw line EF, it must also pass through that point.
3.5.4
STABILITY
This defines whether the object falls over easily or not. When the object is slightly displaced and released, it will
always return to its origin (and not topples over) if the vertical line passing through the C.M. is still kept within the
base of the object or the area enclosed by the base of the object (i.e. it has not gone beyond the point of contact
between the object and the surface it is resting on)
Ways of increasing the stability of a body
a) Lowering the centre of mass
b) Widen the base of the object
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3.5.5
States of equilibrium
When an object is balanced or stable in its position, it is said to be in equilibrium. Its degree of stability is
determined by its position which can be defined as its state of equilibrium.
Three states of equilibrium are:1) Stable equilibrium
2) Unstable equilibrium
3) Neutral equilibrium
1) Stable Equilibrium
A body is in a state or position in which when it is slightly displaced and released it returns to its original position.
When an object in stable equilibrium is slightly tilted, its C.M rises and gain some P.E. When released that extra
P.e will be used to produce an anticlockwise moment about the point of contact that will roll the object back to its
original position.
2) Unstable Equilibrium
A body is in unstable equilibrium if it is positioned such that when it is slightly displaced and released it will move
further away its original position ( topples over).
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3) Neutral Equilibrium
A state in which a body is positioned such that when it is slightly displaced and released it remains at its new
position.
4.0 DENSITY
4.1 Density is defined as the measure of the amount of mass contained in volume of an object. It is usually
expressed as mass per unit volume.
Density = mass/volume
D = m/V or
ρ = m/V
where ρ(Greek letter rho) = density in kg/m3
m = mass in kg
V = volume in m3
SI unit: kilogram per cubic metre (kg/m3)
Other UNIT commonly used is gram per cubic centimetre (g/cm3)
1 g/cm3 = 1000 kg/m3
*NB:- Density of pure water is 1 g/cm3 or 1000 kg/m3
4.2
Experiment #1: Measuring density of regular (shaped) object
-
-
Measure the mass m of the object using a balance
Measure the dimensions of the object and then calculate the volume V of the object using the
appropriate formula. E.g. volume of a cube = l3
Volume of a rectangular block = l x w x h
Volume of a cylinder = πr2h, etc
Find the density of the object using the equation ρ = m/V
4.3 Experiment #2: Determining the density of an irregular shaped object e.g. a stone
A) Using a measuring cylinder method
- Measure the mass m of the stone using a balance
- Partly fill a measuring cylinder with water and then record the reading of the volume V1 of water.
(remember to read the mark at the bottom of the meniscus).
- Gently lower the stone into water and note the reading V2 (volume of water and stone)
- Calculate the volume of the stone V , using the equation V = V2 – V1.
- Work out the density of the stone using the equation ρ = m/ V.
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B) Displacement can method
For larger objects a displacement can may be used
-
A beaker or measuring cylinder is placed under the spout and the displacement can is filled with water
until it overflows. The beaker is emptied and replaced.
Find the mass m of the stone
The stone is lowered with a thread into the can.
Overflow is collected in a beaker and its volume is measured to give the volume V of the stone.
Lastly the density of the stone is found using the equation using the equation ρ = m/V.
4.4.1 Experiment #3: measuring density of a liquid
-
Measure the mass m1 of a dry clean beaker
A convenient volume V of a liquid, let’s say water is run into the beaker and then record the volume V of
the water in cm3.
Find the mass m2 of the beaker with the liquid in it.
Then calculate the mass m of the liquid using the equation m = m2 – m1
Finally calculate the density using ρ = m/V
4.4.2 RELATIVE DENSITY
The density of an object can be determined more accurately by finding its relative density.
The relative density of a substance is the ratio of the mass of any volume of the substance to the mass of an
equal volume of water.
R.D = mass of any volume of the substance/mass of an equal volume water
Therefore the density of a liquid can be accurately measured using a density bottle.
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4.5 Experiment #4: Measuring the density of a liquid using a density bottle.
-
-
Weigh an empty bottle using a balance
Fill it completely with water and weigh it once again
Next replace water with any given substance/liquid e.g. alcohol and then weigh the bottle.
Observations are recorded as below
Mass of the empty bottle = m1
Mass of bottle with water = m2
Mass of water
= m 2 – m1
Mass of bottle with alcohol = m3
Mass of alcohol
= m 3 – m1
Density of water = m2 – m1/V
and density of alcohol = m3 – m1/V
Both the liquid and water have the same volume V since the same bottle was used for the whole experiment.
Then R.D of alcohol = density of alcohol/density of water
= (m3 – m1/V)/m2 – m1 /V
= (m3 – m1/V) X V/m2 – m1
= m3 – m1/m2 – m1
Relative density is a ratio so it’s a number without units. However, its value is the same as that of density of a
substance in g/cm3
4.6
Experiment #5: measuring the density of air
-
Find the mass m1 of a 500 cm3 rounded bottom flask full of air.
Remove air from the flask using a vacuum pipe and then determine the mass m2 of an empty flask.
Fill the flask with water
Transfer water to a measuring cylinder to find the capacity of the flask which the volume V of air.
Find the mass m of the air using the equation m = m2 – m1
Calculate the density of air using the equation ρ = m/V.
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4.7 DENSITY OF A MIXTURE
If A is a substance of mass mA and volume of VA and B is a substance of mass mB and a volume VB, the
density of the mixture, ρm is given by :Ρm = mA – mB/ VA – VB
4.8
FLOATING AND SINKING
An object:Floats in a liquid if its density is less than that of the liquid
Sinks if its density is greater than that of the liquid
Stays anywhere within the body of a liquid if its density is equal to that of the liquid.
4.9
A HYDROMETER
It is used to measure the density of the liquids directly. It consists of a thin hollow tube which is weighed at the
bottom with mercury or lead so that it can float upright. The tube has a scale marked on it
The hydrometer floats at different levels/depths in different liquids, depending on their densities. It sinks less in a
dense liquid and sinks more in less dense liquid.
You read the mark level with the surface of the liquid.
Hydrometers are often used to test beer and milk to see if they have too much water in them.
A special hydrometer called lactometer, used for testing the purity of milk.
A small type of hydrometer enclosed in a larger glass tube fitted with a rubber bulb. It is used for measuring the
density of the battery acid. On squeezing the bulb and then releasing it acid enters the glass tube and density
can be read on the floating hydrometer.
*At constant temperature the densities of the objects made with the same material are the same irrespective of
their sizes (volumes)
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4.10
QUESTIONS
1 Copy and complete the table shown below.
Length
Width
Height
Volume of rectangular block
2 cm
3 cm
4 cm
...........
5 cm
5 cm
...........
100 cm3
6 cm
.............
5 cm
300 cm3
...........
10 cm
10 cm
500 cm3
2 Calculate the density of the following:
a) a piece of steel which has a volume of 6 cm3 and a mass of 48 g.
b) a piece of copper which has a volume of 10 cm3 and a mass of 90 g.
c) a piece of gold which has a volume of 2.0 cm3 and a mass of 38 g.
3 Calculate the mass of the following:
a) 4 cm3 of aluminium. The density of aluminium is 2.7 g/cm3.
b) 20 cm3 of wood. The density of wood is 0.80 g/cm3.
c) 80 cm3 of glass. The density of glass is 2.5 g/cm3.
4 Calculate the volume of the following:
a) 68 g of mercury. The density of mercury is 13.6 g/cm3.
b) 15.8 g of iron. The density of iron is 7.9 g/cm3.
c) 99 g of lead. The density of lead is 11 g/cm3.
5 A block of material is 8 cm long, 2 cm wide and 3 cm high, and has a mass of 46 g.
a) What is its density?
b) Convert the value of density in (a) above to kg/cm3.
1 A plank of wood is 2.00 m long, 30 cm wide and 3 cm thick.
a) What is the volume of the plank?
b) The density of the wood is 700 kg/m3. What is the mass of the plank?
2 The room measures 5 m x 4 m x 3 m. The air in it has a density of 1.2 kg/m3.
a) What is the mass of the air in the room?
b) Another room has only 60 kg of air in it. What is the volume of this second room?
3 A jeweller has a crown which he thinks is made of pure gold. He finds that it has a volume of 100 cm3 and has
a mass of 1.8 kg.
a) Using these two values, what is the density of the crown?
b) The density of gold is 19.3 g/cm3. How can the difference be explained?
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5.0
FORCE
5.1
A force is a push or pull exerted by one object on another.
Force is a vector; it has both magnitude and direction in which it acts.
SI unit: newton (N)
*One newton is a force which gives an acceleration of 1 m/s2 to mass of 1 kg.
Examples of forces
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
5.2
Gravitational force – an attractive force which any two masses pull one another with.
Weight – pulls object towards the centre of the Earth.
Friction – tends to stop movement of objects
Thrust of a (jet) engine – is a push or pull due to the jet engine
Centripetal force – acts on object moving in a circle
Tension – produced on a stretched material
Magnetic force – acts between magnets or between a magnet and magnetic material
Electric force – acts between charges
Air resistance/fluid friction/drag – slows down a body travelling through air
Upthrust – opposes movement of an object moving in a liquid
Force due to expansion/contraction
Reaction/normal force – acts on an object on any given surface. The force is normally perpendicular to
the surface and equal and opposite to the weight of the object. It is exerted by the surface on the object.
EFFECTS OF FORCE
5.2.1
Effects of a force on the shape and size of an object
A force can or tends to change the shape and size of objects, e.g. i) lump of bostik would change shape when
pressed, ii) a inflated balloon changes size when more air is blown into it.
Some of the objects return to their original shapes and sizes when the external force which was previously
applied on them is removed. These objects are called elastic materials, e.g. rubber band, steel spring, etc.
Other objects do not return to their original or sizes even when the force is removed. They will remain
permanently deformed. These are called plastic materials, e.g. plasticine, bostik, clay, etc.
Stretching a spring
LO
L
e
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e = L – Lo
where e = extension of the spring
L = new length of stretched spring
L0 = original/normal length of the spring
When the load (weight) which was applied to the spring is removed, the spring returns to its normal length. The
spring is elastic but only to a certain limit.
Experiment: To investigate the relationship between the extension of a spring and load (stretching force)
Procedure
 Suspend a steel spring from a retort stand as shown above
 Attach a pointer in a horizontal position to the end of the spring with some bostik.
 Place a metre rule vertically near the spring
 Suspend the mass hanger on the spring as shown above
 Adjust the height of the ruler such that the pointer is at a convenient reading, say around 30 cm, record
this as initial scale reading.
 Add 100 g (1.0 N) loads one at a time and note and record the new scale reading after each load.
 Record the observations in a table up to 500 g (5.0 N) and calculate the extension for each load.
TABLE OF RESULTS
e = New reading L – Initial scale reading LO
Mass/kg
0.0
0.1
0.2
0.3
0.4
0.5
Load F/N
0
1
2
3
4
5
Scale reading/cm
54.0
57.8
63.5
69.0
72.4
76.6
Extension e/cm
3.8
9.5
15.0
18.4
22.5
F/e (N/cm)
0.3
0.2
0.2
0.2
0.2
Graph of load F (force)/N against extension/cm
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The graph above is a straight line showing that the extension of the spring is directly proportional to the load i.e.
when the load is doubled the also doubles.
i.e. F α e
then
F = ke -------------> Hooke’s law
where F = force applied in newtons (N)
e = extension of the spring in metres (m)
k = constant of proportionality known as force constant or spring constant in N/m
*Force constant k:
 is defined as the amount of force require to give a spring a unit extension.
 is the measure of the stiffness or softness(strength) of a spring (very stiff spring has a high value of k
than a soft one).
 is measured in N/m, N/cm, N/mm, etc.
*Dividing the load by its corresponding extension always gives the same result. This means every 1N increase in
the stretching force produces the same extra
HOOKE’S LAW
If you add more masses to mass hanger and take the corresponding extensions and draw a graph as before, the
graph will be a straight line a curve towards the end showing that towards end load and extension were no longer
proportional.
The spring behaves elastically only to point E. Then, the Hooke’s law is obeyed only in the region OE.
Therefore Hooke’s law states:
“the extension of a spring is directly proportional to the load/force applied provided the elastic limit of
spring is not exceeded”.
Point E is known as elastic limit or limit of proportionality of the spring. This is point beyond which the spring
loses its elasticity, it would fail to return to its original length even when the load is removed from it. Instead a
permanent extension (deformation) OS will remain on the spring.
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IDENTICAL SPRINGS COMBINED IN:
a) SERIES
Extension for 1 spring e = x
2 springs e = 2x
3 springs e= 3x
4 springs e = 4x
N springs e = Nx
Then Hooke’s law for N springs in series
For 1 spring F = ke
e = F/k; e = x
For N springs, e = Nx
Then
e = N(F/k)
e = NF/k --------------------> total extension for springs in parallel.
b) PARALLEL
For 1 spring e = x
2 springs e = x/2
3 springs e = x/3
4 springs e = x/4
N springs e = x/N
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From Hooke’s law
For N springs in parallel
e = x/N
e = (F/k)/N
e = F/k X 1/N
e = F/Nk ---------------------------> total extension for springs in parallel.
QUESTIONS
1. What is the force constant of a spring which is stretched
a) 2 mm by a force of 4 N
b) 4 cm by a mass of 200 g.
2. The springs below are identical. If the extension produced in A is 4 cm, what are the extensions in B
and C?
3. Tom performed an experiment stretching a spring. She loaded masses on the spring and measured the
extension
Table of results
Extension/cm
Load/N
0
0
4
2
8
4
12
6
16
7.5
20
8.3
24
8.6
a) Plot the graph of extension/cm against load/N
b) Calculate the spring constant in elastic behaviour region.
4 The graph below shows how a spring stretches when a force is applied to it.
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a) Describe what would happen to the spring if forces were applied to it until it reached point A on the
graph and then the forces are removed.
b) Describe what would happen if the spring was stretched to point B on the graph and then the forces
removed.
c) If a force of 10 N caused the spring to stretch by 5 cm what would be the extension of the spring if 20 N
was applied to it?
5.2.2 EFFECTS OF FORCE ON MOTION OF AN OBJECT
A force can change the state of motion of an object by causing:
(i) its speed to increase or decrease
(ii) its acceleration to increase or decrease
(iii) a change in its direction of travel
(iv) a stationary object start to move or an object in motion stop moving.
All the above can be summed up or explained by Newton’s laws of motion
NEWTON’S LAW OF MOTION
A) First law
It states that
“A body at rest will remain rest or if it is moving it will continue to move with constant velocity (uniform speed in
a straight line) unless an external force makes it to behave differently. It is also known as law of inertia.”
B) Second law
It states that :“The acceleration a of a body is


directly proportional to the force applied F for a fixed mass m
inversely proportional to the mass m for a fixed force applied F”
Mathematically, newton’s second law of motion is expressed as:F = ma
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where F = resultant/unbalanced/net force (N)
m = mass of an object (kg)
a = acceleration of the object (m/s2)
C) Third law
It states that:
“if body A exerts a force on body B, body B will exert an equal and opposite force on body A called the reaction
force”
5.3 FRICTIONAL FORCE
5.3.1
Effects of friction on motion of a body
Friction – always acts in opposite to the direction of motion of a body and reduces the acceleration or speed of
the body.
Friction acts between solid surfaces as they move over each other and when objects move through gases or
liquids.
5.3.2
WHAT CAUSES FORCE FRICTION
It is caused by roughness of the two surfaces in contact, even surfaces which look or feel smooth are rough
when seen under a microscope. As a block of wood slides over the table the humps and hollows on one surface
tend to grip those on the other surface, this causes the frictional force
It is also caused by adhesion between the molecules on the surfaces in contact due to intermolecular forces.
The friction which exists between the two objects when there is no movement is called static friction. The object
will start to move if the pulling/pushing force is increased beyond the value of the static friction. Then the frictional
force between the two surfaces when the object is moving is called sliding/dynamic friction. Usually its value is
less than the maximum value of the static friction.
Calculations involving frictional force
Resultant force = forward force – frictional force
F = FF – FR
F = ma --------------> Newton’s second law of motion
a = F/m
then for cases where there is friction
a = F/m = FF – FR/m
© SPANAPODI 2010
where a = acceleration in m/s2
FF = forward force in N
FR = frictional force in N
m = mass in kg
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Examples
1. A car is acted upon by a forward driving force of 700 N which causes an acceleration. The force of
friction between the road and the tyres is 500 N. Calculate the resultant force on the car.
F = FF - FR
= 700 N – 500 N
= 200 N
2. A car of mass 3 000 kg (including the driver) is travelling at a constant acceleration of 2 m/s2. The force
of friction between the tyres and the road is 500 N. Calculate the a) resultant force acting on the car
b) forward driving force
Solutions
a) Data
m = 3000 kg, a = 2 m/s2
F = ma
= 3000 kg X 2 m/s2
= 6000 kg m/s-2
= 6000 N
b) Data
F = 6000 N, FR = 500 N
F = FF - FR
FF = F + FR
= 6000 N + 500 N
= 6500 N
5.4
TURNING EFFECTS OF A FORCE (MOMENT OF A FORCE)
5.4.1 Definition: a moment of a force is the measure of the turning effect of a force. It depends on the size of
the force and how far it is applied from the pivot/fulcrum.
Moment = force X perpendicular distance of line of action of the force from the pivot
M = Fd
or M = Fs
where M = moment of the force in newton-metre Nm
F = force applied in newton (N)
d or s = perpendicular distance of line of action from the pivot (m)
Units: Nm, Ncm, etc
M = Fx D
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M=Fxd
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Moment of a force is a vector quantity, i.e. it has magnitude as well as direction. The direction is either
clockwise or anticlockwise, depending in which the force turns the object.
e.g
5.4.2





Experiment: To verify the principle of moments (law of moments/levers)
Pivot the metre rule at the 50 cm.
Hang the masses m1 and m2 on either side of the pivot until the ruler balances.
Measure the distance d1 and d2 from the pivot
Calculate the anticlockwise moment M1 and clockwise moment M2 using equations, M1 = F1d1 &
M2 = F2d2
Repeat the experiment using different values of m1, m2, d1 and d2
TABLE OF RESULTS
m1/kg
F1/N
d1/cm
M1/Ncm
m2/kg
F2/N
d2/cm
M2/Ncm
What do you notice about clockwise and anticlockwise moments when the ruler is balanced?
Answ: the clockwise moment = anticlockwise moment
This observation proves the principle of moments.
The principle of moments states that:
“when the body is in equilibrium the sum of the clockwise moments about any point is equal to the sum of
anticlockwise moments about the same point”
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5.4.3
CONDITIONS FOR EQUILIBRIUM
1) the sum of forces in one direction must equal the sum of the forces in the opposite direction i.e the net force
is equal to zero
2) the principle of moments should be obeyed, i.e. the resultant turning effect is equal to zero.
e.g. The beam below is equilibrium
Therefore:
i) Force A + Force B + Force C + Force D = Force C
Then A + B + C + D – C = 0
ii) Ax + By = Dz
total anticlockwise moments = total clockwise moment
5.4.4 COUPLE
If two equal forces act on opposite direction they form a couple. A couple cause rotation, e.g turning bicycle
handlebars and steering wheel
To find the moment of a couple, you multiply the value of any of the two forces by the distance between them
M = Fx + Fy
= F(x + y)
= Fd
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5.5
CENTRIPETAL FORCE
This is a type of force that acts on a body moving in a circle/curve and keeps the body in its curved path or orbit.
The centripetal force always points towards the centre of the circular path and that means even the acceleration
of the body (centripetal acceleration) is towards the centre of the curve. The force is provided by the sideways
friction between the tyres and the road surface.
5.6
QUESTIONS
Question 1
A student measures the acceleration of a trolley. The light sensors are connected to a computer
which is programmed to calculate the acceleration. The results obtained are recorded in a table as
follows.
i)
ii)
iii)
iv)
v)
Force(N)
0
1
2
3
4
5
Acceleration(m/s2)
0
0.5
1.0
1.5
2.0
2.5
Plot a graph of acceleration(m/s2) against force(N)
Describe how changing the force affects the acceleration.
Write down, in words, the equation connecting force, mass and acceleration.
Use the data from the graph to calculate the mass of the trolley.
On graph, sketch the graph line that would be obtained for a trolley of larger
mass.
Question 2
A car has a mass of 900 kg. It accelerates from rest at a rate of 1.2 m/s2.
a) Calculate the time taken to reach a velocity of 30 m/s.
b) Calculate the force required to accelerate the car at a rate of 1.2 m/s2.
c) Even with the engine working at full power, the car’s acceleration decreases as
the car goes faster. Why is this?
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Question 3
The diagram below shows some of the forces acting on a car of mass 500 kg.
a) State the size of the total drag force when the car is travelling at a constant
speed.
b) The driving force is increased to 3000 N.
i) Find the resultant force on the car at this instant.
ii) Calculate the initial acceleration of the car.
Question 4
The manufacturer of a car gave the following information; Mass of car = 1000 kg. The car will
accelerate from 0 to 30 m/s in 12 seconds.
a) Calculate the average acceleration of the car during the 12 seconds.
b) Calculate the force needed to produce this acceleration.
Question 5
a). What constant braking force is needed to bring a car of mass 1200 kg to rest in
5 s when it is moving at 20 m s-1?
b). A car of mass 800 kg is moving at 25 m s-1. Calculate the force needed to bring
the car to rest over a distance of 20 m.
c). A body is initially in motion. If no external force acts on the body how will its
motion change?
Question 6
On the diagram show the forces and their direction.
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Question 7
Fig. 6.1 shows a car of mass 500 kg moving from rest with constant acceleration of 10 m/s2. Two
forces act on it, a forward force and a friction force.
Fig. 6.1
a). (i) Calculate the resultant force acting on the car. Show your working.
(ii) If the friction force is 2000 N, calculate the forward force acting on the car.
Show your working.
(iii) After some time, the car reaches a velocity of 20 m/s. How long did it take for
the car to reach this velocity?
Question 8
Fig. 7.1 shows a metal ball being dropped from the surface of oil in a tube of length 2 m. the ball has
a mass of 1 kg and it moves with constant acceleration of 5 m/s2.
Fig. 7.1
(a) Calculate the resultant force acting on the ball.
(b) Calculate the friction caused by the oil. (g = 10 N/kg).
(c) Calculate the time taken by the ball to reach the bottom of the tube.
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Question 8
Fig. 8.1 shows a model crane. The crane has a movable counterbalance.
(a) Why does the crane need a counterbalance?
(b) Why does the counterbalance need to be movable?
Refer to Fig. 8.1
(c) What is the moment of the 100 N force about O?
(d) To balance the crane, what moment must the 400 N force have?
(e) How far from O should the counterbalance be positioned?
(f) Where would you expect the counterbalance to be positioned if the crane is
lifting its maximum load?
(g) What is the maximum load the crane should lift?
(h) Describe two ways of making the design of the crane more stable.
9 The diagram below shows a spanner being used to undo a nut on a car wheel.
a) Calculate the moment created by the force trying to undo the nut.
b) Suggest how you could increase the moment applied to the nut without
increasing the applied force.
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10. The diagrams show forces acting on various beams. For each beam, the fulcrum
is at its midpoint. Which of the beams are in equilibrium? What happens in the
other cases? What is the upward force of the fulcrum on the beam in each
case?
11. A 1 N weight is hung from the 5 cm mark of a metre rule. The rule balances on a
knife edge at the 30 cm mark. What is the weight of the rule?
12 The diagram shows a beam balanced with the fulcrum at the midpoint. How big
is the force X?
13. The diagram shows two beams balanced with the fulcrum at the midpoint. In
each case, what is the distance x?
5.7 SCALARS AND VECTORS
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5.7.1
DEFINITIONS
SCALAR QUANTITY: expressed in terms of magnitude/size only, e.g. distance, temperature, time, etc.
VECTOR QUANTITY: expressed in terms of magnitude and direction, e.g. force, acceleration, moment, velocity,
etc.
5.7.2 Addition of vectors
1. Resultant of 3 N and 7 N forces at a right angle to one another.
i) GRAPHICAL METHOD
Choose a suitable scale; 1 cm : 1 N
After drawing the vector diagram to scale, you measure the length of line that represents the resultant and then
use the chosen scale to find the resultant..
Length = 7.6 cm, therefore resultant = 7.6 N
Direction is obtained by measuring the angle between the resultant force and one of the forces, e.g. 23° to the
7N
R = 7.6 N, 23° to the 7 N
ii) Algebraically
For right-angled triangle – use Pythagoras theorem
c 2 = a2 + b 2
OR2 = OP2 + PR2
= (7 N)2 + (3 N)2
= 58 N2
OR = √58 N2
Resultant R = 7.6 N
for direction trignometrical functions
sinθ = OPP/HYP
e.g. sinθ = OP/OR,
sinθ = 3/7.6
θ = sin-1(0.3974)
= 23°
cosθ = ADJ/HYP
tanθ = OPP/ADJ
cosθ = PR/OR
cosθ = 7/7.6
θ = cos-1(0.921)
= 23°
tanθ = OP/PR
tanθ = 3/7
θ = tan-1(0.4286)
= 23°
2. Forces acting at an angle not 90° to each other
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PARALLELOGRAM RULE
If two forces acting at appoint are represented in magnitude and direction by the sides of a parallelogram,
the resultant is represented in size and direction by the diagonal of the parallelogram.
E.g. Find the resultant of forces of 3500 N and 2500 N acting at an angle of 60° to each other
Using parallelogram rule (graphical method)
Scale 1 cm : 500 N
Resultant force = 10.5 x 500 N = 5250 N
Direction = angle between the resultant and the 3500 N force (measure using a protractor) = 24°
ALGEBRICALLY,
Use cosine rule
C2 = a2 + b2 – 2abcosΦ
To find the direction, use sine rule
a/sin A = b/sin B = c/sin C
5.7.3
Resolving a force
When a single is converted into components it is said to be resolved. Components together have the same effect
as that of the single force. Usually the components are at the right angle to one another.
O
B
The components of the resultant force F are FX (OB) along the x-axis and Fy (OA) along the y-axis.
To find FX and FY
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Using trigonometry
sinθ = OA/OC
sinθ = Fy/F
Fy = Fsinθ
e.g. If F = 200 N,
Fy = F sin
= 200sin30°
= 100 N
5.7.4
cosθ = OB/OC
cosθ = Fx/F
Fx = Fcosθ
θ = 30°
Fx = Fcos30°
Fx = 200cos30°
= 173 N
QUESTIONS
1. How is a scalar different from a vector? Give an example of each.
2. Forces of 12 N and 5 N both act at the same point, but their directions can be varied.
a) What is their greatest possible resultant?
b) What is their least possible resultant?
c) If the two forces are at right angles, find by scale drawing or otherwise the size and direction of their
resultant.
3. Find the resultant of a displacement of 5 m north-east and one of 3.5 m due east.. (State the size of the
displacement as well as its direction). What would your answer have been if the second displacement had
been due south instead of due east.
4. Which of the following quantities are scalar quantities; temperature, potential energy, density, weight
5. Fig. 5.1 shows a heavy block hanging from two ropes so that it does not move. The forces and the angles are
shown. Draw a vector diagram to find the resultant force exerted by the ropes on the block. Say what scale
you have used.
Fig. 5.2
6.0
WORK, ENERGY, POWER AND EFFECIENCY
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6.1 WORK
Work is done when a force moves an object in its direction.
It is given by the product of force and the distance moved in the direction of the force
The SI unit of work is a joule (J).
W = Fs
where W = work done in joules (J)
F = force in newtons (N)
s = distance moved in metres (m)
1J=1NX1m
= 1 Nm
Other units (larger): kilojoule (KJ) ; 1 KJ = 1000 J
Megajoule (MJ); 1 MJ = 106 J
*Note: No work is done if :i) the force applied on the object does not move the object
ii) the direction of motion is perpendicular to the direction of force.
6.2 ENERGY
6.2.1
Energy is a measure of the ability or capacity to do work.
Work done and energy transferred
When a body A does work on body B, body A transfers energy to body B. The amount of energy transferred
from body A to body B is equal to the work done by body A on body B.
WORK DONE = ENERGY TANSFERRED
Energy is also measured in joules (J)
6.2.2 DIFFERENT FORMS OF ENERGY








6.2.3
Chemical energy
Electrical energy
Heat/thermal energy
Sound energy
Mechanical energy
Light energy
Nuclear energy
Radiant energy – given out by source in form of wave, e.g light, microwave, sound, heat, etc
MECHANICAL ENERGY
There are two types of mechanical energy


Potential energy (Pe)
Kinetic energy (Ke)
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(1) Potential energy
Is the energy possessed by a body due to its position or condition. There are two kinds:- i) gravitational
potential energy ii) elastic potential energy
A stretched elastic rubber band has elastic potential energy
An object suspended above the ground has gravitational potential energy
The work done in lifting up a body is converted into gravitational potential energy of the body
Gravitational potential energy = weight X height
Pe = mgh
where g = acceleration due to gravity in m/s2
m = mass of the object in kg
h = height in metres (m)
2) Kinetic energy
Kinetic energy is possessed by a moving object.
Ke = ½ mv2
where m = mass (kg)
v = velocity (m/s)
6.2.4 PRINCIPLE OF CONSERVATION OF ENERGY
It states that:“Energy can neither be created nor destroyed but it can only be converted from one form to
another and the total amount remains constant”.
Examples
#1. In the case of the ball falling vertically downwards from height h


Its energy is all PE at the beginning of the fall
Gains some K.E and loses P.E as it falls and its velocity increases and height decreases.
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

The increase in K.E is equal to the lose in K.E
On reaching the ground all energy will be changed to K.E and P.E is zero.
*K.E = ½ mv2 = mgh
which follows that velocity on reaching the ground is given by:
½ mv2 = mgh
v2 = 2gh


At any moment the total energy is constant; P.E at the beginning = K.E at time the ball hits the
ground = sum of K.E + PE at intermediate positions.
When the ball bounces, only rises to a lower height showing that it has less GPE now compared to
the previous maximum height. This is because some energy is lost during its impact with the
ground mainly as heat.
#2. A swinging pendulum




Energy all PE at the extreme positions.
All energy KE when passing the resting position.
Partly KE and partly PE at the intermediate positions (the sum of the two is always equal to the total
energy)
The pendulum will eventually stop swinging because all the energy would be lost to the surrounding as
heat energy due to doing work against friction (air resistance).
6.2.5 Energy changes/transfers - examples;
Action device/transducer
Energy changes
Lifting a weight
Chemical energy --------→ PE
Dropping the weight
PE ------→ KE -----------→ heat + sound
Electric motor
Electrical ------------→ KE
Burning candle
Chemical ---------→ heat + light
Generator
KE -----------------→ electrical
Microphone
Sound -------------→ electrical
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Loudspeaker
Electrical ------------→ sound
Hot air balloon
Heat ---------------→ PE
Battery torch
Chemical ---------------→ electrical
6.2.6
MAJOR SOURCES OF ENERGY
1. CHEMICAL OR FUEL ENERGY
Sources: coal, oil, food, electric cells, explosives, etc
When a material combines with oxygen, e.g. during burning, their atoms regroup and releases their chemical
energy in some other forms such as heat.
i)
Energy conversion at coal power stations
Chemical energy (coal) -----→ heat energy (water/boiler) -----→ internal energy(steam) ----→kinetic energy
(turbines) --→ kinetic energy (generator) ------→ electrical energy
Internal energy: PE + KE of the molecules.
ii) Energy conversion when a battery is used to light a bulb/lamp
Chemical ------→ electrical ------→ light + heat
iii) Energy conversion when electricity is used to charge a battery
Electrical ------------------→ chemical energy.
Advantages of chemical energy


Currently available in large quantities
Power stations are relatively cheap to build and operate compared to nuclear power station.
Disadvantages


Non-renewable- they will eventually run out.
Cause pollution (which increases the greenhouse effect and also produce acid rain and cause health)
2. HYDRO-ELECTRICITY
When water in a high reservoir is allowed to fall it turns the water turbines which in turn drive the generator and
produce electricity.
GPE(water) -----→ KE(water) -------→ KE(turbines) ------→KE(generator) -----------→ electrical energy
ADVANTAGES


Is a renewable source of energy
Causes no pollution
DISADVANTAGES


Depends on rainfall
Large areas of countryside must be covered with water, displacing people from their homes and animals
from their natural habitants.
3. WIND ENERGY
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Wind is used to turn turbines / blades attached to magnets in generators called AEROMAGNETS. .
KE(wind) ------→ KE(turbines) -----→ KE(generator) --------→ electrical energy
ADVANTAGES




Wind is free
Give high power output
Renewable
Clean
DISADVANTAGES



Unpredictable – wind may not be sufficient enough to turn the generator when electricity is needed.
High cost involved in implementing and maintaining.
Power output is fairly low.
4. SOLAR ENERGY
We receive energy from the sun as radiant energy in form of electromagnetic waves. The source of solar energy
is the nuclear energy released through nuclear fission of the nuclei of hydrogen atoms.
Solar energy can be captured in several ways:



Photovoltaic cells convert light energy into electricity
Solar panels absorb heat from the sun. The energy is usually used to heat water.
Solar furnances: an array of concave mirrors which concentrate the sun rays producing very
high temperatures of more than 3000 °C.
Power generation reflectors are used to focus heat from the sun on tubes filled with oil. The oil
boils water and the steam is sent to the turbines which turns the generators to produce
electricity.
Heat (infrared from the sun) → internal energy (steam)→kinetic (turbines)→kinetic(generators)→electrical
ADVANTAGES



Clean
Relatively cheap
Renewable
DISADVANTAGES

Useful only in places where the sun shines continuously for long period; sometimes the sun
does not shine or not strong enough in some parts of the country.
5. WAVE ENERGY
The rocking motion of the waves generate energy
ADVANTAGES

Renewable source of energy
DISADVANTAGES

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Very inefficient way to capture energy
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6. GEOTHERMAL ENERGY
It is heat energy stored inside the rocks underground. The rocks are heated by some radioactive elements as
they are heated by the sun.
The water is pumped down a borehole to hot rocks underground where it is heated. Steam under high pressure
comes through the other hole, it is used to turn the turbine which in turn drives the generator.
Geothermal (rocks)→internal energy(steam)→kinetic (turbine)→kinetic(generator)→electrical
7. TIDAL ENERGY
Sea water is trapped at high tides behind the dams and released at low tides. The released H2O is used to turn
turbines
ADVANTAGES

Renewable
DISADVANTAGES

High initial cost
8. NUCLEAR ENERGY
a). Fission – splitting of heavy nucleus (U-235) by hitting it with a neutron into nearly two equal parts to release
tremendous amount of energy and two to three more neutrons.
b). Fusion- union of certain light nuclei (e.g isotopes of hydrogen) into a heavier nucleus resulting in the
release of large amount of energy.
Uranium is the fuel in nuclear reactors. By the process of fission, the nuclear energy in uranium is converted to
large amount of heat energy.
Nuclear energy ----> heat---->k.e of steam ---> k.e of turbines----> k.e of generator---->electrical energy
ADVANTAGES




Lots of energy from little amount of fuels
Little atmospheric pollution provided strict precautions are taken
Reliable- most viable source of large amount of electrical energy
Low cost once up and running
DISADVANTAGES




6.2.7
Can be dangerous
High cost of building power station
Non-renewable
High cost of dismantling once they can no longer be used.
Sources of energy in Botswana
1. Biogas: cow dung ferments in a closed container can produce a gas that is used as fuel. This gas burns
and so it can be used in cookers.
2. Petrol and Diesel:- vehicles and borehole pumps are driven by engines that burn these fuels
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3. Morupule Power Station:- coal is mined at Morupule and is burned in power station. The heat is used
to boil water and produce steam. The steam goes through the turbine and makes it rotate. The turbine
makes the generator rotate and produce electricity.
4. Wind power
5. Solar power
6. Others are: candles, wood, bottle gas
6.3
POWER
Power is the rate of doing work or transferring energy to other form/s.
Power = work done/time taken
P = w/t
OR
P = E/t
SI unit:- watt (W)
1 W = 1 J/s
Other units:
1 kilowatt (kW) = 103 W
1 megawatt (MW) = 106 W
MEASURING HUMAN POWER
A person’s power can be calculated by timing the work she/he is doing, e.g. running up on stairs
Suppose a girl weighing 500 N climbs 6 stairs each 25 cm high in 5 seconds
W = weight X height
= 500 N X (6 X 0.25 m)
= 750 J
Calculate the average power
P = w/t
= 750 J/5 s
= 150 W
6.4
EFFICIENCY
-is the ratio of useful work done by a machine to the energy input, often written as a percentage
Efficiency = (useful work done/total energy input) x 100 %
OR
Efficiency = (power output/power input) x 100 %
NB:- in real life, there is no machine that is 100 % efficient because there is always some energy lost as heat as
result of work done against friction between the moving parts of the machine.
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6.5
QUESTIONS
1. A horizontal force of 50 N is applied onto a box which then moves a distance of 2 m. How much work is done
on the box?
2. A can of 500 g is lifted onto a shelf through a vertical height of 1.5 m. How much work is done?
3. A man pushes a box across the floor by applying a horizontal force of 100 N. The box travels with a constant
speed of 0.5 m/s.
a) What is the distance moved by the box in 10 s?
b) Calculate the work done on the box in 10 s.
4. A builder lifts 10 bricks to the top of a building through a vertical distance of 5 m. Each brick has a mass of
500 g.
a) Calculate the work done by the builder.
b) If it takes 20 s to lift the bricks at what rate is the builder working?
c) State form of energy gained by the bricks.
5. A body of mass 5 kg falls from rest and has k.e of 1000 J just before it touches the ground. Assuming there is
no friction and using the value 10 m/s2 for the acceleration due to gravity. Calculate the loss of potential
energy during the fall.
6. A 100 g steel ball falls from a height of 1.8 m onto a plate. Calculate
a) the G.P.E of the ball before the fall.
b) its k.e as it hits the plate.
c) Its velocity as it hits the plate.
7. The diagram below shows a model power-station. A small steam engine drives a generator which
lights a bulb. Decide where each of the following energy changes is taking place. (You can answer
by writing one of the letters A – D in each case.)
a)
b)
c)
d)
Kinetic energy to electrical energy: …………………………………….
Heat energy to kinetic energy: ………………………………
Electrical energy to heat and light energy: ………………………..
Chemical energy to heat energy: ………………………..
8. Some workers on a building site have set up an electric winch in order to lift a
bucket with tiles up to the roof. The bucket and tiles weigh 500 N.
a) What is the minimum force that must be applied in order to lift the bucket of
tiles off the ground?
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b) How much energy is spent in lifting the tiles 20 m from the ground to the
roof?
c) What energy transformations are taking place as the tiles are raised?
d) If the tiles are lifted 20 m in 10 s, what is the power of the winch?
e) If the winch is only 50 % efficient, how much energy must be fed into the
electrical motor to lift the tiles through the 20 m?
f) Suggest one or two reason why the system might be less than 100 % efficient.
g) How can the efficiency of the system be improved?
9. In a certain ward in Serowe people use solar panels and windmills as energy
sources.
(a) Write down one advantage of using each of these energy sources
i)
ii)
solar panels:
windmills:
(b) Write down one disadvantage of using solar panels
(c) Write down one disadvantage of using windmills
10. The diagram below shows a hydroelectric scheme. Water rushes down from the
top of the lake to the power-station. In the power-station, the water turns a
turbine which drives a generator.
a) What type of energy does the water have when it reaches the powerstation?
b) Some of the water’s energy is wasted.
(i) Why is energy wasted?
(ii) What happens to the wasted energy?
c) The hydroelectric scheme is a renewable energy source. What is meant by
a renewable energy resource?
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d) When water flows from the lake, potential energy is lost. How is this energy
replaced?
e) What advantages does a hydroelectric scheme have over a fuel-burning
power-station?
f) What environmental damage does a hydroelectric scheme cause?
11. At night time when most of us are asleep the demand for electricity is quite
small. The generators at the power stations, however, are still working as it is very
wasteful and inefficient to turn them off. In some power stations the excess
electrical energy they are manufacturing is used to pump water into dams.
Then during the day the water is released and used to drive
generators when demand is high.
a) What weight of water can be pumped 50 m uphill if the surplus energy from
a generator is 2 MJ?
b) When released, how much kinetic energy will this have after it has fallen
(i)
25 m
(ii) 50 m?
c) What assumptions have you made in order to answer (b) above?
d) Suggest why off-peak night-time electricity is cheaper than daytime
electricity.
13. To be a good pole vaulter it is essential not only to be strong and agile but also
to have good sprinting speed.
a) What kind of energy does a vaulter possess;
(i) before starting his run?
(ii) as he sprints down the runway?
(iii) as he clears the bar?
b) When a competitor has completed his vault where has all the energy
gone?
7.0
PRESSURE
7.1
Pressure is force per unit area
Pressure = force/area
P = F/A
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SI unit :- pascal (Pa)
1 Pa = 1 N/m2
Pressure increase with:i). Increase in force
ii). Decrease in the area of contact
Examples
#1. A concrete block has a mass of 2600 kg. If the block measures 0.5 m by 1.0 m by 2.0 m. What is the
maximum pressure that it can exert when resting on the ground?
Data
F = 26000 N, A = (0.5 X 1.0) m = 0.5 m2
P = F/A
= 26000 N/0.5 m2
= 52 000 N/m2
= 52 000 Pa = 52 kPa
#2. What force is produced if a force of 1000 Pa acts on an area of 0.2 m2.
Data
F = 1000 N,
A = 0.2 m2
P = F/A
F = P(A)
=1000 N/m2 x 0.2 m2
= 200 N
#3. Explain why a tractor’s big tyres stop sinking to far into the soft soil
Answ: Exert less pressure on the soil because of small area contact between the tyres and the
soil/ground
7.2
LIQUID PRESSURE
1. Pressure in a liquid increases with depth; the further down you go, the greater the weight of the liquid
above.
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Water spurts out fastest and furthest from the lowest from the lowest hole.
2. Pressure at one depth acts equally in all directions
The can of water has similar holes all round it at the same level. Water comes out as fast as far from each hole.
Hence the pressure exerted by the water at this depth is the same in all directions.
3. A liquid finds its own level
In the U-tube the liquid pressure at the foot of P is greater than at the foot of Q because the left hand
column is higher than the right one. When the clip is opened the liquid moves from P to Q until the
pressure in both is the same and the levels of liquid in both column are equal.
b.
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The liquid is at the same level. This confirms that pressure at the foot of a liquid column depends only
on the vertical depth of the liquid and not the width or shape of the tube.
7.3
HYDRAULIC MACHINES
A liquid is incompressible therefore its volume cannot be reduced by squeezing. Pressure in a liquid is therefore
transmitted in hydraulic machines to magnify a force.
Pressure, piston A
PA = FA/AA
= 1.0 N/0.01 m2
= 100 Pa
The pressure is transmitted wholly through the liquid to piston B
Force in piston B
FB = PBAB
= 100 N/m2 x 0.5 m2
= 50 N
note: PB = PA
A force of 1.0 N is therefore magnified 50 times.
Note:
PA = PB
FA/AA = FB/AB
FA = (AA/AB)FB;
7.5.1
AA/AB = force multiplying factor
ATMOSPHERIC PRESSURE (AIR PRESSURE)
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Owing to its weight, air exerts pressure at the surface of the earth and objects on the surface of the Earth. The
air pressure at the sea level (known as the standard atmospheric pressure, PO) is 105 Pa (100 kPa)
7.5.2
EFFECTS OF AIR PRESSURE
Collapsing/crushing a can
If air is removed from the can it collapses because the pressure inside the can becomes or is less than outside.
Magdeburg hemisphere
After removing (pumping out the air) it becomes very difficult to separate the spheres because air pressure inside
is less than outside.
7.5.3
AIR PRESSURE GAUGES
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a) U-tube manometer
In diagram (a) atmospheric pressure acts equally on both arms of the tube. The levels of the water (liquid) inside
therefore are the same. In diagram (b) arm one arm is connected to a gas cylinder which exerts pressure to the
liquid and it rises to the height h in the other arm.
Pressure of the gas = Atmospheric pressure + Pressure due to the liquid column h
P = PO + hρg
Pressure of the liquid column h is therefore equal to the amount by which the gas supply exceeds atmospheric
pressure.
b) Mercury Barometer
A mercury barometer is a manometer which is used to measure atmospheric pressure. Atmospheric pressure
acts on the surface of the mercury in the bowl and maintains the height of the liquid column h. This height is 760
mm at sea level. When the pressure acting on the surface of the mercury in the bowl is reduced, the height h
decreases. When the barometer is slightly tilted the height h is not affected because atmospheric pressure acts
equally in all directions.
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Pressure at x due to the liquid column h equals the atmospheric pressure on the surface of mercury in the bowl.
This pressure is stated in terms of height of the mercury column e.g. 760 mmHg (at sea level), 74 mmHg, etc.
Increasing the diameter of the tube doesn’t change the pressure at x because the weight of the liquid column
(force) will now be acting on a large surface area.
7.6 Weather maps
Weather maps are constructed by plotting of pressure readings from different weather stations in a region. When
this has been done, lines known as isobars are drawn.
Isobars are lines drawn on the map weather to join places of equal atmospheric pressure. Closely spaced
isobars indicate a big pressure difference over a short distance and suggest that strong winds are likely to occur.
Widely spaced isobars indicate a small pressure difference over a large area and suggest light winds,
Winds blow from places of high atmospheric pressure to places of low atmospheric pressure. Because of the
rotation of the Earth, winds blow more or less along the isobars. Winds blow in a clockwise direction in the
northern hemisphere and in an anticlockwise direction in the southern hemisphere for an anticyclone. For a
cyclone they blow in clockwise direction in the southern hemisphere and in the anticlockwise in the northern
hemisphere.
In weather a region of high atmospheric region surrounded by places of low pressure is called a HIGH OR AN
ANTICYCLONE and region of low atmospheric pressure in the middle of high pressures is called a LOW OR
CYCLONE OR DEPRESSION
CYCLONE
ANTICYCLONE
7.7
QUESTIONS
1.
a) A thumb tack is squeezed between finger and thumb as shown in Fig. 1.1. Which experiences the
greater pressure, thumb or the finger? Explain your answer.
Fig. 1.1
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b) A hippopotamus has very large feet. How do the large feet help the hippo to walk on soft mud?
c) Why is a dam built thicker at the bottom than at the top?
2. Explain why air pressure decreases as height above the Earth increases.
3. Explain, in terms of pressure, how you are able to drink liquid by using a straw.
4. Fig. 4.1 shows a simple mercury barometer.
a) What occupies the space labelled X?
b) Copy the diagram and show on it the distance which would be measured to find the atmospheric
pressure?
c) If the atmospheric pressure rises, what happens to (a) the mercury level in the tube, (b) the mercury
level in the reservoir?
d) Explain what would happen to the mercury if the barometer is slowly slanted out of the vertical.
5. The oil in a tank is 1.5 m deep and it has a density of 800 kg/m3. What pressure does the oil exert on the
base of the tank, in pascals?
6. A bench top measures 2 m x 1 m. atmospheric pressure is 100 000 Pa. What is the downward force of the air
on the bench top? How many tonnes of air would have this weight? (1 t = 1000 kg) Why does the bench top
not collapse?
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8.0
THERMAL PHYSICS
8.1
MATTER
Matter is defined as anything that occupies space and has mass.
8.1.1 Kinetic molecular model of matter
The kinetic theory of matter states that



All matter is made up of very tiny particles (molecules).
The particles of matter are in constant, random motion.
There are forces of attraction between the particles (the force is called a bond). It holds particles
together in solid and liquid. But it is almost negligible in gases.
 There spaces between the molecules.
8.1.2 Intermolecular forces
-
Are electromagnetic in nature due to electric and magnetic forces between particles.
Can either be attractive or repulsive depending on the distance between the particles. If the particles
come closer together than their normal spacing, the force is repulsive and is relatively large to push
them apart. If the separation of the particles is slightly more than their normal spacing, the force is
attractive and relatively large to push them back.
8.1.3 SOLIDS





8.1.4





Particles are close together and arranged in regular form lattice.
Most of true solids exist as a regular three dimensional structures called crystals.
Have definite shapes and volumes
Each particle has a fixed position in the crystal lattice.
Particles vibrate slightly from their fixed positions but the intermolecular forces are strong enough to
prevent the molecules from moving out of their positions to other positions.
LIQUIDS
Particles are little further apart than those in solids
Particles have no fixed positions.
Have definite volumes but no definite shapes.
Have slightly weaker intermolecular forces
Particles are free to slide over each other in a random motion.
8.1.5 GASES




Particles are much further apart (so gases are less dense and can easily be compressed)
Particles are in continuous motion with high speed in all directions (random motion), completely
independent of one another.
Intermolecular forces are negligible (almost non-existent) except during collisions.
Have neither fixed volumes nor fixed shapes (always expand to fill the whole container).
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A diagram to illustrate a typical motion of a gas particle
8.2.1 TEMPERATURE AND KINETIC ENERGY
The average of the kinetic energy of molecules is directly proportional to its temperature in kelvins. Doubling the
kelvin temperature of a gas doubles its molecular energy.
The total energy of molecules consists:a). kinetic energy which depends on temperature.
b). potential energy which depends on the force between molecules and the distance in-between.
*NB:- At any instant, different particles have different amount of kinetic energy. On heating, the kinetic energy of
the particles (also their average kinetic energy) increases.
The temperature of a substance is the measure of the average kinetic energy of its particles.
At any given temperature, particles of any two gases have the same kinetic energy but their average speed are
not the same.
8.2.2
Pressure of a gas in terms of molecular forces
Gases consist of large of particles in constant random motion. Gas pressure is a result of force exerted on the
surface of the container walls by the gas particles when they strike walls and rebound.
8.3 GAS LAWS
8.3.1
PRESSURE AND TEMPERATURE
The pressure of a gas increase with in temperature because the particles collide with the container walls:- i) more
frequently each second and ii) with greater force as the increase in temperature increase their kinetic energy.
PαT
when volume is constant. --------------> Pressure law
P/T = a constant
Pressure law states that:“ The pressure of a fixed mass of gas at constant volume is proportional to its temperature”
8.3.2
PRESSURE AND VOLUME
When the volume of a given mass of a gas is decreased;
a). the particles have less space to move in,
b). so particles collide more frequently each second with the walls,
c). as a result the force and pressure increase.
P α 1/V
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when temperature is constant --------------------------> Boyle’s law
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Boyle’s law states that:“The volume of a fixed mass of gas is inversely proportional to the pressure, provided the temperature
remains constant”.
8.3.3
VOLUME AND TEMPERATURE
When a gas is heated, its temperature rises as its particles move faster. If pressure of the gas is to remain
constant, the volume must increase so that the number of collisions of the particles with walls does not more
frequent and violent and hence increase the pressure.
VαT
when pressure is constant---------------------------------> Charles’ law
8.4 EXPERIMENTAL EVIDENCE FOR THE EXISTENCE OF MOLECULAR MOTION
8.4.1
DIFFUSION
Diffusion is the spreading of a fluid on its own accord and is due to molecular motion. It takes place from region
of high concentration to a region of low concentration.
It is slow process and it continues till the distribution of the molecules is even. Solids do not diffuse through solids
but gases and liquids can diffuse through solids.
The speed of diffusion of a gas depends on:a). the speed of its molecules
b). mass of its molecules (light molecules diffuse faster than heavy ones)
*If a small amount of a gas is released into another gas, it will spread much more slowly than it would if it
were released into a vacuum because its molecules will collide with molecules of the other gas.
8.4.2 BROWNIAN MOTION
The random motion of small sized particles in a fluid (such as smoke particles in air) that is seen when viewed
through a microscope. The motion of the particles is due to the collision with fast moving air molecules.
Experiment : Demonstration of Brownian Motion
Apparatus are set as shown above in a dark room. The smoke cell is filled with smoke from smouldering paper
and it is brightly lit.
On viewing through a microscope, the smoke particles (seen as pin point of light due to light reflected by them)
are seen to move at random (womble). Since there is no wind present in the box, the motion of the smoke
particles can only be due to the collision of air molecules with the smoke particles.
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Explanation of Brownian motion using the kinetic theory
Brownian motion is due to the continuous bombardment of tiny smoke particles by numerous air molecules which
are too small to be seen.
The air molecules move with different velocities in different directions. The resultant force on the smoke particles
is therefore unbalanced and irregular in magnitude and directions. This causes the smoke particles to move to a
new position now and then when another unbalanced force acts on it. All these result into the random motion of
the particles.
8.5 QUESTIONS
1 Describe the spacing of molecules and their movement in solids, liquids and gases.
2 What do each of the following statements tell you about the forces between atoms?
a) It is not easy to stretch or compress a metal.
b) If the extension is not too big, a stretched copper wire regains its original length when the stretching force
is removed?
3 A gas is heated in a closed container. What happens to the temperature and to the pressure of the gas?
Explain your answer in terms of molecules.
4 A gas in a closed container is compressed to half its volume. Explain, in terms of molecules, why the pressure
doubles if the temperature is not allowed to change.
5 A bubble of air released from a diver’s helmet under water rises to the surface. As it rises, its diameter
increases. Explain why.
6 Explain the following results.
a) A gas inside a container exerts a pressure on the walls of the container.
b) The pressure increases when the mass of the gas in the container is increased.
7 Some smoked-filled air is put into a clear plastic box and viewed through a microscope.
a) Describe carefully what is seen through the microscope.
b) Use the molecular model of gases to explain what is seen.
8 The diagram shows the main parts of a bicycle pump with the end blocked up. When a bicycle tyre is pumped
up, the volume of the air trapped in the pump is reduced and its pressure is increased.
a) Explain, in terms of the motion of molecules, why the pressure increases.
b) The volume of air in the pump at start of the stroke is 20 cm3, and the pressure of the air is 1.00 x 105 Pa.
Calculate the pressure when the volume has been reduced to 8.0 cm3 assuming that no air has escaped
from the pump and the temperature of the air is constant.
c) In practice, the temperature of the air increases as it is compressed. Explain why this is so.
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8.6 THERMAL EXPANSION
8.6.1
IN SOLIDS
Most solids expand when heated and contract on cooling. When a solid is heated, its particles vibrate more
vigorously and faster. As the vibrations become larger the particles will need more space for movement, so
particles are pushed further apart and the solid expands slightly in all directions.
When it is cooled, the vibrations become smaller then the particles are pulled closer together by force of
attraction between and hence the solid contracts.
Demonstration of expansion of solids
1).
Ball and ring experiment
When the ball and the ring are at the same temperature, the ball fits into the ring and can pass through easily.
Procedure :
- Heat the ball strongly several minutes
- Try to pass the ball through the ring
Observation: the ball does not fall through the ring
Conclusion: solid expands when heated.
b) Then, leave the ball to rest on the ring for some minutes.
Observation: The ball falls through the ring
Conclusion: The ball lost heat to the ring and contracts as it cools and at the same time the ring expands as it
gains the heat.
2).
Bar and gauge
The gauge consists of a slot that fits in the length of the bar and a circular hole that fits in the diameter of the slot
when both the gauge and bar are at the same temperature.
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Procedure:
- Fit the bar into the slot and the hole on the gauge when both the gauge and bar are at room temperature to
check if the bar fits in.
-Heat the bar strongly over the Bunsen burner for a couple of minutes. Try to fit it into the slot and hole on the
gauge after being heated.
Observation: the bar does not fit into the slot as well as the hole.
Conclusion: solid (bar) expands when heated.
b) Leave the bar to cool and test again
Observation: The bar once again fits into the gauge (through the slot and the hole)
Conclusion: Solid (bar) contracts when it cools.
8.6.2
IN LIQUIDS
Liquids expand when heated. They expand more than solids because the molecules are not tightly bound
together as those in solids.
8.6.
8.6.4
IN GASES
GASES also expand when heated. They expand much more than solids and liquids. This is because gas
molecules have negligible attractive forces between them since they are far apart.
8.6.5
Experiment to compare the expansion of water (liquid) and air (gas)
Two identical flasks A and B are filled with water and air. Flasks A and B are at the same time placed into warm
water in a small bowl C.
The water level in flask A is seen to rise very slowly but the coloured pellet in flask B rises up the capillary tube
rapidly. This shows that air expands more faster than water.
Roughly the relative order of magnitude of expansion of solids, liquids and gases is 1 : 10 : 100
respectively
Most expansion -------------------------------------------------------------------------> least expansion
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Gases
8.6.6
liquids
solids
APPLICATIONS OF THERMAL EXPANSION IN EVERYDAY LIFE
A). Bimetallic strip – it is a device based on the different expansion of solids. It consists of two metal strips of
equal size but different rates (amount) of expansion, e.g. iron and brass. The strips are riveted or welded
together. On heating, the bimetallic strip bends with brass on the outside of the curve and iron inside. This is
because the brass expands more than iron for the same temperature rise.
Bimetallic strip is used in thermostats to work as electric switch. Thermostats are useful to control
automatically temperature of:
1).
Electric iron
2).
Electric and gas ovens
3).
Waters heaters
4).
Refrigerators
5).
Fire alarms
6)
Bimetallic thermometer, etc.
*NB;- Some of the above appliances have control knobs. When the control knob is screwed down the
strip has to bend to bend more to break the heating circuit and this needs a higher temperature.
B). Riveting metal plates
Rivets are used to join two sheets of metals very tightly. During riveting, holes are bored in the two sheets, then a
very hot rivet is pushed through and hammered strongly on both sides to make head on each end. The heads
hold the sheets together. As the rivets cools, it contracts and this pulls the sheets even more firmly together.
C). Shrink fitting – This is method to fit axles in gear wheel. An axle which is slightly too large to fit into the gear
wheel is cooled in liquid nitrogen. The axle contracts until it can easily fit into the gear wheel. Then when the
axle warms up later, it expands and this produces a very tight fit between the wheel and the axle.
D). Liquid-in-glass thermometer:- mercury or alcohol expand when heated (or contract when cooled). This
fact is used to measure temperature.
E). Hot air balloon:- propane gas expands and becomes lighter when heated. It fills up a balloon which will
then because of the density difference between the propane inside and air outside will rise upwards and fly
around.
8.6.7
EVERYDAY CONSEQUENCES OF THERMAL EXPANSION
1). When railway tracks were laid with the ends of individual rails closely and firmly fixed together with no gaps
between, expansion made the tracks buckle.
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To allow for expansion and avoid destruction, gaps are left between the end of one rail and the next.
The rails are tapered at each end, then each end overlaps with the end of the next rail. As the rails expand or
contract their ends slide over one another.
2). Steel bridge
One end of the bridge is supported on the rollers and the other end is fixed. As the bridge expands the end on
the rollers can move slightly, enough to avoid any damage to the bridge.
3). Telephone and power-lines:- are hung slightly slack ( too loose) if they are put up in summer to allow for
safe contraction in winter or at night without pulling the poles down or the wire snapping (breaking). If they
are put up in winter, they are tightened up a bit so that they do not become loose (slack) when they expand
in summer or during the day.
4). Tyre bursting:- more common during very hot days. It is caused by the expansion excessive expansion of
air inside the tyre.
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Unusual expansion of water
If we start with water that is warmer than 4 °C, as the water cooled to 4 °C it contracts as any liquid would do.
But surprisingly as it is cooled from 4 °C to 0 °C it expands. Water therefore has a minimum volume (and
maximum density) at 4 °C. The expansion of water between 4°C and 0°C is due to the rearrangement of the
molecules that make up the water, hence takes up more volume therefore cancels out any contraction due to a
decrease in temperature.
This is water expansion can cause the water pipes burst in very cold weather.
The unusual expansion of water between 4 °C and 0 °C helps the fish to survive in a frozen pond.
The water at the top cools first, contracts and becomes denser and sinks to the bottom. The less dense water
rises to the surface to be cooled, become denser and then sinks as well. When all the water is 4 °C, the
circulation ceases. If the temperature of the surface water falls below 4 °C the water becomes less dense and
remains at the top and eventually forming a layer of ice of 0 °C, which insulate the remaining water, which is
protected from freezing. The temperatures in the pond are then as shown above.
*NB:- When water is heated from 0 °C to 4 °C instead of expanding it contracts and also reaches its minimum
volume at 4 °C. From 4 °C upwards it expands as we would expected.
6). Creaking noises in the roofs of buildings:- caused when the corrugated iron sheets slide over each other
as they expand or contract.
7). Freezing of water in the car radiators:- car radiator should have anti-freeze added to it to lower the
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freezing point of water.
KELVIN TEMPERATURE
Various types of thermometers give different readings when used to measure the same temperature
scale, even though they may be marked in the same temperature scale and this is because the value
obtained depends on the properties of the substance used in the thermometer.
ABSOLUTE ZERO: the lowest possible temperature, which is equal to -273.15 ˚C. Kelvin scale is denoted
by the letter K
Kelvin units = Celsius degrees + 273
T= 273 + ϴ
8.6.8 QUESTIONS
1. A student sets up the apparatus as shown below. When the student holds his hands on the flask, air bubbles
flow out from the bottom of the tube. Explain this, mentioning in your answer the behaviour of the air
molecules. When the student removes his hands from the flask, water goes up the tube to a point than it was
before. Explain why this happens.
2. The diagram shows electricity cables that have been put up between their poles on a day when the weather
was quite warm
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Why do you think the cables have been left slack?
3. Explain why
(a)
(b)
(c)
(d)
thick glass vessels often crack if placed in very hot water.
a stubborn screw lid on a jar can often be unscrewed after being warmed in hot water.
a bimetallic strip bends when heated
water pipes likely to burst during a very cold weather
4. The diagram shows a bimetallic strip. Given that brass expands more than iron, draw diagrams to show how
the strip will appear:
(a) if it is heated up
(b) if it is cooled down
5. The diagram below shows a thermostat. It contains a bimetallic strip made of brass and steel. When heated,
brass expands more than steel. The bimetallic strip is used to switch the heater off when the temperature
rises above the pre-set value.
(i) When the bimetallic strip is heated the heater is switched off. Explain why.
(ii) How would you use the control knob to make the heater switch off at a higher temperature?
6. The diagram shows a warning system containing a bimetallic strip. The bimetallic strip has two metals X and
Y firmly joined together.
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(a) Explain how and why
(i) lamp B lights when the temperature of the strip increases by 20 °C.
(ii) lamp A lights when the temperature falls by 20 °C.
(b) State what effect moving the metal contacts nearer to the bimetallic strip would have on the warning
system.
7. A glass bottle was heated. State whether the following properties were unchanged, decreased or increased.
(a)
(b)
(c)
(d)
mass of the bottle
density of the bottle
external diameter of the bottle
volume inside the bottle.
8.7 MEASUREMENT OF TEMPERATURE
8.7.1 Temperature can be defined as the measure of the degree of hotness or
Coldness of a body. The temperature is measured using a thermometer.
Temperature describes the extent to which heat is concentrated in an object.
Thermometers make use of some physical properties that change linearly/uniformly with
temperature to make measurements. These properties could be referred to as thermometric
properties.
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Examples:
TYPE OF THERMOMETER
THERMOMETRIC PROPERTY
Liquid-in-glass thermometer
Change of volume of liquid
(expansion/contraction of liquid)
Thermocouple thermometer
Change of electric current/ e.m.f
Platinum resistance thermometer
Variation in electrical resistance of platinum wire
Gas-volume thermometer
Change in pressure of a gas
8.7.2 Liquid-in-glass thermometer
A. LABORATORY (LAB) THERMOMETER
Main features:



A thin capillary tube/bore
A bulb with a thin glass wall
A liquid in bulb (alcohol, mercury)
A vacuum above the liquid in the capillary tube
Heat is transferred to the liquid inside bulb by conduction and radiation through the glass wall. After
some time the heat will reach the liquid. The heat is transferred through the liquid by convection.
The glass and the liquid will begin to expand. The liquid rises up the column of the capillary bore
because it expands faster than the glass.
Thermometric liquid
The liquid should have the following properties:
 It should have a linear expansion when heated
 It should be a liquid over a wide range of temperatures and expands by large amounts.
 It should not wet i.e. should not stick to the glass.
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NB: Alcohol should be coloured to make it visible through glass.
Comparing alcohol and mercury as thermometric liquids
1) Alcohol
 Its expansion is about six times that of mercury
 Has lower freezing point (about -122 °C) so can be used in very cold temperature
region.
Disadvantages
 Has a lower boiling point (78° C)
 Colourless so it always needs to be coloured for it to work as thermometric liquid.
2) Mercury
 is opaque so it can easily be seen
 does not vaporises easily
 conducts heat rapidly
 does not wet the glass (does not cling to the walls of the capillary bore)
 it has a higher boiling point (375 ° C)
Disadvantages
 it has a higher freezing point (-39 ° C) so it is not suitable to measure low
temperatures in very cold regions
 poisonous
Calibrating or graduating a thermometer
This is a process of marking a scale on a thermometer. Calibrating a thermometer in degrees celsius
(Celsius scale of temperature) involves several stages.
(a) First, the lower and upper fixed points must be marked on the scale. Fixed points are
standard temperatures which their values are known and fixed. Lower fixed point (or ice
point) is defined as the temperature at which pure ice melts at sea level and its value is
taken to be 0 °C. The upper fixed point (steam point) is the temperature of steam above
boiling water at standard atmospheric pressure of 760 mmHg and is taken to be 100 °C.
(b) Determining the fixed points experimentally
(i)
LOWER FIXED POINT (L.F.P)
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-
(ii)
Place the thermometer in crushed pure melting ice placed in a funnel above a beaker.
The mercury thread falls and eventually stabilises at one point. That point represents the
L.F.P.
Mark on the stem against the level of the mercury thread and label it 0 °C.
UPPER FIXED POINT (U.F.P)
-
Next, place the thermometer in the steam above boiling water in a flask.
Allow the mercury thread to rise until it stabilises at a particular point. That point
represents U.F.P.
- Mark against the level of mercury thread on the stem and label it 100 °C.
(c) Measure the distance between L.F.P and U.F.P and divide the space into 100 equal divisions.
Each division is equal to 1 °C.
NOTE: When using a thermometer without scale marks but only with lower fixed point and
upper fixed point marked, one may use the following equation to find the value of
temperature for any given length of the column.
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θ = Xθ – X0 / (X100 – X0) x ∆T
where θ – unknown temperature
X0 – length of mercury thread at 0 °C (L.F.P)
X100 – length of mercury thread at 100 °C (U.F.P)
Xθ – length of the mercury thread at temperature θ (unknown
temp).
∆T = difference between known temperatures (= 100 °C in the
diagram above)
Examples #1.
A student puts the bulb of an unmarked liquid-in-glass thermometer into melting ice, then into
steam above boiling water and finally into sea-water. Each time she waits until the liquid level is
steady and then marks the level. The diagram shows the liquid levels measured from the bulb. What
is the temperature of the sea-water?
Data:
X0 = 2 cm,
Xθ = 4 cm,
X100 = 12 cm, θ = temp. of sea-water, ∆T = 100 °C
Θ = Xθ – X0 / (X100 – X0) x ∆T
= 4 – 2/(12 – 2) x 100
= 2/10 x 100
= 20 °C
Example #2.
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Find temperature X
Data: X0 = 2 cm, Xθ = 5 cm,
X100 = 7 cm, ∆T = 100 °C, θ = X
Θ = Xθ – X0/(X100 – X0) x 100 °C
X = 5 – 2/(7 – 2) x 100
= 3/5 x 100
= 60 °C
Example #3
Find temperature X
Data: X-10 = 2 cm, Xθ = 9 cm, X110 = 14 cm, ∆T = 120 °C, θ = X
Θ = Xθ – X-10/(X110 – X-10) x ∆T
X = 9 – 2/(14 -2) x 120
= 7/12 x 120
= 70 °C
B. CLINICAL THERMOMETER
Clinical thermometer is designed to measure human temperature. It has the following features: Thin-walled glass bulb
 Narrow capillary bore
 Constriction in the capillary just above the bulb
 Short temperature range (35 °C – 42 °C).
 Vacuum above the mercury
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EXPLANATION OF PURPOSE OF DIFFERENT FEATURES
 A vacuum – allow free movement of the mercury inside the capillary bore.
 Glass bulb with thin wall allows heat to pass quickly into the mercury. Even though the glass bulb of a
clinical thermometer is smaller than that of a laboratory thermometer, but in relation to its bore, it is
large and this improves its sensitivity.
 Narrow capillary makes the thermometer sensitive to small changes in temperature.
 Constriction prevents mercury from falling back into the bulb when removing the thermometer from
the body, before a reading is taken. The mercury above will be trapped and this allows the nurse to
take accurate reading from the thermometer. When the reading is taken the thermometer is
shaken/flicked carefully so that mercury moves back into the bulb.
 Short temperature range- this is so because the normal body temperature is 37 °C and does not vary
much from this value. With a few degrees marked on the scale, the distance between unit degrees is
greater and this makes the thermometer very sensitive and easy to read accurately.
 Lastly the stem of the clinical thermometer is specially shaped, it has a triangular cross-section. This
shape produces a lens effect which would magnifies the bore and make it more visible for easy
reading.
 Uses only mercury because it is quick responding since it has a low specific heat capacity and great
conductivity.
Question :- Why should we not put a clinical thermometer inside boiling water?
Answer :- Temperature of boiling water is 100 °C but the maximum temperature that can be read by a
clinical thermometer is only 42 °C. So if sterilized in boiling water, the large expansion of mercury will cause
the thermometer to break.
8.7.3
SENSITIVITY, RANGE AND LINEARITY
SENSITIVITY OF A THERMOMETER:- refers to its ability to detect even small changes in temperature. It can
also be defined in terms of the distance between unit degrees marked on the scale. For a very sensitive
thermometer, the degrees are far apart and are close together for less sensitive thermometer. Sensitivity
depends on the following: Bulb :- if the bulb is small, heat will be distributed quickly throughout the whole liquid and the liquid
will expand quickly. But the bulb needs to be large in relation to the size of the bore for higher
sensitivity.
Thermometer A with a large bulb and a narrow bore is more sensitive than thermometer B with a
small bulb but wide bore.
 Thickness of the glass wall:- bulb should be made of thin walled glass for heat to easily reach the
liquid in the bulb
C
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Thermometer C with a thin glass wall responds quickly because heat passes quickly through the thin
glass to the liquid inside. Thermometer D with a thick glass wall responds slowly because heat passes
slowly through the thick glass to the liquid.
 Width of the bore:- for higher sensitivity the bore of the thermometer should be very thin (narrow) so
that a small expansion of the liquid can result in a larger change in the position of the level of the
mercury (length of mercury thread) inside the thermometer.
Note: Mathematically, sensitivity can be expressed as change in the length of the mercury column per
unit temperature increase.
e.g. If a column of a thermometer increases by 10 mm for every 2 °C increase in temperature, what is
the sensitivity of the thermometer?
Sensitivity = 10 mm/2 °C = 5 mm/°C
RANGE OF A THERMOMETER:- is the temperature interval (value of the lowest temperature and highest
temperature) that can be measured by a thermometer.
e.g. A clinical thermometer; range = 35 °C – 42 °C
A laboratory thermometer; range = -10 °C – 110 °C
The range of the thermometer also depends on the size of the bulb and the width of the bore:- If the bore is
small relative to the size of the bore, the thermometer will be able to measure a wide range of temperature.
The range of a thermometer is also affected by the length of the stem. Thermometers with long stem have
large ranges whilst those with shorter stems have smaller ranges.
Summary of the effects of bulb size and bore width on range and sensitivity
Range
Sensitivity
Volume
of bulb
Large
low
high
Small
high
low
Wide
high
low
Narrow
Low
high
Width
of bore
LINEARITY OF TEMPERATURE SCALE
It refers to whether the temperature degree marks are uniformly/equally spaced on the scale.
Linear scale: temperature scale on the thermometer should have equal temperature divisions of equal
size/length/spacing (equal temperature differences equally spaced). This is so because change in temperature
is proportional to change in the length of the liquid column (or any thermometric property).
But for the temperature scale to be linear, the tube must have a uniform diameter.
8.7.4 THERMOCOUPLE THERMOMETER
This is an electrical thermometer. A simple thermocouple is made from three pieces of two kinds of wires with
some of their ends twisted together to form junctions and the free ends connected to a sensitive
galvanometer. They wires can be arranged so that they alternate, e.g. Cu – Ni – Cu or Ni – Cu – Ni
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To use the thermometer, one junction X (cold junction) must be put into melting ice. The other junction Y (hot
junction) is placed into the body of substance of which its temperature is to be measured, e.g. warm water.
Difference in temperatures at the two junctions induces an e.m.f (voltage) across the junctions which causes
the current to flow through the circuit. This will result with a deflection on the sensitive galvanometer.
Note:
 The deflection is greater when the temperature difference is greater.
 If the temperature of both junctions is the same then no voltage is produced.
Advantages of a thermocouple
i) A thermocouple responds quickly to temperature changes, because metal wires are good conductor
of heat and also only a small part can be put into a substance, it can quickly attain the temperature of
of the substance.
ii) A thermocouple can be used to measure very high and very low temperatures (-200 °C – 1500 °C),
e.g. used to measure high temperature inside blast furnaces and car engines.
8.7.5 ABSOLUTE ZERO AND KELVIN SCALE
When the temperature falls, the kinetic energy of its particles fall as well and move more and more slowly. At
lowest temperature that can be reached by the object the particles have the minimum energy possible. This
temperature is known as absolute zero. And its value is taken to be -273 °C or 0 K.
Another temperature scale that is used is the Kelvin scale, in which the temperature is expressed in kelvin (K).
One Kelvin (1 K) has the same size as one degree Celsius (1 °C). The Kelvin scale uses absolute zero as its zero
(0 K).
The Kelvin and Celsius scales can be connected by the equation below:
T = θ + 273
where T = temperature in kelvin (K)
θ = temperature in degree Celsius (°C)
E.G.
Absolute zero
Melting point
Boiling water
Celsius scale
-273 °C
0 °C
100 °C
Kelvin scale
0K
273 K
373 K
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#2 Convert a) 50 °C to K
b) 100 K to °C
ANSW: a) Data: θ = 50 °C, T = ?
T = θ + 273
= 50 + 273
= 323 K
b) Data:
T = 100 K, θ = ?
T = θ + 273
THEN
θ = T -273
= 100 K – 273
= 173 °C
8.7.6 QUESTIONS
1. The scale on a thermometer used for measuring the temperature includes two fixed points. What are the
values of these?
Explain why the length of the mercury thread changes when the temperature rises?
2. (a) A clinical thermometer, used to measure human body temperature has a constriction just above the
bulb, why is the constriction necessary?
(b) The thermometer temperature is 35 °C – 42 °C, why is the range made to be so small?
(c) How is the thermometer made very sensitive?
3. The diagram shows a laboratory thermometer.
(a)
(b)
(c)
(d)
(e)
Name the substance labelled A.
Name the section labelled B.
Why is part C of the tube enlarged?
Is the wall of the tube marked D thin or thick? Explain why it is so.
Using a well-labelled diagram, describe how you would check the accuracy of the point marked 0 °C on
the thermometer.
4. (a) Convert these to kelvin (K): i) 27 °C
ii) -3 °C
iii) 150 °C
iv) -90 °C.
(b) Convert these to degrees Celsius (°C):
i) 373 K
ii) 200 K
iii) 1000 K.
5. The scale of a mercury-in-glass thermometer is linear. One such thermometer has a scale extending from
-10 °C to 110 °C. The length of that scale is 240 mm.
(a) What is meant meant by the statement that the scale is linear?
(b) Calculate the distance moved by the end of the mercury thread when the temperature of the
thermometer rises
(i) from 0.0 °C to 1.0 °C
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(ii) from 1.0 °C to 100 °C.
6. A mercury thermometer is calibrated by immersing it in turn in melting ice and then boiling water. The
column of the mercury is respectively 2.0 cm and 22.0 cm long. What would be temperature reading when
the column is 7.0 cm long?
8.8 MELTING AND BOILING
8.8.1 Whenever a substance undergoes a phase change (boils, melts or condenses, etc) energy is taken away
or added to the substance. But surprisingly there is no temperature change during a phase change.
*Phase – refers to a state in which a substance (matter) can exist.
8.8.2 Melting
Melting is a process in which a substance changes its state from solid to liquid and the reverse process (liquid to
solid) is called freezing or solidification.
When a pure solid melts it stays at the same, definite temperature is called its melting point and it also
bbsolidifies at the very same temperature (now it would be called its freezing point). During melting or freezing,
the temperature does not change even though the substance continues to gain or lose (heat) energy. The
energy gained is used to re-arrange the particles/molecules/atoms of the substance.
The heat absorbed by the substance during melting or given out during solidification is called latent heat of
fusion. The energy is used to overcome the attractive forces between the particles that keep them in their fixed
positions. Latent heat changes the state of the substance without change in the temperature (“latent” literally
means hidden)
8.8.2 Boiling
Boiling is a process in which the substance changes state from liquid to gas and the reverse process is called
condensation (gas -----> liquid).
If the energy is supplied to a liquid, e.g. water, its temperature rises until it boils. During boiling the temperature
of water remains constant. The temperature at which a liquid turns into a gas by boiling is called its boiling point.
As water turns into steam, the energy supplied does not cause a rise in temperature instead is used to enable
molecules to break the attractive forces holding the particles together. The energy absorbed and used to change
a liquid to a gas without changing the temperature of the substance is called latent heat of vaporisation. The
latent heat of vaporization is given out during condensation to change a gas to a liquid.
8.8.3
PLOTTING A GRAPH OF TEMPERATURE AGAINST TIME
1) BOILING CURVE
When ice at a temperature below 0 °C, say -10 °C is allowed to warm up slowly, its temperature will rise to 0 °C
and remain constant until all the ice has melted. The temperature will begin to rise up to 100 °C where it remains
constant until all the water has vapourised into steam and the temperature of the steam will rise above 100 °C.
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BOILING
MELTING
2
COOLING CURVE
We can also plot a graph of temperature against time (boiling curve) when the steam of temperature above
100 °C.
steam
condensation
Water + steam
water
Freezing/solidification
water + ice
ice
8.9 Evaporation
8.9.1 It is the process in which a liquid changes into a gas at a temperature below its boiling point. All molecules
do not have the same energy. During evaporation, molecules with greater energy than others and are
nearer to the surface escape into the space above the liquid....... The escape of high
energetic molecule
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*Liquids which evaporate and boil at low temperatures are called volatile liquids.
8.9.2
a).
Factors increasing the rate of evaporation.
Temperature of the surrounding
At higher temperature, molecules gain more energy and move faster and time for them to reach the surface
decrease. Therefore a larger number of molecules can escape from the surface.
b). Surface area
If the surface area is large, more molecules will evaporate because more molecules are near the surface and
also there is more room for them to escape.
c). Humidity
When the humidity is high (i.e. water vapour is present in air in greater proportion) the molecules which escaped
from the liquid collide with the water molecules in the atmosphere, so some of the escaped liquid molecules will
return into the liquid.
d). Draught (wind) over the surface
If wind blows over the surface of the liquid, the escaped molecules from the surface of the liquid will be rapidly
carried away by the draught and thus reducing the possibility of their return into the liquid.
8.9.3 Cooling by evaporation
During evaporation, the high energy molecules escape from the liquid leaving the low energy molecules behind.
Therefore the average kinetic energy of the remaining molecules decreases. This lowers the temperature of the
liquid because the temperature of a substance is proportional to the average kinetic energy of its molecules.
8.9.4 Some applications of evaporation
i). Cooling our bodies- your body sweats in hot weather, as the sweat evaporates it takes in latent heat from
your body and cools it, this helps get rid of excessive internal energy.
ii) In refrigerators and freezers
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Refrigerator has sealed system of thin pipes with compressor, a condenser and an evaporator. A volatile liquid
(such as Freon or ammonia) known as refrigerant is pumped through the coiled pipes around the freezer
compartment in the top of the refrigerator. The refrigerant evaporates and takes latent heat from its surroundings,
producing cooling inside the refrigerator. A pump is used to draw the vapour (so reducing its pressure, loweing its
boiling point and encouraging further evaporation and removing more from the refrigerator) and then forces it into
the heater exchanger at the rear of the refrigerator. Here the vapour is compressed. It liquefies, giving out latent
heat of vapourisation into the surrounding air. The liquid, now at room temperature, returns to the coils, returns to
the coils in the freezer and the cycle is repeated.
iii). In air conditioners
It works in the same way, but on a larger. The refrigerant liquid evaporates in the coil inside the building and
extracts latent heat from the air in the room, cooling it down. The resulting vapour then condenses under
pressure in the coil outside the house releasing the latent heat to the outside air.
8.9.5
Evaporation and Boiling
During boiling, the average k.e. of particles is high enough for some groups of particles to form separate bubbles
of vapour throughout the liquid, these bubbles will be seen moving rapidly and will burst at the surface during
boiling. At the boiling point, some of the particles near the surface gain enough energy to escape from the liquid.
These escaping particles form vapour above the surface of the liquid. This is evaporation.
Differences and similarities between boiling and evaporation
Both processes involve a change in state from liquid to gas, but evaporation is not the same as boiling.
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A). Differences
Boiling
Evaporation
1). quick
1). Slow
2). Occurs at only one temperature – boiling point
2). Occurs at all temperatures
3). Occurs throughout the whole body of the liquid
3). Occurs only at the surface
4). Bubbles seen
4). Nothing visible happens (no bubbles)
5). Source of energy is needed
5). Energy supplied by the surroundings
6). Boiling point increases with increase pressure
6). Rate of evaporation decrease with increase in
pressure
7). Decrease with increase in altitude
7). No effects
B). Similarities
1). Both form vapour
2). Both take place in liquids
3)
Both occur as a result of increase of k.e in the molecules
4)
Latent heat of vapourisation is needed for both processes
8.10
QUESTIONS
1. A boy has been swimming in a pool. He comes out of the water onto hot sunshine but he feels cold until he
has dried himself. Why did he feels cold when he was still wet?
2. Table shows the melting points and boiling points of four substances. Which state are the substances in at
room temperature (say 15 °C)?
Substance
Melting point / °C
Boiling point / °C
A
B
C
D
-73
-39
17
29
-10
357
118
669
b) For which substance(s) would the state change on a warm day?
3. A large piece of ice is taken from a refrigerator has a temperature of -2 °C. Its temperature is measured as it
is warmed. Sketch a graph to show how its temperature changes with time until the water is boiling.
4. The diagram below is the outline of a heat pump system. A suitable refrigerating liquid or its vapour is
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circulated round a loop of pipes. In one part of the loop (the compressor) the vapour condenses into liquid; in
another part (the expansion valve) the liquid evaporates. Explain what transfer of thermal energy (heat)
occurs (i) when a liquid evaporates and (ii) when a liquid condenses.
5. The graph shows how the temperature of a pure substance changes as it is heated.
(a) At what temperature does the substance boil?
(b) On the graph, mark with an X any point where the substance exists as both a liquid and gas at the same
time.
(c) i) All substances consists of particles. What happens to the average kinetic energy of these particles as
the substance changes from a liquid to a gas.
ii) Explain, in terms of particles, why energy must be given to a liquid if it is to change to a gas.
6. The graph below shows how the temperature of some liquid in a beaker changed as it was heated until it was
boiling.
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(a) What was the boiling point of the liquid?
(b) State and explain what difference, if any, there would be in the final temperature if the liquid was heated
more strongly.
(c) State two differences between boiling and evaporation.
8.11.1
HEAT CAPACITY
Same amount of heat transferred to different objects does not cause the same temperature in each of them.
Experiments show that:
i. The temperature change is inversely proportional to the mass of the object which is heated.
∆T α 1/m
ii.
The temperature change differs from material to material. For any one material (e.g. water, iron,
mercury, copper, etc.) exists a constant, C. For objects of the same mass;
∆T α 1/C
The constant C is called heat capacity of an object. Heat capacity, C, is the quantity of heat which is required
to raise the temperature of an object by 1 °C or 1 K.
SI Unit is joule per celsius (J/°C or J °C-1) OR joule per kelvin (J/K or J K-1).
From the definition, mathematically heat capacity can be expressed as:C = Q/∆T
Which means that;
Q = C∆T -----------------------------------------> (1)
Where Q = amount of heat transferred/supplied to the object in joules (J)
∆T = change in temperature (final temp Tf - initial temp Ti) in °C or K
C = heat capacity in J/°C or J/K
8.11.2
SPECIFIC HEAT CAPACITY
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Specific heat capacity, c, of a material is the quantity of heat which must be supplied to a mass of 1 kg of that
material to raise its temperature by 1 °C or 1 K. Its SI unit is joule per kilogram per degree celsius ( J/kg/°C or J
kg-1 °C-1 or J/(kg °C)) OR joule per kilogram per kelvin (J kg-1 K-1)
Specific heat capacity is in fact heat capacity per unit mass, which means that
c = C/m ----------------------------------------> (2)
substituting eqn (1) above into the equation (2) we have
c= (Q/∆T)/m
which follows that
Q = mc∆T
where Q = amount of heat transferred or supplied in joules (J)
m = mass of the material in kg
c = specific heat capacity of the material in J kg-1 °C-1 or J kg-1 K-1
∆T = change in temperature
*Note that the symbol for the specific heat capacity is c, not C. C is the symbol for heat capacity.
∆T = |∆T|, this means ∆T should always be positive even if Tf is less than Ti
Problems
#1Find the specific heat capacity of the liquid given that:
i.
energy transferred = 12 209 J
ii.
mass of liquid = 0.8 kg
iii. original temperature = 26.8 °C
iv.
final temperature = 33.0 °C
Answ
Data: Q = 12209 J,
m = 0.8 kg,
Ti = 26. 8 °C,
Tf = 33.0 °C,
c =?
Q = mc∆T
c = Q/m∆T
= 12209/(0.8(33.0 – 26.8))
= 301 600 J
#2. Calculate the heat required to raise the temperature of 10 kg of brass from 10 °C to 90 °C. Specific heat
capacity of brass = 377 J kg-1 °C-1.
Answ:
Data:-
m = 10 kg,
Ti = 10 °C,
Tf = 90 °C,
c = 377 J kg-1 °C-1,
Q=?
Q = mc∆T
= 10 x 377 x (90 – 10)
= 301 600 J
#3 A kettle containing 1 kg of water (c = 4200 J kg-1 °C-1) is placed on top of an electric heater of power 1000 W.
It takes 5 min for the water temperature to rise from 20 °C to 90 °C. Find:
a. the energy released by the heater
b. the energy absorbed by the water. Account for any losses in energy
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Answ:
a)
Data:-
P = 1000 W,
Q = E = Pt
= 1000 x 300
= 300 000 J
b) Data:m = 1 kg,
t = 5 min = 300 s,
Q=?
c = 4200 J kg-1 °C-1, Q = ?
Q = mc∆T
= 1 x 4200 x (90 – 20)
= 294 000 J
6000 J of energy are lost to the surroundings and cointainer by conduction, convection and
radiation.
#4 If 2 kg of water cools from 70 °C to 20 °C, how much thermal energy does it lose?
Answ:
DATA:m = 2 kg, Ti = 70 °C,
Q = mc∆T
= 2 x 4200 x (70 – 20)
= 420 000 J.
Tf = 20 °C,
c = 4200 J kg-1 °C-1,
Q =?
#5 In an experiment, 920 000 J of energy is transferred to 2 kg of iron (c = 460 J kg-1 °C-1). The initial
temperature of iron is 25 °C. What is the final temperature of the iron?
Answ:
Data:-
Q = 920 000 J,
m = 2 kg,
Ti = 25 °C,
c = 460 J kg-1 °C-1
Q = mc(Tf – Ti)
Tf = (Q/mc) + Ti
= 920 000/(2 x 460) + 25
= 1000 + 25
= 1 025 °C
8.11.3 SPECIFIC LATENT HEAT OF VAPORIZATION
The specific latent heat of vaporization LV of a substance is the amount of heat needed to change mass of 1 kg
of a liquid to vapour without change its temperature. It measured in J/kg or J/g
Q = mLV
where Q = energy supplied (J)
m = mass of the liquid (kg)
LV = sp. Lat. Heat of vaporization (J/kg)
8.11.4 SPECIFIC LATENT HEAT OF FUSION
It is the amount of heat needed to convert mass of 1 kg of a solid to liquid without temperature change. It is
measured in J/kg or J/g.
Q = mLf
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m = mass of the solid (kg)
Lf = sp. Lat. Heat of fusion (J/kg)
8.12
QUESTIONS
1. A heater supplies 42 J of energy every second (its power is then 42 W). It is used to heat some water. The
temperature rises by 5 °C in 100 seconds. What is the heat capacity of the water? A boy says it would take
times as long to raise the temperature to 50 °C. Is he right? Explain ypur answer.
2. A beaker of oil and a beaker of water are heated on the same electric hot plate. The beaker of oil has a
lower thermal capacity than the beaker of water. What can you say about how the temperatures change?
3. The heat capacity of a thermocouple is mall. Give two advantages which result from this.
4. What is meant by the specific heat capacity of a substance?
5. Calculate the energy lost by 2.5 kg of steam at 100 °C when it condenses, cools down to 0 °C and solidifies
at that temperature.
Specific latent heat of steam = 2 260 000 J/kg
Specific latent capacity of water = 4200 J/(kg °C)
Specific latent heat of water
= 336 000 J/kg
6. A heater raises the temperature of 1.25 kg of water by 20 °C in 30 seconds. The specific heat capacity of
water is 4200 J/(kg °C). Calculate an approximate value for the power of the heater. Use this value for the
power to calculate M, the mass of water boiled away each second when the temperature reaches 100 °c.
Assume that the specific latent heat of vapourisation of water is 2.26 x 10 6 J/kg. Explain whether the actual
rate at which water is boiled away is greater than or less than M
7. Explain why a drink is cooled more by ice than by the same mass of water at 0 °C.
8. It takes 80 000 J of heat to raise the temperature of 500 g of porridge from 20 °C to 50 °C. Calculate the
specific heat capacity of porridge.
9. An experiment was conducted to measure the specific latent of fusion. Ice was placed in a funnel and
heated for a fixed time. The water from the melted ice was collected in a beaker as shown in the diagram.
The mass of the empty beaker was 50 g.
A 100 W heater was used to heat the ice for 2 min. After the jeater was switched off the mass of the
beaker and the melted ice was 83 g. Use the results to calculate a value for L f, the specific latent heat of
fusion of ice. Explain why your answer is different from the accepted value of 340 J g -1.
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8.13 HEAT TRANSFER/ TRANSFER OF THERMAL ENERGY
8.13.1 Heat/thermal energy is always transferred from place at a high temperature to place at a lower
temperature.
There are three common methods or ways by which heat can be transferred, viz:(i) Thermal conduction
(ii) Convection
(iii) Thermal radiation
8.13.2
Conduction
This is flow of heat through a substance from places of higher temperature to those of lower temperature
without any movement/flow of the substance (matter) as a whole. It is a main method of heat transfer in
solids and heat can be conducted in all directions.
NB: Conduction can take place in all the three states of matter but at different rates.
1. Molecular explanation of conduction in a solid
When one end of a metal rod is heated, the particles (atoms/molecules) in portion nearest to the source of
heat, gain more kinetic energy and start to vibrate faster and more vigorously. These atoms collide with the
neighbours and pass on some of their energy during those collisions. The neighbours will also begin to vibrate
faster and will in turn transmit the energy to the surrounding atoms. The chain process continues until all the
particles are affected and the whole substance is heated even the farthest parts.
2. Good and bad thermal conductors
Most solids are good conductors of heat. Liquids and gases are bad conductors. Bad conductors of heat are
called thermal insulators.
Experiment #1: To demonstrate that different metals conduct heat at different rates
Procedure:
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i) Stick a pin to each piece of metal with candle wax
ii) Pour boiling water into the pan.
Note: In the experiment the following should be done
i) Length of all the metal rods should be the same
ii) All the metal rods have the same thickness (cross-sectional area)
iii) Pins attached at the ends of the metal rods should be identical and have equal weights
iv) Metals should be placed into the hot water to same length to ensure equal distribution of heat to all
the metals.
Observation:
The pin attached to the copper falls off first followed by that attached to the aluminium, then zinc and lastly
iron.
Conclusion: copper conducts heat fastest and iron slowest.
All four metals can be listed in order of the rate of conduction as follows:- copper, aluminium, zinc, iron.
Experiment #2: To show that wood is a poor conductor of heat.
Apparatus are arranged as follows
Observation
When the rod is passed through the flame several times, paper over the wood scorches (burns) but not that
over brass.
Explanation: The brass conducts heat away from the paper very quickly, and prevents it from reaching the
temperature at which it can burn. But the wood conducts heat away slowly and hence more heat builds on the
paper, enough to make it burn.
Note: Metal objects below body temperature feel colder to touch than those made of non-metals because
metals conduct heat away from the hand faster.
Experiment #3: To show that liquids are poor conductors of heat.
Procedure:
i) Wrap an ice cube in a metal gauge and place it at the bottom of a boiling tube filled with water.
ii) Heat the water at the top using a low Bunsen flame.
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Observation: The water starts to boil at the top before all the ice at the bottom has liquefied (melted).
Reason: Heat is slowly conducted from the top of the boiling tube to the bottom of the tube. Therefore the ice
melts very slowly. This shows that water is a poor conductor of heat.
Note:
i) Metals are good conductors of heat because they have a large number of free moving electrons.
As the electrons travel over the piece of metal, they take some heat with them. So in metals heat is
transferred by electrons and also by the vibrations of the atoms.
ii) On the other hand insulators conduct heat slowly because they have very few free moving electrons
and also their particles are less closely packed together and so they collide less frequently.
iii) Conduction of heat requires a medium and hence it cannot take place in a vacuum (therefore this
means a vacuum is the best insulator/worst thermal conductor)
3. Applications of conduction – uses of good and bad conductors.
Good conductors of heat are mostly metals. They are used where heat needs to be transferred very quickly.
Good conductors (metals) are often used to make:i) Bases of cooking utensils (kettles, saucepans, pots, etc)
ii) Base of laundry irons
iii) Bits of soldering irons
iv) Branding irons
v) Dehorning irons, etc.
Poor conductors of heat are mostly non-metals (e.g. air, wood, glass, water, etc). They are used where heat is
to be insulated. Poor conductors are used to make:i) The handles of cooking utensils, soldering, soldering iron, laundry iron and many other heating
appliances
ii) Clothes – cloth is made up of fibres. The fibres trap small pockets of air. The trapped air helps to
reduce heat loss by conduction.
b). Other materials which trap air like fur, polystyrene, fibre glass, foam/sponge are used for lagging to insulate
water pipes, hot water cylinders, oven, refrigerators and also used in house roof insulation and cavity wall
insulation to prevent or reduce the rate of heat flow in our house. And air trapped between two window
panes is used in double glazing insulation method in our homes.
8.13.3
Convection
It is the transfer of heat through fluids (liquids and gases) by the upward movement of warmer, less dense
parts of fluid. This movement is actually caused by the difference in densities in different parts of the fluid.
When a fluid, (e.g. water or air) is heated, it expands and becomes less dense than the colder surrounding
fluid. Therefore it floats or rises upwards and is replaced by colder dense fluid which sinks down to take its
place. That fluid will be heated too and in turn rises upwards. At the top, the warm fluid cools, becomes denser
and begins to sink down where it will be re-heated and rises again. Thus, a circulating movement sets up in the
liquid until the whole fluid is at the same temperature. These circulating parts of the fluid are called convection
currents.
*Convection can also be used to cool a substance. When fluid is cooled, molecules contracts and becomes
denser. The cool, dense fluid sinks and is replaced by warmer fluid which will be cooled and sinks as well.
And this produces convection currents which cool the liquid.
Experiment #1: To demonstrate convection in liquids.
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The two sets of apparatus can be used
Observation
Purplish stream of water is seen rising upwards to the top. At the top the stream changes its direction of
motion and now sinks to the bottom.
*This movement is represented by the arrows drawn on the diagrams above. The arrows also show the
direction of the convection current.
Discussion
The liquid nearest to the heat source expands. This lessens its density. The less dense liquid floats and rises up.
More dense, cold liquid moves in to take its place.
Experiment #2: To show convection in air
The arrows on the diagram show the direction followed by the smoke.
Explanation:
The air around the candle flame becomes hot and expands. It becomes less dense and rises. Cool, denser air
moves over to the candle to take the place of the air that has risen up. This causes cool air from outside to
enter the box carrying the smoke with it.
Application of convection
a.
Water heating system (geyser)
-
The cold water comes into the system at the bottom and is heated by the heat element
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-
b.
c.
d.
8.13.4
Water expands, becomes less dense and rises up
It is replaced by more cold water to heated and the convection current is set to heat all the water
in the tank.
The hot water pipe is near the top because hot water would always be at the top.
If the water cools whilst at the top, it sinks to the bottom to be heated again.
Overflow pipe is included to prevent build up of vapour which will increase pressure inside the
tank and cause some explosions or cause some airlocks inside the water pipes.
The car cooling system
The arrows on the diagram show the flow of the water
The petrol burns in the engine cylinders.
Water surrounding the engine cylinders becomes hot.
Hot water rises to the top of the radiator by convection
Heat is passed from the water to the copper radiator by conduction.
Heat is passed to the air from the radiator by conduction, convection and radiation.
The cool water flows from the lower end of the radiator back into the engine and the whole restart and thus the convection currents are set.
In electrical kettles, heating elements are placed at the bottom to allow for all the water to be heated
by convection or convection currents. Also to allow for a radiator or heater to warm up a house by
convection, it should be placed very low near the floor.
But when an air conditioner is installed, it is placed up near to the roof so that when convection
currents are set would move down and cool the entire house and the same principle is used in
refrigerators so that its inside could be cooled by convection currents.
Radiation
This is a way of transferring heat in form of invisible heat waves. This is how heat travels from the sun
to the Earth. The heat waves (radiant heat) are called infrared radiation (E.M WAVES)
Note:
 Heat can be transferred by radiation through a vacuum or a transparent medium
 All objects give out some infrared radiation and the hot objects give out more radiation
compare to cool ones.
 Warm or hot objects (at higher temperature than the surrounding) will emit the radiation
whereas cool objects (at lower temperature) will usually absorb the radiation from the
surrounding.
Experiment #1: Investigating good and bad absorbers of radiant energy (infrared)
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-
The apparatus are set up as shown above with a pin attached to back each of the above two
objects (one with dark/black surface and the other with bright/shiny/silver surface). The
candle should be equidistant from both objects for equal radiation to either object.
Observation:
The pin attached to the dark surface fall off first showing that the dark or black surface absorbs
radiant heat from the candle more quickly than the bright surface.
Conclusion: Dark surfaces are good absorbers of radiation whilst bright (shiny, white or silvery)
surfaces are bad absorbers.
In fact the dull black surface is the best absorber while a white or silvery polished surface is the
worst absorber because it is a good reflector of radiation.
Experiment #2: Investigating good and bad emitters of radiant heat.
-
The two flasks in the diagram above with boiling water are allowed to cool.
It is observed that temperature falls more rapidly for the thermometer in the flask with a
dark (black) surface and slower for the thermometer in a flask with a bright/shiny surface.
- This shows that blackened surface loses heat more quickly than the silvered or shiny one.
Conclusion: dark colours emit radiant heat more quickly than bright colours, i.e. dark surfaces are
good emitters of radiant heat whereas bright surface a bad emitters. The best emitter is a dull black
surface while a silvery polished surface is the worst. However, all surfaces emit more radiation as they
get hotter.
*NB: Dark surfaces are both good absorbers and bad emitters of radiation. Generally good absorbers
are also good emitters whereas bad absorbers are bad emitters as well.
Applications of thermal Radiation
Pots and kettles have shiny outer surfaces to prevent them from emitting radiant heat
quickly and make their contents cold.
Houses in hot climates and petroleum tankers are often painted with bright paint to reduce
absorption of radiant. For the same reason white (or bright coloured) clothes are cooler to
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8.13.5
1.
wear in summer because they reflect much of the heat and dark coloured or black clothes
are ideal for cold weather to keep you warm.
Curved surfaces on electric are made of shiny metal to reflect heat
The cooling fins on the back of a refrigerator are black so that they lose heat more readily
Marathon runners, at the end of a race, wrap themselves in shiny blankets to prevent them
from cooling down too quickly.
The surface of a black bitumen road gets far hotter on a sunny day than the surface of a
white concrete one.
SOME CONSEQUENCES OF HEAT TRANSFER IN NATURE
Land and Sea Breezes
Diagram 1
Diagram 2
During a daytime the land gets hotter than the sea. The warm air rises upwards and is replaced
by cool air that blows from the sea towards the land. This sets up some convection currents
known as Sea Breezes (diagram 1).
But, at night the land loses heat faster than sea. Now the warmer air over the sea rises and then
is replaced by cool air that blows from the land to the sea and sets up convection currents that
will be called Land Breezes (diagram 2).
2. Cyclones
Usually air above warm parts of sea will be warmed as well.
The warm air rises up carrying moisture high into the atmosphere.
The rotation of Earth causes the airflow to spin.
This huge spinning mass of moist air is called a cyclone.
The cyclone causes wet cloudy weather with strong winds.
If the winds become very strong (120 – 130 km/h) the storm is called a hurricane or a
typhoon.
3. Greenhouse Effects
The Earth’s atmosphere contains a small amount of carbon dioxide gas. This has similar effect to the
glass in a greenhouse (read more on this), it allows short wavelength infrared from the Sun to pass
through and get absorbed by the Earth. The Earth becomes warm and now radiates long wavelength
infrared radiation. This radiation is absorbed by carbon dioxide and water vapour in the atmosphere
and causes the atmosphere to become warmer. The atmosphere reflects some of the energy back to
the Earth. This process is called greenhouse effect and it helps to keep the Earth warmer.
But extra carbon dioxide in the atmosphere as a result of burning of fossil fuels may add to this effect
and lead to global warming.
4. Global warming
It results in the temperature of the atmosphere and sea (Earth). That increased temperature causes
melting of the polar ice-caps. This melting results in the rise of the seal level leading to flooding of
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coastal areas. Global warming can also lead to some changes in the Earth climate which will cause the
disappearance of some species of plants and animals.
5.
8.13.6
Days and nights in a desert and desert Breezes
During the day the bare land in the desert absorbs much more heat. Therefore the desert sand
becomes hotter than areas covered by vegetation. Then the wind (breeze) blows from the forest
(area covered by the vegetation) to the desert.
But in nights in a desert are very cold because at night the desert loses heat faster. The warmer
air rises from the forest and a breeze develops from desert to the forest.
A VACUUM (THERMOS) FLASK
It is designed to keep liquids hot or cold by reducing heat transfer to or from the liquid by the aid of the
following features:
Feature of flask
Reduces transfer of heat by ........... Explanation
Silvered inner and outer walls
radiation
Silvered surfaces are bad
absorbers and emitters of radiated
heat
Vacuum between walls
Conduction and convection
Conduction and convection cannot
occur through a vacuum
Stopper or lid
Convection and evaporation
The stopper traps a layer of air
above the liquid, preventing
convection and evaporation
Glass walls
conduction
Glass is a poor conductor of heat
8.13.7 SOLAR HEATING SYSTEM
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It has the following features:
(i) a solar panel containing a coiled copper tube/pipe and blackened layer on the background. Copper is used
because is a good conductor of heat and also it does not corrode. The tube is coiled to increase the surface
area to increase amount heat absorption. The black surface increases amount of radiation energy
absorbed from the sun as a black colour is a good absorber.
(ii) a glass cover – to trap the radiation energy within the panel.
(iii) the pipe carrying heated water from the panel enters at the top of the storage tank. This allows
the heated water to circulate in the tank by convection.
8.13.8
QUESTIONS
1. The metal rod has one end placed in a fire. Explain how heat gradually travels along the rod to a
person’s hand at the other hand at the other end.
2. Why does the door handle feel colder than the wooden door in a cold weather?
3. The rods A and B are the same thickness but made of different metals. They are coated with wax
and fixed with their ends through the wall of a can. Hot water is poured into the can, and after a
short time it is found that the wax has melted as far as Y on rod B but only as far as X on rod A.
Explain why the wax melts further along B than along A.
4. Heat energy can be transferred from one place to another by the three processes; conduction,
convection and radiation.
(a). Which one of these processes is used to transfer energy by means of the infra-red part of the
electromagnetic spectrum?
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(b). Which two processes cannot occur in a vacuum?
(c). Which two processes can occur in a solid?
(d). Which process can only occur in a liquid or in a gas?
5. In a double-glazed window, two panes of glass are separated by a few centimetres . Why does
this reduce the heat loss through the window?
6. Why are loosely knitted clothes likely to keep a person warmer during the cold months?
7. Explain how heat energy is transferred through a container of soup cooking on an electric stove.
When the soup has heated sufficiently, the stove is switched off and the soup cools. Explain how the
soup loses heat.
8. A person seating on a beach on a hot sumer’s day is feels a cool breeze blowing from the water
(sea breeze).
(a) Explain why there is a sea breeze.
(b) Late at night the same person feels a breeze blowing in the opposite direction (from land to the
sea). Explain why the direction of the breeze often reverses late at night.
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WAVE MOTION
General wave properties
A wave is any periodic disturbance through a medium which transfers energy from one point to another
without the transfer of matter.
 A wave can be created along a rope by fixing one end and flicking the other end up and down. The
humps and hollows (pulses) which travel along the rope form a wave.

A wave can also be created along a slinky spring by fixing one end and moving the other back and
forth. The compressions (regions where the coils are close together) and rarefactions (where the coils
are further apart) which travel along the spring form waves.
TYPES OF WAVES


transverse wave
longitudinal wave
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Transverse wave: a wave in which the displacement or vibrations of the particles are perpendicular to the
direction of the wave travel.
Examples of transverse
-
waves on a spring or string
water waves
all electromagnetic waves (radio waves, infrared, light, ultraviolet, x-ray, gamma rays)
Longitudinal wave: a wave in which the displacement particles is parallel to the direction of the wave travel (in
the same direction as the direction of the wave travel).
Wavelength is equal to the distance from the centre of one compression (or rarefaction) to the centre of the
next.
Examples of longitudinal waves
-
waves on the slinky springs
sound waves
DEFINATION OF TERMS WITH RESPECT TO A TRANSVERSE WAVE
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Amplitude (a): height of the crest or the depth of the trough from the undisturbed position of the medium. SI
unit is a metre (m).
Period (T): time taken to produce one complete wave or cycle. SI unit: second (s).
Period = total time taken/no. of complete waves (cycles).
Frequency (f): number of complete waves generated in one second. Its SI unit is hertz (Hz). If a source vibrates
such that it produces 2 waves in one second, we say that its frequency is 2 waves per second which is 2 Hz. The
frequency of wave is the same as that of the source.
Frequency = no. of complete waves (cycles)/total time taken
Then note that: F = 1/T
or
T = 1/f
Which means 1 Hz = 1/s
F= frequency
T = period
Wavelength (λ): the distance between any two points on a wave that are moving in-phase. SI unit is a metre
(m).
Wave speed/velocity (v): distance travelled by the crest or any point on the wave in one second.
Wave fronts: lines joining points on different waves produced by same source at the same time OR lines
drawn to represent the positions of the crests on a wave.

A circular wavefronts are used to represent circular waves (ripples) and are concentric. Circular waves
can be produced by a single point source(e.g. a finger or vibrating dipper in a ripple tank)

Straight wavefronts are used for straight water waves and are parallel. Straight waves can be
produced using a vibrating bar or a ruler.
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*wavefronts are always perpendicular to the direction of the wave travel.
WAVE EQUATION
Wave speed = frequency x wavelength
v = fλ
where v = wave speed in m/s
f = frequency in Hz
λ = wavelength in metres
PROBLEMS
#1 The speed of sound wave in air is 330 m/s. What is wavelength of a sound wave of frequency 170 Hz?
Data : v = 330 m/s, f = 170 Hz, λ = ?
v = fλ
λ = v/f
= 330 m s-1/170 Hz = 1.94 m
#2 Determine the speed of a wave with a frequency of 1.0 kHz and wavelength of 0.2 m?
Data: f =1.0 kHz = 1000 Hz, λ = 0.2 m, v= ?
v = fλ
= 1000 Hz x 0.2 m
= 200 m/s
9.2 WAVE GRAPHS
There are two ways of representing waves; plotting


a displacement- distance graph
a displacement- time graph
displacement- distance graph
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wavelength = 2.0 cm
amplitude = 5.0 cm
In a displacement – distance graph, one complete cycle represent one wavelength.
Displacement – time graph
This graph can be used to find the period (T) of a wave. One complete cycle represent the period (T).
Period T = 2.0 s
Frequency f = 1/2.0 s =0.5 Hz
Amplitude a = 3.0 cm.
9.4
REFLECTION AND REFRACTION OF WAVES
Reflection: waves can undergo reflection when they meet an obstacle (barrier).
This can be shown using a ripple tank (to demonstrate reflection of water waves)
-
A flat/plane surface is placed a short distance from a vibrator. Waves are then produced. The straight
wavefronts are reflected from the boundary as shown below
The angle at which wavefronts bounce off the barrier is equal to the angle at which they meet the surface
The angle of incidence = the angle of reflection
Circular wavefronts are reflected as shown below. Notice that the reflected waves seem to be coming from an
imaginary source behind the boundary and the reflected waves are the mirror image of the incident waves.
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The distance from the real source to the barrier is the same as from the imaginary source to the barrier.
Refraction: if a small glass is placed in the centre of ripple tank the depth of the water here is reduced. As
the water waves enter this region we can see that the wavelength changes because the speed changes but
the frequency remains the same. The wavelength will increase when the wave enters the deeper water
again indicating that the speed has increased.
The ratio of the speed (velocity) v1 of waves in deep water to the speed v2 water in shallow water is known as
refractive index.
Notice that if the boundary between shallow and deep water is at an angle to the direction in which water
waves are moving, the direction of the wave of travel will change. The wave is said to have been refracted or
undergone refraction.
The waves bend towards the normal as they enter shallow water and are slowed down. They bend away from
the normal as they leave shallow water and enter deep water.
9.5
DIFFRACTION
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When waves enter/pass through an opening (gap), they often spread out even to regions that are not directly
in front of the entrance. When the waves spread through a gap or around an obstacle, this effect is called
diffraction.
When a wave is diffracted, its wavelength does not change. However, the size of its wavelength affects how
much it is diffracted.
Note: a) if wavelength is similar to the size of the gap, the waves are strongly diffracted.
b) If the wavelength is much smaller than the size of the gap, the waves are weakly diffracted.
c) If the gap is much wider, diffraction is also weaker (see diagram (a) above).
9.6
QUESTIONS
1. How is a wave produced? Give two examples of different ways of producing waves.
2. What is the difference between the longitudinal and transverse waves? Give two examples for
each.
3. What is meant by a compression and rarefaction in a spring?
4. What is the speed of a wave of frequency 400 kHz with wavelength 2.0 m?
5. Water waves are produced with a frequency of 4 Hz, by hitting the water surface with the tip of
a pencil. If the waves travel 20 m in 10 s, what is:a) The speed of the wave?
b) The wavelength of the wave?
6. A sound wave of frequency of 300 Hz and wavelength 4 m is travelling in water. Calculate the
speed and period of the wave.
7. Fig 7.0 shows a transverse wave at a certain instant. The vertical arrows indicate the direction of
motion of some individual points on the wave at a particular instant.
Fig. 7.0
On the diagram use arrows to show:
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a) The direction of energy flow
b) wavelength
c) Amplitude
8. In the diagram on the below, waves are moving towards a harbour wall
a) What will happen to waves striking the harbour wall at A?
b) What will happen to waves slowed by the submerged sandbank at B?
c) What will happen to waves passing through the harbour entrance at C?
d) If the harbour entrance were wider, what difference would this make?
9. The diagram below represents water waves travelling across a boundary between deep water
and shallow water. The waves in deep water have been drawn, but those in the shallow water
are missing. Waves travel more slowly in shallow water than in deep water. Copy the diagram
and complete it to show how the waves might behave in the shallow water.
10. The diagram below shows waves being produced in a ripple tank by a wave machine.
a) How many water waves are shown in the diagram?
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b) If the above waves were produced in 2.5 s what is their frequency?
c) If the wavelength of the water waves is 5 cm calculate their speed.
10.0
REFLECTION OF LIGHT
10.1 Definition
Light travels in a straight line but when it encounters a medium (obstacle) it can be reflected, refracted or
absorbed.
When light rays strike shiny surface they will bounce back. This is known as Reflection of light. The ray
that moves towards the surface is the incident ray while the one that bounces back is called the reflected
ray.
The following experiments can be performed to show the reflection of light.
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#1) Ray method: light ray is sent towards a plane mirror from a ray box. Mark the incident ray and the
position of the mirror. Trace the reflected ray. A normal is drawn and the angle of incident i and the angle
of reflection r are measured.
#2) Pin method:
place a plane mirror on a sheet of plain paper and mark its position.
Insert two pins P1 and P2 in a line, at an angle to the mirror to represent the incident ray.
Look through the mirror and place two other pins P3 and P4 such that they are in line with the images
of P1 and P2.
Remove the mirror and pins
Join pin holes of P1 and P2 to produce an incident ray and those of P3 and P4 to trace a reflected ray.
Draw the normal and measure the angle of incidence and angle of reflection.
Both experiments can be repeated using different values of i including i = 0 (where the incident ray is
along the normal).
Laws of reflection
1.
2.
3.
The incident ray, normal and reflected ray all lie on the same plane (so they can be shown on the
same flat sheet of paper)
The angle of incidence i is equal to the angle of reflection r (i = r)
A ray along the normal (where i = 0) will be reflected along its own path, i.e. back along the normal.
10.2 FORMATION OF IMAGES BY PLANE MIRRORS
One application of reflection is in locating the images formed by/on mirrors. When an object is placed in front
of a plane mirror, incident rays from the object to the mirror can be drawn. The reflected rays are also drawn
and are extended backwards to locate the image position. The image will be formed where the imaginary rays
meet.
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CHARACTERISTICS OF THE IMAGE
The image formed is:





Virtual (cannot be formed on the screen)
Same size as the object
Upright/erect
Literally inverted
Same distance behind the mirror as the object is in front of the mirror
The image formed will be along the same axis with the object. Therefore a line drawn joining to the object
should cut the mirror at the right angle.
10.3
CURVED/SPHERICAL MIRRORS
Two types:
-
Concave mirror
Convex mirror
i)
CONCAVE MIRROR
It curves inwards; the reflecting surface is inside
When parallel rays (beam) of light strike a concave mirror, the rays are reflected (with i = r) such that they
converge to cross at the point called a focus. If the point is on the principal axis is called the principal focus (F).
ii)
CONVEX MIRROR
It curves outwards
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When parallel rays strike a convex mirror, the rays are reflected such that they diverge/spread out. If the
reflected rays are extended backwards, they cross at focus behind the mirror. This principal focus behind the
mirror is said to be virtual because they rays do not actually originate from or pass through the point, they only
appear to diverge from or pass through the point. (But for the concave mirror the principal focus is said to be
real because the rays actually pass through the point).
Definition of terms
Centre of curvature C: is the centre of the sphere of which the mirror appears to be part of. It is in front of a
concave mirror and behind for a convex mirror.
Radius of curvature r: the distance from the centre of curvature to the pole P (centre of the mirror)
Principal axis: is the line joining the pole P to the centre of curvature C
Focal length f: is the distance from the principal focus to the centre of the mirror P (distance FP in the diagram
above).
Focal length = half the radius of curvature
f = r/2
Following rays are needed to locate the images formed by curved mirrors
i). A ray parallel to the principal axis is reflected through the principal focus.
ii). A ray through the centre of curvature strikes the mirror normally and is reflected back along its own path
(NB: radius of curvature is perpendicular to the surface where it meets the mirror).
iii). A ray through the principal focus is reflected parallel to the principal axis.
10.4 USES OF MIRRORS
a) Plane mirrors
Besides everyday use in our homes to look at oneself when dressing, doing make-ups or seeing through
awkward angles, plane mirror have other uses in a laboratory, e.g.
-
Used to help to reduce parallax errors when reading pointer instruments.
Used in making simple optical instruments e.g. a periscope
A SIMPLE PERISCOPE
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Periscope can be used to see over the top of an obstacle which otherwise blocks the direct view.
b) Curved mirrors
-
-
concave mirrors are used as reflectors in headlamps of vehicles, hand torches, searchlights, etc.
Reflected rays from these parabolic (curved) surfaces can travel long distances without becoming
weak. But the bulb should be at the principal focus F of the mirror.
Concave mirror can be used by a dentist to see teeth inside the mouth and can also be used
when shaving and doing make-ups.
Convex mirrors can be used as security mirrors in shops
Convex mirror also used as rear view mirror in vehicles because they give wide field of view.
10.5 QUESTIONS
1.
For each of the following cases find the angle of incidence and the angle of reflection
2.
A ray of light strikes a mirror surface with angle of incidence of 60°. Draw a diagram to show the
reflected ray plus the normal to the surface. If the angle of incidence was 0°, what would the angle of
reflection be?
3.
On the diagram below, draw two rays to locate the image of the object seen by the observer.
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4.
5.
6.
A girl holding a ball of diameter 30 cm stands 1 m in front of a large flat mirror. Where and how large
is the image of the ball?
A boy walks towards a plane mirror with a speed of 0.5 m/s. Does the boy’s image appear to move
towards or away from him? At what speed does the image move?
Is the image formed by a periscope upright or inverted?
7 A photographer wishes to take picture without being noticed. He attaches two plane mirrors to his camera.
Which arrangement of mirrors will allow the photographer to take pictures of someone behind the camera?
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11.0
REFRACTION OF LIGHT
11.1 DEFINITION
The bending of light as it passes from one transparent medium to another (of different optical density). When
a light ray moves from one medium/material to the other, its speed changes (as well as the wavelength) and
this cause a change in its direction of travel.
O – point of incidence
NN’ – normal (line)
AO – incident ray
OB – refracted ray
i – angle of incidence
r – angle of refraction
Some of examples of effects of refraction in everyday life
1) A stick appears bent or broken at the interface when partly immersed in water.
2) Landscape shimmers on a hot summer day.
3) If you look into a swimming pool it appears to be shallower than it really is.
SOME FACTS ABOUT REFRACTION
When light travels from a medium where the refractive index is smaller into a medium where it is larger, the
refracted ray is bent toward the normal.
2. When light travels from a medium where the refractive index is larger into a medium where it is smaller, the
refracted ray is bent away from the normal.
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1) A ray moving from a less (optically) dense medium to a more (optically) dense medium ( e.g. air to
glass) will bend towards the normal.
2)
A ray moving from a more dense medium to a less dense medium will bend away from the normal.
3) The ray along the normal is not refracted (i = r=0)
Experiments: To show refraction of light
Experiment #1: RAY METHOD




Place a glass block above a plain sheet of paper and trace its outline.
Direct a thin ray of light from the ray box towards the glass block.
Trace the incident and emergent rays onto the plain paper.
Remove the glass block and trace the refracted ray by joining the incident ray to the emergent ray
where they enter and leave the glass block.
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Light refraction through:
a) a rectangular glass block
b) semi-circular glass block
c) glass prism
Experiment #2: PIN METHOD
Apparatus: glass block, four optical pins, soft board, protractor, few sheets of A4 plain paper
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PROCEDURE:
 Place the glass block on the sheet of plain paper and draw its outline. Remove the glass block.
 Draw a normal at point O.
 Using a protractor draw a line AO such that the angle AON (i = angle of incidence) = 30°
 Place two pins P1 and P2 on the line AO.
 Replace the glass block onto the outline and view images of the pins P1 and P2 from the side BC. Then
place two others pins P3 and P4 such that they are in line with images of P1 and P2.
 Remove the glass block and join the pins P3 and P4 to meet the line BC at point D.
 Join O and D to make line OD and measure the angle MOD (r = angle of refraction).
 Calculate sini and sinr.
 Repeat the experiment for values of i = 40°, 50°, 60° and 70°.
 Plot a graph of sini against sinr and determine the refractive index of the glass by finding the gradient
of the graph line.
11.2
REFRACTIVE INDEX (n) AND SNELL’S LAW
Experiments show that:
- when the angle of incidence i increases so does the angle of refraction r but the two are not directly
proportional to each other.
- the graph of sini against sinr is a straight line passing through the origin indicating that for any light ray
passing from one medium to another, the sine of angle of incidence is proportional to sine of angle of
refraction.
i.e.
sini α sinr
which follows that:
sini/sinr = a constant
sini/sinr = n
-----------------------------> Snell’s Law
Snell’s law states that:
“The ratio of the sine of angle of incidence to the sine of angle of refraction for a given pair of
media is a constant”
*NB: Refractive index can also de defined as the ratio of the speed of light in a vacuum to the speed of light in
a medium.
n = speed of light in air or vacuum/speed of light in a medium
Refraction can also be calculated by using formulae;
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n=1/Sin C where C = critical angle
n= real depth/apparent depth
3.3 LAWS OF REFRACTION
1.
2.
11.4
The incident ray, refracted ray and the normal all lie in the same plane
Snell’s law: the ratio of sine of angle of incidence to the sine of angle of refraction for a given pair of
media is a constant.
APPARENT AND REAL DEPTH
When light moves from water to air, it will bend away from the normal. Due to the refraction of light, an
object at the bottom of the pool will appear closer to the surface, i.e. the light rays from the object will appear
to be coming from a point much closer to the surface. The depth which the object appears to be is called the
APPARENT DEPTH while the actual depth of the pool is called the REAL DEPTH.
The ratio of the real depth to the apparent depth is equal to the refractive index n of water
n = Real depth/Apparent depth
11.5
TOTAL INTERNAL REFLECTION AND CRITICAL ANGLE
When light strikes a transparent material, both reflection and refraction take place. When light ray moves from
a more dense medium like glass to a less dense medium like air, it will bend away from the normal. This makes
the angle of refraction r greater than angle of incidence i. When i increases so does r. r will eventually be equal
to 90°. The angle of incidence for which angle of refraction is 90° is known as the critical angle (C)
(a)
a)
(b)
(c)
When angle of incidence i is less than the critical angle (i < C) the ray is refracted and there is also
little reflection at the surface.
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b) When angle of incidence is equal to the critical angle ( i = C) both reflection and refraction take place
with the refracted ray running along the surface of the denser materials (glass), which means r = 90°.
c) When the angle of incidence is greater than the critical angle ( i > C) the ray is wholly/totally reflected
into the glass. No refracted ray is observed. When this happens, it is said that the light (ray) has
undergone TOTAL INTERNAL REFLECTION (T.I.R)
*NB :- To find the critical;
Sin C = 1/n
TOTAL INTERNAL REFLECTION IN PRISMS
Total internal reflection will occur in glass prism if the angle of incidence is greater than the critical angle of
glass which is about 42°
A right angled glass can be used as shown in (a) above to turn light through 180° in a rear reflectors in bicycles
or cars as well as in cats eyes (roadside reflectors).
Two right angled prisms can be used to turn light through 90° in a periscope.
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
T.I.R also helps in focusing distant objects using a pair of a binoculars.
OPTICAL FIBRES
These are thin, flexible rods of glass (or transparent plastic). When light ray is shone into the fibre it bounces
from one edge (side) of the optical fibre to the other by total internal reflection. Light can be transported over
large distance with very little loss of light intensity.
USES OF OPTICAL FIBRE
a)
Telecommunications:
Nowadays, telephone signals (messages) can be transmitted from one telephone to another by sending light
signals through optical fibres instead of using electricity carried through copper cables. Telephone systems
that use optical fibres instead cables are more efficient and much faster.
b) Endoscope
Doctors can see inside patients’ bodies using optical fibres in an instrument called an endoscope. A very small
camera is attached to one end of an optical fibre. This end is pushed down the throat and into the stomach.
The other end is attached to a television near to the patient. The doctor can see pictures of the inside of the
stomach on the television screen.
MIRAGE
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It is an optical illusion which results when air near ground or road surface is much warmer than the one high
up. It is caused by the progressive refraction of the light ray from sky as it passes through different layers of
air. Near the road surface, the light ray will meet the warmer air at an angle greater than the critical angle and
suffers total internal reflection. The reflection of light produces an image of the sky which will appear as pool
of water on the road to an observer driving along the road.
11.6 QUESTIONS
1) A ray of light travels from air into water at an angle of incidence of 60°. Calculate the angle of
refraction, given that the refractive index of water is 1.33.
2) Use a diagram to explain why a drinking straw appears bent when partially immersed in a glass of
water.
3) A pond of water (n = 1.33) is 2 m deep. What is the apparent depth of the pond when a person looks
vertically downwards from above?
4) State two necessary conditions for light to be totally internally reflected.
5) If the refractive index of water is 1.33, how deep will a pond really be if it appears to be 6 m when
looking vertically downwards?
6) What advantages do optical fibre cables have over copper cables in communication systems?
7) The diagram shows rays of light in semi-circular glass block.
a) Explain why the ray entering the glass at A is not bent
b) Explain why the ray AB is reflected at B and not refracted.
c) Ray CB does not stop at B. Copy the diagram and draw its approximate path after it leaves B.
8) Copy the diagrams below and complete the paths of the rays.
9). A ray of light is directed at a rectangular glass block (see Fig. 13.0 below). Copy the diagram and complete it
by drawing the ray which emerges at C. Name what is happening at A and at B.
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10 The diagram shows a long block of glass over an object O. Light from O reaches the top surface of the glass
at X, Y and Z.
a) What is the name given to the bending of the light at X?
b) Fill in the two missing words in the following sentence.
At Z light is ..................... ........................... reflected.
c) What is the angle marked R called?
d) Why is light reflected as shown at Z?
12.0 LENSES
12.1 Introduction
Lenses are usually used in various optical instruments to produce images. A lens would bend or refract a light
ray to produce an image. They often have spherical surfaces. There are two types of lenses, namely
i)
ii)
Convex/converging lens
Concave/diverging lens
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A converging lens is thicker at the middle and thinner at the edges and it bends light inwards.
On the other hand a concave is thinner at the middle and thicker at the edges and it spread out light.
When a parallel beam of light passes through a convex lens the rays bend inwards and converge or meet at a
point known as a FOCUS. When the rays pass through a concave lens and are parallel to its axis, they bend
outwards (spread out or diverge). The point from which the rays appear to diverge is the principal focus of the
lens.
*NB:- for a convex lens the rays actually converge at the principal focus so it is said to be real.
DEFINING TERMS




Optical centre (c):- centre of the lens
Principal axis:- a straight line through the optical centre at a right angle to the lens.
Principal focus (F):- a point on the principal axis where parallel rays converge or a point where parallel
rays appear to diverge from for a concave lens. Rays can pass through the lens from either direction
so there is another principal focus F’ on the opposite side of the convex lens and is the same distance
from the lens as F.
Focal length (f):- distance from the principal focus to the optical centre.
MEASUREMENT OF THE FOCAL LENGTH.
A simple method of determining the focal length of a convex length is by focusing the image of an object which
is far away from the lens on a wall/screen. The distance from the lens to the screen on which the image is
formed is approximately the focal length of the lens.
 PLANE MIRROR METHOD
A more accurate method involves the use of a plane mirror which reflects rays from an illuminated object
(cross-wire) in front of the lens. The lens position is adjusted until a real image is formed next to the object.
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AN ACTION OF A THIN CONVEX LENS ON A RAY OF LIGHT
When a light ray strikes a thin convex lens it is refracted at both surfaces of that lens. When light ray strikes
and passes through the first surface it will bend towards the normal since it is moving from less dense to more
dense medium (air → glass). When it leaves the second surface it will bend away from the normal because the
ray is now moving from denser to less dense medium (glass → air).
12.2 FORMATION OF IMAGES BY A THIN CONVEX LENS
A converging lens can produce both real and virtual images. The properties of the image formed depend on
the position of the object from the lens in front of the lens. They can be obtained experimentally or graphically
by drawing ray diagrams. In constructing ray diagrams any two of the following standard rays maybe used:
i)
Ray I: A ray parallel to the principal axis is refracted through the principal axis after leaving
the lens.
ii) Ray II: A ray through a principal focus F, when it leaves the lens , it is refracted parallel to the
principal axis.
iii) Ray III: A ray through the optical centre passes straight through the lens undeviated (not
refracted).
EXAMPLES
Case I: Object beyond 2F’
Image is:- real, Diminished/reduced, inverted and between F and 2F.
Case II: Object at 2F’
Image is:- real, inverted, same size as the object and at 2F.
Case III: Object between 2F’ and F’
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Image is:- real, inverted, magnified/enlarged and beyond 2F.
Case IV: Object at F
Image is at infinity.
Case V: Object between F and the lens
Image is:- virtual, enlarged, erect (upright) and behind the object
12.3
OPTICAL INSTRUMENTS
1) MAGNIFYING GLASS
A convex lens can be used as a magnifying glass if the object is placed between the lens and the principal
focus. The images will be enlarged, virtual, erect and on the same side of the lens as the object. (See case V
above)
2) CAMERA
A convex lens used in a camera to form a small, inverted, real image on a piece of film.
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



The Lens:- focuses the image of the object on a light sensitive photographic film placed at the back of
the camera. The lens is moved in or out to make focusing adjustment.
The Shutter:- opens and shuts quickly to let a small amount of light into the camera.
The film: is kept in darkness until the shutter opens. It is coated with light sensitive chemicals which
are changed by different shades and colours in the image. When the film is processed, the changes
are fixed and a negative is developed. The negative is later used to print the photographs.
The diaphragm:- is a set of sliding plates between the lens and the film. It controls the aperture
(diameter) of the hole through which light passes. In bright scenes, a narrow aperture is used but in
dark a wider aperture is necessary.
*NB: i) For closer object, the lens must be moved further away from the film.
ii) For very distant object, the film needs to be at F.
3) SLIDE PROJECTOR
A slide projector uses a convex lens to form a large, inverted, real image on the screen. The object is a brightly
lit piece of transparency (slide) with a picture/information on it.





The projection lens: forms the image on the screen. To get a large image the lens has to be a long way
from the screen. The focusing adjustments are made by moving the lens backward and forward in its
holder.
The transparency or slide: must be upside down to get an upright picture (image) on the screen. The
slide must be positioned just outside the principal focus F of the lens in order to obtain an enlarged
image on the screen.
The condenser lens system: a special convex lenses arrangement which helps to concentrates the
light on the slide so that it is very bright and evenly lit.
The lamp: produces light that illuminates the object (slide) in order to produce a bright/sharp image
on the screen.
Concave mirror: reflects light to the condenser lens system.
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4) PHOTOGRAPHIC ENLARGER
-Uses the same principles as the slide projector. The only difference is that with the photographic enlarger the
screen is a film which is coated with light sensitive chemicals e.g. silver salts.
12.6
QUESTIONS
1. Fig. 1.0 shows three parallel rays of light reaching the front surface of a converging lens. Copy the diagram
and continue the rays to show what happens to them as they pass through the lens and into the air on the
other side.
2. Where must the object be placed for the image formed by a convex lens to be
a)
b)
c)
d)
Real, inverted and smaller than the object,
Real, inverted and same size as the object,
Real, inverted and larger than the object,
Virtual, upright and larger than the object?
3. A lens has a focal length of 4 cm. An object 2 cm high is placed 8 cm from the centre of the lens. Where is
the image formed? Describe the image: is it real or virtual, upside-down or upright, enlarged, same size or
smaller? What happens to the size and position of the image if the object is moved further away from the
lens?
4. The diagram shows an object O in front of a converging lens. The points marked F are focal
points of the lens.
a) Draw two rays from the top of the object in order to locate the position of the image.
b) The image is upright. State two other characteristics of the image.
5. Lenses are used in many optical devices. Copy and complete the table below about the images
formed by some optical devices.
Optical device
Projector
Magnifying glass
camera
Nature of image
Size of image
Magnified
Position of image
Behind the object
Real
6. An object is placed closer to a converging lens than its principal focus. The figure shows an
incomplete ray diagram for the formation of the image.
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Copy and complete the ray diagram and draw the image formed.
7. The diagram shows a converging lens forming a real image of an illuminated object. State two
things that happen to the image when the object is moved towards F.
8. a) An object 1 cm high is placed 3 cm from a thin converging lens with a focal length of 5 cm.
Draw a ray diagram to find the position of the image.
b) What is meant by magnification? How is the magnification in (a) above?
c) Name one application of a converging lens used in this way.
13.0
ELECTROMAGNETIC SPECTRUM
13.1 INTRODUCTION
Electromagnetic spectrum is a family or an array of electromagnetic waves arranged according to their
wavelengths or frequencies in the ascending or descending order.
Electromagnetic waves have some similar characteristics but have different wavelengths and frequencies.
They are produced by the movement of electrons in the materials. An E.M wave is a wave consists of electric
and magnetic field (force) vibrations/oscillations which travel perpendicular to each other as well as the
direction of the wave travel.
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13.2 COMMON PROPERTIES OF E.M WAVES



All E.M waves do not need medium to travel through. They can all travel through a vacuum.
They all travel at the same speed in space which is the speed of light in a vacuum (c = 3 x 10 8 m/s)
They are all progressive transverse waves. Therefore they exhibit interference, diffraction, reflection
and polarization.
 They obey the wave equation
C= fλ
C = speed of light
f = frequency
λ = wavelength
 They can carry energy from one place to another and can be absorbed by matter and cause heating
and other effects.
*NB: The space occupied by each type of wave in the E.M spectrum is called a BAND.
13.3 COMPONENTS OF E.M SPECTRUM (E.M WAVES)
a)
GAMMA RAYS
Source: nuclei of radioactive elements (e.g. cobalt-60) and cosmic rays
Wavelength: 10-12 m
Detectors: photographic film, cloud chamber, Geiger Muller tube
Properties: - very penetrating
-transmit more energy than x-rays
- ionize gases
Uses: -used in radiotherapy to treat cancer cells and destroy tumours inside the body
-used to find flaws in metals
-used to sterilize medical equipment & dressings
- used to irradiate food to kill germs in them
- used to take x-ray type pictures
Sideeffects: - harmful to humans ; damage body cells(cause mutation and cancer) and can cause
sterility.
b) X-RAYS
Source: produced when high energy electrons are fired at a metal in x-ray tube.
Wavelength: 10-10 m
Detectors: photographic film, fluorescent screen
Properties:- very penetrating (but less than gamma rays)
-have high energy
- ionize gases
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Uses: -used in radiography (to take x-ray pictures)
-used to kill cancer cells (cancer cells absorbs x-ray more readily than normal healthy cells) and treat skin
disorders.
Side efffects: - causes cancer
c)
ULTRAVIOLET RAYS
Sources: - sun (U.V is the sun rays that gives suntan)
-Mercury vapour lamps – created by passing the current through mercury vapour in fluorescent
tubes
Wavelength: 10-8 m
Detectors: photographic film, fluorescent chemicals, photocells
Properties: -absorbed by glass
-causes suntan
-causes chemicals to fluorescence/glow
Uses: -kills bacteria
-produce vitamin D and melanin in the skin
-used to detect forgeries eg bank notes
Side effects: -causes sunburn or even skin cancer if in excess
-harmful to eyes
d) VISIBLE LIGHT/WHITE LIGHT
Sources: -sun, lamps and all luminous objects
Wavelength: 10-6 m
Properties: -is a mixture of different colours and can be split by a prism into the visible spectrum.
-ocupies a small part of the spectrum but is the only component that can be detected by
human eyes
Detectors: eye, photographic film, photocells ,plants always grow towards light
Uses: useful for vision/sight
Used for photography
Useful in some chemical reactions, e.g. photosynthesis.
Side effects: too much light damage the eyes
e) INFRARED
Sources: sun, warm and hot objects (e.g. heaters, grills, etc.), remote controllers
Wavelength: 10-4 m
Detectors: skin,special photographic film, phototransistor, sensitive thermometer, thermopile
Properties: All objects give out infrared radiation; the hotter the object is the more radiation it gives out.
-causes heating when absorbed by matter
Uses: - used for heating and cooking
- used for photography through haze and fog and in dark
- used in remote controls
- night vision
- detecting warm and cool skin and tracing infection.
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f)
RADIO WAVES
Sources: microwave oven (microwaves)
-Tv and radio transmitters using electronic circuits and aerials
Wavelength: 1 cm – 1 km
Detectors: aerials connected to radio and tv sets, mobile (cellular) phones, satellite dishes, radar
Properties: -They have the longest wavelengths and lowest frequencies.
Uses:
 Microwaves: are high frequency radio waves (but have shortest wavelength amongst radio waves).
They are used in RADAR (Radio Detecting And Ranging) to find the position of aeroplanes.
Microwaves are also used for cooking- water particles in food absorb the energy carried by
microwaves.
 UHF (Ultra High Frequency) and VHF (Very High Frequency) waves
UHF- used in tv transmissions
VHF- used in local radio transmissions
 Short, Medium and long radio waves:
Medium and long waves are used to transmit over long distances because their wavelengths allow
them to diffract around obstacles such as buildings, hills, etc.
Communication satellites above Earth receive signals carried by high frequency short waves.
These signals are amplified and re-transmitted to other parts of the world.
13.4 QUESTIONS
1) This is a list of types of waves:
gamma
infrared microwaves radio ultraviolet visible x-rays
choose from the list the type of wave that best fits each of these descriptions.
a) stimulates the sensitive cells at the back of a human eye.
b) necessary for a suntan.
c) used for rapid cooking in an oven.
d) used to take a phograph of the bones in a broken arm.
e) emitted by a video remote control unit.
2) Gamma rays are part of electromagnetic spectrum. Gamma rays are useful to us but can also be very
dangerous.
a) Explain how the properties of gamma rays make them useful to us.
b) Explain why gamma rays can cause damage to people.
c) Give one difference between microwaves and gamma rays.
d) Microwaves travel at 300 000 000 m/s. what speed do gamma rays travel at?
3) Write down the parts of the electromagnetic spectrum in order of increasing wavelength.
4) The spectrum of electromagnetic waves can be divided into several regions, in order of increasing
frequency, the diagram below shows this. Name the regions represented by the letters A and B. What
common properties are shared by the waves from each region?
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14.0
14.1
SOUND
INTRODUCTION
Sound is produced by vibrating objects such as drums, tuning forks, loudspeakers, ticking clock, etc. As the
object vibrates back and forth, the particles around it are compressed (squashed) and rarefacted (stretched).
This compression-rarefaction process continually repeats itself while the vibration continues. The series of
compressions and rarefactions form a sound wave.
In a compression, particles are squashed together and hence this is a region of high pressure whilst in a
rarefaction particles are further apart, stretched over relatively larger space and therefore this is a low
pressure region.
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*A sound wave can also be defined as a form of radiation consists of series of pressure variations
propagating through a medium
Sound waves are longitudinal i.e. the vibrations of the particles are parallel to the direction of the wave travel.
Definition;
a) Wavelength (λ) of a sound wave:- the distance between two successive compressions or rarefactions.
b) Speed (v) of a sound wave is the distance travelled by the wave in one second.
c) Frequency (f) of a sound wave:- number of complete waves produced in a second or number of complete
oscillations (vibrations) made by the source in one second.
* The sound waves obey the wave equation; v = fλ
14.2 SPEED OF SOUND
There are two ways to find the speed of sound in air
i) Experiment 1: Echo method
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............................... s .........................................
Two people stand a distance s from a large hard wall/cliff. One produces sound by banging two pieces of
metals together and the other holds a stopwatch and records the time taken for the sound to go to the hard
wall and back
To find the speed of the sound, divide the total distance travelled by the time taken recorded by the stopwatch
v = 2s/t
V = speed
s = distance
t = time taken
ii) Experiment 2: Pistol method
A<------------------- 100 m ------------------------->B
Two students stand distance s (let say s = 100 m) apart. Student A has a gun and student B has a stopwatch.
Student A fires the gun. Student B starts the watch when he sees the smoke from the gun and stops the watch
when she hears the bang. The speed of sound is calculated by dividing the distance travelled (100 m) by the
time taken, recorded by the stopwatch.
i.e. v = s/t
NB: i) The observer will always see the action (smoke) before hearing the sound (or during a storm, the
lightning flash is seen before the thunder is heard). All these show that the speed of sound is much slower than
the speed of light.
ii) Speed of sound in solids, liquids and gases: Sound travels at different speeds in different materials. It travels
fastest in solids, then liquids and slowest in gases.
Fastest --------------------------------------------------------> slowest
Solids
liquids
gases
(6000 m/s in steel)
(1500 m/s in water)
(330 m/s in air and this is far less than speed of light)
Sound waves needs media for transmission. Therefore if there are no particles, sound waves cannot be
transmitted. This means that it is impossible for sound to travel through a vacuum. This is usually
demonstrated using a bell jar, a bell and a vacuum pump.
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The sound of the bell fades when the air is removed from the jar. If the jar is completely evacuated, no sound
is heard even when the hammer continues to hit the gong. The sound returns when air is let back into the jar.
14.3
TYPES OF SOUND WAVES
Different sounds have different frequencies.
Infrasonic waves | audible sound waves | ultrasonic waves/ultrasound
20 Hz
20 kHz
i) Infrasonic waves(infrasound):- have frequencies below 20 Hz e.g. earthquake/seismic waves and can be
detected by dogs.
ii) Audible sound (waves) – sound that can be detected by human ears. Their frequency ranges from 20 Hz to
20 kHz.
iii) Ultrasonic waves (ultrasounds) - have frequencies higher than 20 000 Hz (20 kHz). They can be detected by
bats. A bat emits and receives ultrasonic waves and this helps them to navigate at night and judge the distance
of obstacles ahead.
Uses of Ultrasound
a) Used in spectacles for the blind
b) Used in echo sounding or sonar (sound navigation and ranging) in ships to determine the depth of the sea.
c) Used in ultrasound scanning in hospitals. Ultrasound waves are reflected from different layers of tissues in
the body and so can produce quite clear images. They also have lower energy than X-rays and so are less
hazardous to human cells.
Ultrasound scans are especially useful for obtaining pictures of unborn babies in the womb. Very high
Frequency sound waves are transmitted into the womb of a pregnant mother. The sound is reflected from the
embryo and the information is used to produce an image of the baby.
d) Used to clean delicate machinery or street light covers – machinery is put in a tank of liquid which has an
ultrasonic vibrator in the base.
e) In hospitals, a concentrated beam of ultrasound is used to break up kidney stones and gall stones without
patients needing surgery.
d) Used to detect flaws in metals using the idea of echo-sounding. A pulse of ultrasound is sent through the
metal. If there is a flaw (tiny gap) in the metal, two pulses are reflected back to the detector; one from the
flaw and the other from the far end of the metal.
14.4
MUSICAL NOTES
Irregular vibrations such as those of motor engines produces noise whilst regular vibrations such as those
that occur in musical instruments produce musical notes which have three properties; namely;
a) pitch
b) loudness
c) timber
a) Pitch
Pitch of a musical note depends on the frequency of the sound wave. Sound with high frequency is heard as
high note and is said to be high-pitched. Low notes have low frequencies and said to be low-pitched.
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Sound A has a higher pitch than sound B because has higher frequency. With a higher frequency more waves
are produced and the waves are closer together.
NOTE: i) A high-pitched sound also has a short wavelength while a low-pitched sound has a longer
wavelength.
ii) Musical notes are said to be octave apart if the frequency of one is twice that of the other.
b) Loudness
The loudness of sound depends on the amplitude of the sound wave. Quiet sounds (notes) have small
amplitude, loud sounds have larger amplitude. The loudness of sound is measured in decibels (dB).
Sound B is louder than sound A because the wave has a larger amplitude.
*The greater the amplitude, the louder the sound.
c) Timbre
The timbre of a sound describes the purity or quality of sound. Pure note (e.g. one emitted by a turning fork)
has only one frequency but other notes consist of a main or fundamental frequency with others, called
overtones (which are usually weaker and with frequencies which are exact multiples of the fundamental
frequency). The number and strength of the overtones decides the quality of a note.
Sound B is a pure note from a turning fork. Sound A is produced from a piano. The two sounds have almost
the same pitch (main frequency) and loudness but differ in quality because sound A is actually a combination
of several different sounds with slightly different frequencies.
Note:
The frequency (pitch) of a note produced by a vibrating material (e.g. string) depends on:
i) length of the material; short strings produce high notes and therefore halving the length doubles the
frequency
ii) tension in material: tight wires produce high notes
iii) mass per unit length; thin strings give high notes.
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14.5
ECHO AND REVERBERATIONS
14.5.1 ECHO
Sound is reflected when it meets some kind of obstruction such as a wall, high cliff or the bottom of an ocean.
The reflected sound (wave) is called an echo. In ships, echo can be used to find how deep the ocean is or to
detect the shoals of fish.
A pulse of sound is transmitted to the sea bed and is reflected back to the boat. The time interval between
transmitting and receiving the pulse is measured. Then the depth of the sea is calculated using the total
distance travelled by the pulse which is twice distance to the obstruction.
Example:
A sound pulse is transmitted from the boat, and 10 s later an echo is received. How deep is the ocean? (The
speed of sound in water is 1500 m/s).
Data:
v = 1500 m/s, t = 10 s,
d = depth of sea = ?, total distance travelled by pulse = 2d
v = 2d/t
d = (v x t)/2
= (1500 x 10)/2
= 7500 m
14.5.2 Reverberations
When playing a musical instrument, e.g. piano, in an enclosed area (e.g. inside a hall), some of the sound of
the piano will be reflected off the walls of the hall. You will hear the direct sound first, then early reflections
and then multiple reflections all in a very short time and this will cause the sound to die off gradually over
some time. This effect is called reverberation. A reverberation can also be obtained when a sound is reflected
from a surface which is nearer than 15 m, here the echo joins the original sound and then the sound seems to
be elongated or prolonged.
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The shape and size of the hall will affect the amount of reverberations reaching the listener. These factors are
called the acoustics of the hall. Rooms with good acoustics are very important when recording music or when
designing conference centres. Optimum reverberations are desirable but too much causes confusion.
14.6 NOISE POLLUTION
Unpleasant sound which may be even harmful to people is called noise. Sound is unpleasant if it is very loud
or has a very high frequency. Noise can damage the ears, cause loss of concentration and if very loud result in
sickness and temporary deafness.
Ways of reducing unwanted noise (noise pollution)




14.7
Designing quieter engines and better exhaust systems.
Using sound-insulating materials such as carpets, curtains and double-glazed windows in our houses
Tractor drivers, factory workers and other people regularly exposed to noise often have to wear ear
protectors/muffs.
Where practical keep as much greater distance away from the source of the noise as possible.
PROBLEMS
Q1. A ship searching for fish emits sound waves which are reflected from the sea bed. If the speed of sound in
is known and the time that elapses before the echo is heard is measured, it is possible to calculate how
deep the water is at that point.
a) What will the operator hear if a shoal of fish swims under the ship? How could the operator very roughly
assess how deep the shoal is?
b) Suggest one way in which the detector might be receiving a false signal (i.e. there are no fish below).
c) If sound waves travel through water at 1500 m/s,
i) how deep is the sea-bed if echo is heard after 1 s?
ii) how long will it take an echo to be heard if a shoal of fish swims 250m below the ship?
Q2. A microphone is connected to an oscilloscope (CRO). When three different sounds A, B and C are made in
front of the microphone, these are the waveforms seen on the screen.
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a) Comparing sounds A and B, how would they sound different?
b) Comparing sounds A and C, how would they sound different?
c) Which sound has the highest amplitude?
d) Which sound has the highest frequency?
e) Sound A has a frequency of 220 Hz. If the speed of sound is 330 m/s, what is the wavelength of sound A?
f) What is the frequency of sound C?
Q3. The diagram below shows the oscilloscope traces of two different sounds A and B. The oscilloscope setting
is the same in both cases.
a) A and B sound different.
Write down two differences in the way they sound. Explain your answers as fully as you can.
Q4. A man standing on a beach 340 m from a tall cliff hears his echo after 2 s.
a) What is an echo?
b) Explain how echoes can be used to discover the depth of water under boat.
c) Using the information above calculate the speed of sound in air
d) What are ultrasonic waves?
e) Give at least two uses of ultrasonic waves.
Q5. Sound X: frequency 10 000 Hz.
Sound Y: frequency 30 000 Hz.
Upper limit of human hearing: 20 000 Hz.
a) (i). What is the upper limit of human hearing in kHz?]
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(ii). Which of the above sounds is an example of ultrasound?
b) Ultrasound can travel through some human tissues and can be reflected by different layers in the body.
(i). State one example of how ultrasound is used in hospitals.
(ii). For producing medical images, why does doctors prefer to use ultrasound if they can, rather than Xrays?
(iii). State one example of the industrial use of ultrasound.
Q6. The diagram below shows a travelling sound wave.
a) Draw a second sound wave which is the same loudness as the first but a higher frequency.
b) Draw a third wave which has the same pitch as the first but have a quieter sound.
c) The sound wave in the above diagram was created in 1/10 s. What is the frequency of this sound?
15.0
MAGNETISM
Magnet is an object that attracts certain objects which are made from magnetic materials.
Magnetic materials: are materials attracted by a magnet e.g. iron, cobalt, nickel and alloys such as steel, alnico
and alcomax. These magnetic alloys usually contain iron, cobalt, nickel and aluminium. These materials
(magnetic materials) are also called ferromagnets.
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Non-magnetic materials: substances that cannot be attracted by a magnet. These include copper, brass, zinc,
tin and non metals (e.g wood, glass, etc)
15.1 PROPERTIES OF MAGNETS
a) Magnets attract magnetic materials and do not interact with non-magnetic materials.
b) Magnets have magnetic poles. These are areas in a magnet where magnetism (magnetic force) seems to be
concentrated and stronger. To determine the magnetic poles dip a magnet into iron filings. Most of the
filings stick in clumps around the ends of the magnet with few if any in the middle.
c) North and south poles
If a bar magnet is suspended so that it can swing freely it will always come to rest in approximately N-S
direction. The end pointing to the earth geographical north is called the North seeking pole or North pole (N)
and the end pointing to the geographical south is called the South seeking pole or South pole (S).
d) Law of magnetic poles
If a north pole of a magnet (test magnet) is brought closer to a north pole of another magnet, repulsion will
take place. If a North pole of one magnet is brought close to the south pole of another magnet attraction
takes place.
*Likes poles repel, unlike poles attract.
15.2 INDUCED MAGNETISM
This is the magnetism that appears or develops in a magnetic material due to bringing the material near or in
contact with a permanent magnet. The inducing pole of the magnet will always induce an opposite pole to
nearer end of the material.
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15.3
1)
METHODS OF MAGNETISATION- MAKING A MAGNET
Stroking
a) single stroking/touch
- stroke the magnetic material (steel rod) from end to end with the
same pole of a magnet.
- lift the magnet high above the rod and repeat the stroke several times (always in
one direction).
- the end where stroking ends will have an opposite polarity to the stroking pole ( and
the end where stroking started will have the same polarity as the stroking pole).
b) Double touch (Divided touch)
- use opposite poles of two magnets to stroke the rod from the centre outwards at
the same time.
- repeat several times
* if the same the same poles are used, similar poles will be formed at the ends of
the magnetic material and this will not be a proper magnet.
2) Electrical method: The industrial way of making magnets is by making use of the magnetic field created
when current flows through a conductor. The magnetic material is placed inside a solenoid (a long coil of
insulated copper wire) through which D.C (direct current) is passed. The current is switched on and off,
when the material is removed it would be found to be magnetized. (The coil should be placed in the N-S
direction).
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To determine the polarity, the right hand grip rule is used. The fingers are placed such that they follow the
direction of current around the coil and thumb will point to the North pole.
15.4 METHODS OF DEMAGNETISATION
i) Electrical Method :- a bar magnet is placed inside a solenoid through which A.C (alternating current) is
passed. The bar is slowly withdrawn from the solenoid whilst the current is still on. The solenoid should be
placed in the E-W direction.
ii) Magnets can be demagnetized by heating them strongly and then leave them to cool placed in the E-W
direction.
iii) can also be demagnetized by hammering (whilst lied in the E-W direction)
15.5
MAGNETIC SATURATION
Magnetic materials such as iron and steel have individual atoms which act like atomic magnets or magnetic
dipoles. The neighbouring atoms set themselves with their magnetic axis parallel. The grouping of atomic
magnets or atomic dipoles with parallel axes is called magnetic domain.
In an unmagnetised material, the magnetic domains will point in different directions and hence the material as
a whole will show no polarity. When a magnetic material is magnetized, the domains are re-aligned such that
most of them have their axes pointing in the same direction. There is a maximum level of the magnetization
which is called magnetic saturation. This happens when the atomic dipoles in all magnetic domains have been
re-aligned and their magnetic axes are parallel and pointing in the same direction.
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15.6
MAGNETIC FIELD
Magnetic field is the area or space around a magnet where the magnetic force is effective or felt. The force is
not is equally distributed but follows a pattern of lines.
The magnetic force of a magnetic field is along curved path known as a field line. It is usually directed from
North to South pole.
The magnetic field around a magnet can be detected by using iron filings or a plotting compass.
i) iron filings:- place a sheet of paper over the magnet. Sprinkle iron filings onto the paper and tap the paper a
bit. The iron fillings turns around in the direction of the magnetic lines of force. They form a pattern showing
magnetic field lines around the magnet.
ii) plotting compass: the bar magnet is placed on top of a sheet of paper. Place the plotting compass at the
end of the bar magnet. When the compass has settled mark on the paper the ends of the needles of the
compass. Move the compass to a new position so that its other end is over the last mark previously made.
Mark another dot where the needle is pointing. Repeat the procedure until the compass reaches the other
end of the magnet (expt. Pg 223 GCSE). Join the dots to form a single line from one end of the magnet to
the other.
PATTERNS OF ELECTRIC FIELD
i)
Field lines around a single magnet
Field lines always move from north to south. They never cross each other. And where the lines are closer
together shows areas with stronger magnetism (magnetic force).
ii)
field lines between unlike poles
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iii)
field lines between like poles
There is a neutral point X between the poles where the field cancel out each other.
15.7 MAGNETIC PROPERTIES OF STEEL AND IRON
Both iron and steel can be induced to form magnets.
EXPERIMENT 1
Each pin or clip magnetises the one below it by induction and unlike poles so formed will attract. When the
chain of iron nails is removed from the magnet, it will collapse. When the chain of the steel paper clips is
removed from the magnet, the clips will remain attached to each other. These indicate that magnetism
induced in iron is temporary while magnetism induced in steel is permanent
Conclusion: steel is a hard magnetic material i.e. it is very hard to magnetize steel but once magnetized steel
will not lose its magnetism easily.
Iron is a soft magnetic material i.e. iron can be magnetized easily but it will lose its magnetism easily.
EXPERIMENT 2
Attach a strip of soft iron and a strip of steel to the N pole of a magnet.
Dip the free ends of the strips in iron filings
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More filings stick to the soft iron. So the induced magnetism in the iron is slightly greater. When the strips are
detached from the magnet, most of the filings fall from the soft iron but few fall from the steel. This shows
that the induced magnetism in soft iron is temporary but magnetism induced in steel is permanent.
15.8
USES OF MAGNETS
1). Permanent magnets
They are used in construction of electric motors, bicycle dynamos, generators, loudspeakers, electricity
meters, microphones and can also be used as door catches.
2). ELECTROMAGNET
This is a temporary magnet made by winding a coil of wire around a soft iron.
The soft iron will only be magnetized when current flows through the coil. When there is no current flowing,
the soft iron will lose its magnetism. Steel is not suitable to be used as a core since it is a hard magnetic
material. With steel the electromagnet will keep its magnetism even when the current is switched off.
*NOTE:
1. Without the iron core, an electromagnet would be much weaker. The core concentrates the magnetic
field into a small volume of space and hence producing a stronger electromagnet.
2. The strength of the electromagnet can be increased by:
 Increasing the current
 Increasing the turns in the coil
 Using an U-shaped core so that the poles of the electromagnet would be close to each other.
Uses of Electromagnet
1.
Large electromagnets are used for lifting heavy magnetic materials in scrap-yards. A crane moves the
material to its new place and when the current is turned off, the material is released from the
electromagnet.
2.
Electric bell
It consists of an electromagnet that repeatedly switches itself on and off very quickly.
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When the press-button switch is pressed, the current flows through the electromagnet, which pulls the
springy metal together with the hammer so that it hits the gong and the sound is made. This movement, at the
same time, separates the contacts and switches off the circuit. The hammer goes back, the contacts close
again, the current flows once more and the electromagnet pulls the hammer across again, this goes on and
produces continuous sound until the circuit is switched off.
3. The magnetic relay
This is a switch operated by an electromagnet. In a relay a small switch with thin wire can be used to turn on
the current in a much more powerful circuit.
When the switch S in the input circuit is closed, the current flows through the electromagnet. This pulls one
end of the iron armature towards electromagnet and cause the other end to push and close the contacts at C
and completing the output circuit. As a result, a current flows through the motor.
4).
Reed switch
When the current moves through the coil, the magnetic field created would magnetize the reeds (thin
strips inside the glass tube). The current flows such that the ends of the two reeds develop opposite poles
and then the reeds will attract each other thereby completing the circuit connected to their other ends
(AB). The reeds separate once they the current in the coil is turned off.
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Reeds switches are also operated by permanent magnets.
In the above diagram, a burglar alarm is activated by a reed switch. When the door is closed the magnetic
fields from the two bar magnets cancel out each and the reed switch remains open. But once the door is
opened with the switch closed, the reeds would be magnetized by the magnet in the door frame. The ends
of the reeds will be induced with opposite ends, they will attract, and completing the circuit and this will
causes the alarm bell to ring.
5.
The telephone earpiece
When someone speaks into the microphone (mouthpiece) on the other end of the line a varying
electric current is set up having the same frequency as the sound waves. Similar current will be fed to
the earpiece on the other end, when this varying current passes through the coil in the earpiece, the
magnetic force on the diaphragm also varies. Therefore the diaphragm (made of magnetic substance)
moves to and fro in step with the current. This sets the air nearby into vibration and sound waves are
set up.
15.9 MAGNETIC SHIELDING OR SCREENING
Besides being used as core for electromagnets or making permanents magnet, magnetic materials can be used
for magnetic screening where an iron ring will act as a magnetic shield for anything inside it.
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Iron is said to be more permeable to magnetic field than air is. Therefore magnetic field lines appear to be
drawn into the iron and concentrated through it and none through the air inside the iron. Then anything inside
the iron ring would be shielded or screened from magnetic field. This effect is known as magnetic screening or
shielding.
Magnetic shielding is put to practical use when used to protect delicate measuring instruments which could be
affected by magnetic fields by enclosing them in thick-walled soft-iron boxes.
15.10
1.
2.
QUESTIONS
A student has a piece of metal that he thinks is a magnet. He holds it near another magnet and it is
attracted. The student says this proves that his metal is a magnet. Explain why the student is wrong.
A, B, C and D are small blocks of different materials. The table below shows what happens when
two of the blocks are placed near one another.
Use one of the phrases below to complete the sentences that follow. Each word may be used once,
more than once or not at all.
A MAGNET
3.
4.
A MAGNETIC MATERIAL
A NON-MAGNETIC MATERIAL
a) Block A is ......................
b) Block B is .......................
c) Block C is ......................
d) Block D is ......................
What is the diference between a magnetically hard material and a magnetically soft material? Give an
example of each.
a) What is a magnetic material? Give three examples of magnetic materials.
b) Name three non-magnetic metals.
5. Study the magnets in the diagram below. What would happen in each case?
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6. What is meant by a magnetic field?
7. a) Circle the names of two materials which are attracted to magnets
aluminium brass copper
iron
steel
tungsten
b) The diagram shows a pattern of lines around a magnet.
Give the name/s of:
(i)
this type of magnet ..................................
(ii)
the points marked • ...................................
(iii)
lines ..............................................
c). Two magnets, like the magnet shown above, were used to get the pattern of the lines
shown below.
Describe what you would do with the two magnets so that you got this pattern.
9. An electromagnet is made by winding wire around an iron core.
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The diagram shows an electromagnet connected to a circuit.
a) State two ways of making the strength of the electromagnet weaker.
b) Explain why the core is made of iron instead of steel.
10. a) Given a bar magnet, how would you find out which pole of the magnet is its north
pole
b). How would you magnetized a steel needle and how would you tell that it is magnetized?
c) How can this magnetized needle be effectively demagnetized?
c) Is it possible to make a magnet with a single pole?
d) If you cut a magnetized steel in half. You will find out that each half is a bar magnet. What
will happen if you cut one of the halves in two? Does this produce a magnet with a single
pole?
11. A current is passed through a solenoid (coil) as shown below
a) The solenoid in the diagram above behaves like bar magnet. Mark its polarity.
b) An iron rod is placed in the solenoid. What happens to it when the current is
i)
Switched on
ii)
Switched off
c) How would your answers in (i) and (ii) above change if the rod were made of steel?
d) What is purpose of the core in the electromagnet?
e) Give one use of an electromagnet.
12. The figure below shows a circuit that includes an electrical relay, used to switch on a motor
M.
Explain in details, how closing switch S causes the motor M to start.
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ELECTRICITY
*Static electricity/electrostatics – charges at rest/ not moving.
Electrostatic charges can be induced and easily detected in insulators (non-metals) because these kinds of
materials do not allow charges to flow through them. Metals are generally good conductors so it is difficult to
induce electrostatic charges in them.
*Current electricity – moving/flowing charges (electrons)
Unit of electric charge
The SI unit of electric charge is a coulomb. A charge of one coulomb is the charge on 6 x 1018 electrons
1 C = 6 x 1018 electrons
And this means that the charge on one electron is 1.6 x 10-19 C.
The symbol for electric charge is Q and the symbol for the coulomb is C.
STATIC ELECTRICITY
All materials are made out of groups of atoms. The atoms contain electrically charged particles being protons
and electrons. Normally an object is electrically neutral since it has an equal number of positive and negative
charges. The two charges can be separated by rubbing objects together.
Electrostatic charging by friction: illustration
The force of friction between two objects can cause electrons to be transferred from one object to the other.
One object will gain extra electrons and become negatively charged. And the other one will become positively
charged since it would have lost some electrons and remained with excess positive charges.
A
B
A. polythene strip will be negatively charged and the cloth will be positively charged
B. cellolose acetate strip will be positively charged and the cloth will be negatively charged.
Explanation: when polythene is rubbed, electrons from the cloth are transferred to the polythene making the
polythene negatively charged and the cloth will be positive because there will be a deficit of electrons.
On the other hand when perspex (cellulose acetate) is rubbed with the cloth it loses some electrons to the
cloth and remains short of electrons and with more unbalanced protons and as a result the Perspex rod
becomes positively charged and the cloth negatively charged because it would have some extra electrons
(negative charges).
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POSITIVE AND NEGATIVE CHARGES
There are two types of charges, namely positive(+) and negative (-).
Positively charged object
negatively charged object
Experiment: positive and negative charges
-
Rub a piece of polythene strip with a cloth
Hang it up as shown in the diagram
Rub another polythene strip and bring it near the first one.
Observation: repulsion occurs
Now
bring
a
piece
of
rubbed
polythene
close
to
the
hanging
cellulose
acetate
strip.
Observation: attraction occurs
This shows that the two strips became charged in different ways. The charge on the cellulose acetate is
taken to be positive and the charge on the polythene is negative.
Conclusion: “like charges repel and unlike charges attract”
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INDUCED CHARGES
A charge can be built up on an uncharged object by holding a charged object close to it as shown below.
These charges that would appear on an uncharged object due to a charged object nearby are called
induced charges.
A metal sphere is being charged by induction and ends up with an opposite charge to that on the rod.
Note the two never actually touched.
GOLD-LEAF ELECTROSCOPE
An instrument used for detecting the presence of an electric charge. It consists of a metal rod on top of
which there is a metal cap (plate). The rod is insulated from the case. A thin gold leaf is attached to the
bottom of the rod.
1.
Detecting an electric charge
When a positively charged rod is brought near the top plate, the leaf rises. This so because the positively
charged rod attracts free electrons in the brass rod (stem) upwards so that the plate has an excess of negative
charges. The lower rod and the leaf are left with an excess of positive charges. The leaf diverges from the stem
because they are both positively charged. On removal of the charged rod, the leaf falls as the extra electrons in
the top plate move back down the stem.
The leaf also rises if a negatively charged rod is brought near the top plate. This time, the rise of the leaf occurs
because free electrons in the top plate are pushed downwards (repelled) by the negatively charged rod.
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2.
Charging an electroscope
a. Charging by contact
An electroscope can be charged by rubbing (pressing) a charged insulator firmly across the edge of
the top plate. The charge on the rod is shared with the electroscope.
NB
When using a negatively charged insulator (polythene) electrons will be deposited from insulator to
the electroscope. The electroscope will be left negatively charged.
When using a positively charged insulator (Perspex) electrons will move from electroscope to the
Perspex. The electroscope will be left positively charged.
b. Charging by induction
1(a) A positively charged rod is brought near the top plate. Electrons move upwards because they are
attracted to the rod, leaving a positive charge on the leaf and the stem.
(b) When the top plate is touched with a finger, the electrons on the plate remain because they are
held there by the attraction of the positively rod. The electrons flow in from Earth to replace the
missing electrons on the leaf and the stem. The charge on the leaf and stem is neutralised. The leaf
collapses.
(c) and (d) The finger is removed, followed by the rod. This leaves a net negative. The leaf rises to
show repulsion.
*an electroscope can be discharged by touching it with a finger or connecting it to the earth. This
earths the electroscope. Earthing is a process of sharing charges with the Earth.
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Charging metal spheres by induction
A
B
Charges separated by bringing a charged rod close to the sphere.
While the rod is still kept at its position, the sphere is earthed by touching with hand electrons flow out to earth.
Charges are evenly distributed around the sphere when the rod and the earth (hand) are removed.
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DISCHARGING
A charge can be built up on an object through friction. The charge can be discharged to the Earth by contact
with a conductor. The charge stored can also be released to the nearest object with a neutral charge or by
bringing discharging object with opposite charge.
e.g. when sliding out of a car, friction between the seat and clothes causes a charge on the person. When the
person touches the car body the charge passes from his body to the car, giving a slight shock.
*NB: an isolated charged insulator will slowly become discharged. The charge on the insulator is neutralized by
ions (charged particles) in the air.
The Van de Graaff generator
The Van de Graaff generator produces a large and continuous supply of electric charge. In this machine a
rubber belt rubs against a plastic roller and becomes charged. The charge is carried on the moving belt up to
the metal dome, where it is collected. A large quantity of charge therefore builds up on the dome.
*woollen threads attached to the dome will repel each other strongly after the generator has been running for
a while.
*when a metal sphere, connected to Earth with lead, is brought near the metal dome, electric sparks are
produced. This occurs as charges from the dome pass through the air to sphere and then to the earth. This
discharges the dome.
LIGHTNING
Friction between particles rubbing against each other in a large cloud can build up a large charge on the cloud.
When the charge becomes very large it may discharge through the air to the earth or to the neighbouring
clouds and this would be in a form of flash of lightning, therefore lightning is an electric discharge between the
Earth and a highly charged clouds.
Lightning conductors
A lightning conductor is a thick copper strip fixed to the outer wall of a building or a tall pole near the building.
The top of the rod ends are sharp spikes. At the bottom of the strip there is a copper plate buried in the
ground. Its purpose is to stop or reduce strength of lightning.
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Thunderclouds contain a large quantity of negative charge. When passing over a building it induces a build-up
of opposite charge (positive charge) on the roof. If the electric field (voltage) between the opposite charges is
strong enough, there may be a spark of lightning as the charges flow through the air towards each other.
With a lightning conductor, the sharp spikes at the top reduce the chance of a lightning strike. By effect of
action at points ( charge concentrate at the sharp points), the conductor let charges on the building leak away
before a spark can occur and some of the charges flow even up to the clouds and cancel out some of the
negative charge on the clouds, making it less likely that the lightning will strike. However, if a flash does occur
it is less violent and the conductor gives it (negative charge) an easy path to the ground.
ELECTRIC FIELD
A region around an electric charge where there is an electric force. The field lines have both the magnitude
and direction. They always move away from the positive charges and move towards negative charges.
PATTERNS OF FIELD LINES
a) A field around an isolated electric charge
b) Field lines around unlike charges
c)
Around like charges
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INSULATORS AND CONDUCTORS
Insulators or bad conductors- they can hold charge on their surfaces. The charge does not move through
insulators.
Examples:- plastics (e.g. PVC, polythene, Perspex, etc.), glass, rubber, dry air, sulphur and oil.
Conductors – metals are good conductors of electricity since they have free electrons in their outermost shells.
A conductor cannot be charged as the charge will flow easily through it.
Examples:- most metals (e.g. silver, copper, aluminium), carbon, graphite, acid solutions, salt solutions
Semi-conductors:- are in-between materials. They are poor conductors when cold but much better conductors
when warm, e.g. silicon, germanium
NB
Water, human body, earth and air are called poor conductors – they conduct very slowly.
DANGERS OF ELECTROSTATICS
1.
Usually electric charges build up on the surface of the car as it moves through air along the road that
is why a passenger may get an electric shock when getting into or out of the car. Therefore if charges
are allowed to build up on trucks carrying flammable goods (e.g. petrol) a very small spark can cause a
fire or explosion. It is then important that such trucks are earthed by attaching a conducting strip that
will be dragged behind the truck or run on conductive rubber tyres.
2.
Occurrence of lightning
APPLICATIONS OF ELECTROSTATICS
1.Paint spraying – the paint becomes charged due to friction as it is forced out of the nozzle of the spray
gun. If the object to be painted is given the opposite charge the paint will stick to it very well. This
technique is used by farmers when crop spraying and also used to coat cars with paint.
2.Dust and ash precipitator - ash in factory chimneys and power stations can be removed by electrostatic
precipitation. Wires inside the chimneys are negatively charged and give a similar charge to the ash
particles. The negatively charged ash particles are attracted to positively charged metal plates inside the
chimney walls. The ash particles are then removed by washing
3.In electrostatic photocopying machines – inside the photocopier, there is a light-sensitive plate that
would be given a negative charge. The image of the document to be copied is projected onto the drum.
The bright areas on the drum lose their charge because of reflected light from the corresponding white
parts on the document paper but the dark areas on the plate keep their charge. The powdered ink (toner)
is attracted to the charged (dark) areas. A blank sheet of paper is pressed against the plate and picks up
the toner. The paper is heated so that the powered ink melts and sticks to it. The result is a copy of the
original document.
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QUESTIONS
Q1.a) Name two types of electric charge.
b) A student wants to charge his plastic comb. Describe one way he could charge the comb.
c) the student then holds his charged comb near some small pieces of paper. What happens? Explain.
Q2. When a balloon is rubbed in your hair, the balloon becomes negatively charged.
(i)
Explain how the balloon becomes negatively charged.
a)
the negatively charged balloon is brought up to the surface of a ceiling. The balloon sticks to the
ceiling. Explain how and why this happens.
Q3. Say whether the following attract or repel
a) two negative charges
b) a negative charge and a positive charge
c) two positive charges
Q4. In an atom, what kind of charge is carried by i) protons
ii) electrons
c) neutrons
Q5. a) Why is it easy to charge polythene by rubbing, but not copper?
b) What makes copper a better electrical conductor than polythene?
c) name one non-metal that is a good conductor.
Q6. When one pulls a plastic comb through their hair, the comb becomes negatively charged.
a) Which ends up with more electrons than normal, the comb or the hair?
b) Why does the hair become positively charged?
Q7. a) Give an example of where electrostatic charge might be a hazard.
b) How can the build-up of electrostatic charge be prevented?
Q8. In the diagram below, a charged rod is held close to a metal can. The can is on an insulated stand.
a)
b)
c)
d)
Draw in any induced charges on the can.
Why is the can attracted to the rod even though the net charge on the can is zero?
If you touch the can with your finger, electrons flow through it. In which direction is the flow?
What type of charge is left on the can after it has been touched?
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Q9. Two charged balls are hung side by side. They settle as shown. What can you say about the charges on the
balls?
Q10. a). A girl rubs a Perspex ruler on her sleeve. He holds it near water flowing from a tap. The water moves
towards the ruler. Explain?
b). What difference would it make if the ruler were made of polythene?
Q11. Use words from the list below to complete the following sentences. You can use them more than once.
attract(s)
duster
repel
rod
electrons insulators
like
negatively
opposite positively protons
A polythene rod is rubbed with a duster. ____________ leave the ____________ and move to the
______________. The polythene becomes ______________ charged and the duster ____________ charged.
Conductors allow ______________ to travel through them but __________ do not.
A positively charged object attracts tiny pieces of paper to it. It __________ electrons in the paper. This leaves
the surface of the paper _____________ charged. They stick together because ________ charges
___________.
Q12. Fig. 12.1 shows two positively charged conducting spheres mounted on rods made of a good electrical
insulator.
Fig. 12.2 shows a section through oppositely charged parallel plates.
a)
Draw the electric field pattern on each diagram.
Q13. Three hollow copper spheres are placed near each other in air. The large sphere carries a positive charge
and the two small spheres touch each other, as shown in Fig. 13.1.
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Fig. 13.1
The two small spheres are pulled apart, using their insulated handles, and then taken well away from the large
sphere, as shown in Fig. 13.2.
Fig. 13.2
a)
The charge on the large sphere has been drawn in for you. On Fig. 13.1. On fig. 13.2 draw in the
charges, if any, on each of the smaller spheres.
b) Explain why energy is needed to separate the two small spheres.
Q14. An electrically charged sphere C is brought near a small uncharged conducting sphere S suspended as
shown in Fig. 14.1. S is attracted towards C until it touches the surface of C and then repelled to the
position shown in Fig.14.2
Fig 14.1
Fig 14.2
a) i. Explain carefully why S is first attracted towards C.
ii. Explain why S is repelled after touching the surface.
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16.2.0
CURRENT ELECTRICITY
16.2.1 ELECTRIC CURRENT: The amount of charge passing through a given point in a conductor per unit time
OR
The rate of flow of charge in a circuit.
Current = charge/time
I = Q/t
Q = It
------------------------->Coulomb’s law
SI unit : ampere/amp (A)
Other units: milliamps (mA), microampere (μA), kiloampere (kA)
Current is measured using an ammeter. Small quantities of current can be measured using a milli-ammeter.
When the ammeter is used, it should be connected in series with the component through which the current is
to be measured.
16.2.2
ELECTROMOTIVE FORCE (E.M.F)
A cell is a source of electric current. The cell drives the charge around the electric circuit. In doing this energy is
used up.
Electromotive force is the measure of the energy dissipated (used) by a source to drive a unit charge around a
complete circuit. Energy dissipated can also be described as work done.
e.m.f = work done per unit charge
e.m.f = W/Q
The SI unit of e.m.f is a volt (V). A battery with an e.m.f of 1 volt (1 V) gives 1 J of energy to a coulomb of
charge which it drives around a circuit.
1 V = joule/coulomb
1 V = J/C
USING A VOLTMETER TO MEASURE E.M.F
To measure the e.m.f of a cell or a battery of cells, connect a voltmeter in parallel with the cells without any
other components in the circuit. This kind of connection is known as open circuit. The red (+) terminal of the
voltmeter is connected to the +ve of the battery and the black (-) terminal of the voltmeter to the –ve terminal
of the battery.
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16.2.3
-
POTENTIAL DIFFERENCE (P.D)/VOLTAGE
The work done in moving a unit charge between two points of different electric potential in the
external circuit
OR
-
The amount of the electrical energy being transferred to other forms when a charge flows through a
component in the external circuit.
Potential difference is also known as voltage.
Potential difference (p.d) = work done/charge = energy transferred/charge
V = W/Q
or
V = E/Q
P.D is also measured in volts (V)
In an electric circuit, chemical energy in the battery is converted into electrical energy in the electrons. Some
of this energy is used up in passing through the lamp. Therefore there is p.d across the lamp.
The p.d is measured with a voltmeter. The voltmeter is connected in parallel across the components of the
circuit where we want to measure the potential difference.
Voltmeters must not be connected in series with other components in a circuit or else it will change the
current through the circuit because they have very high resistance. On the other hand the ammeters, which
are connected within the circuit, must have very low resistance
16.2.4
RESISTANCE
-
Is the measure of the ability of a conductor to oppose the flow of current/ electrons.
-
Current can pass easily through components with a low resistance but it cannot flow easily through
components with a high resistance (very good conductors have almost no resistance and insulators
have extremely high resistance)
-
All electrical components have a certain amount of resistance.
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-
Resistance (R) is measured in ohms (Ω), kilohms (kΩ), megaohms (MΩ)
FIXED RESISTORS
-
Are special components (materials) designed to have a certain resistances. They are used to control
the amount of current in a circuit.
RESISTOR COLOUR CODE
Resistors are colour coded to show their resistance. This consists of three or four coloured bands around the
resistor. The first three bands indicate the value of the resistance in ohms. Bands 1 and 2 are the digits of the
value, and band 3 represents the number of zeroes following the first two digits. The fourth band on the
resistor shows the tolerance of the stated value.
*NOTE:

To decide which is the first, remember that the fourth band, if present, will either be gold or silver (or
on rare occasions pink)

The following may help you to recall the colour codes and their values;
(Bad Boys Rape Our Young Girls But Violet Gives Willingly) OR
0 1
2
3 4
5
6 7
8
9
(Black Birds Roaming On Your Garden Bring Very Great Woes)
VARIABLE RESISTORS
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The resistance of a variable resistor is not fixed. It can be changed or set to different values. They are used in
circuits when the current through the circuit needs to be varied.
A rheostat is a variable resistor consists of a coiled length of resistance wire with either end attached to a
terminal. A third terminal is attached to a sliding contact which can be moved along the length of the coil. By
moving the sliding contact along the coil, the amount of wire through which the current passes can be changed
and hence the resistance changes.
MEASUREMENT OF RESISTANCE
The resistance of a conductor can be found using a voltmeter and an ammeter. A conductor of unknown
resistance is connected in series with an ammeter and a rheostat which is used as a variable resistor. The
voltmeter is connected across the ends of the conductor.
The rheostat is altered to give a series of different values of I and corresponding values of voltage.
VOLTMETER READING V(V)
AMMETER READING I (A)
V/I (V/A)
1.6
1.7
1.9
2.2
2.6
0.12
0.14
0.16
0.18
0.20
13.3
12.1
11.9
12.2
13.0
GRAPH OF VOLTAGE V (V) AGAINST CURRENT I (A)
The graph is straight line passing through the origin (0,0). This indicates that the voltage and current are
directly proportional to each other. The gradient of graph is constant and it represent the resistance of the
conductor.
The ratio V/I = a constant. The value of the constant is equal to the resistance of the conductor.
Gradient = R = ∆V/∆I
R = V2 – V1/ I2 – I1
R = V/I ---------------------> OHM’S LAW
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OHM’S LAW
Ohm’s law defines the relationship between the voltage across a component, the current flowing through the
component and the resistance of the component.
The ohm’s law states that;
“the amount of electric current passing through a conductor is directly proportional to potential difference
provided the temperature and other physical quantities remain the same”
V α I ; R = a constant
V = IR -------------------------------------------> ohm’s law
It can also be expressed as:
I = V/R
OR
R = V/I
RESISTANCE, LENGTH AND CROSS-SECTIONAL AREA
The resistance of a conductor is directly proportional to its length and inversely proportional to its crosssectional area. This means when the length is doubled, the conductor will double its resistance but when its
cross-section is doubled its resistance will be halved.
Therefore;


Short and thick conductors have low resistance
Long and thin conductors have high resistance
Mathematically;
Rαl
and
R α 1/A
→ R α l/A
→ R = ρl/A
where R = resistance in Ω
ρ= resistivity in Ωm
l = length in metres (m)
A = cross-section area in m2
Examples
#1. Find the resistance of an aluminium conductor 200 m long with a cross-section area of 4 mm2 (ρ for Al is
2.83 x 10-8 Ωm)
Answ;
Data
l = 200 m
A = 4 mm2 = 4 x 10-6 m2
ρ = 2.83 x 10-8 Ωm
R=?
R = ρl/A
= (2.83 x 10-8 X 200 m)/4 x 10-6
= 1.42 Ω
#2. A wire of length 0.40 m and a diameter 0.60 mm has a resistance of 1.5 Ω. Find the resistivity of the
material it is made of.
DATA
l = 0.40 m
R = pl/A
ρ = RA/l
= 1.5(2.8 x 10-7)/0.40
= 1.06 x 10-6 Ωm
© SPANAPODI 2010
d = 0.60 mm = 0.0006 m
R = 1.5 Ω
ρ=?
A = πr2 = π(d2/4) = π(0.0006 m)2/4 = 2.8 x 10-7 m2
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INTERNAL RESISTANCE
The energy supplied per unit charge is not all used in the external circuit. There is some energy which is
needed to overcome the internal resistance and drive the charge across the battery or cell.
In above diagram, the voltage drop across the resistor will be less than the e.m.f. This is because some energy
has been used to drive the charge through /across the cell.
The internal resistance of the cell is given by:
r = (E – V)/I
Where E= e.m.f
r = internal resistance of the cell
I = current
→ E – V = Ir
E – IR = Ir
E = IR + Ir
E = I(R + r); where R = external resistance
PROBLEMS
#1. A cell of unknown e.m.f (E) and internal resistance of 2 Ω is connected to a 5 Ω resistor. If the terminal p.d
(V) is 1.0 V, Calculate the e.m.f of the cell?
Data
R=5Ω
r=2Ω
V = 1.0 V
I=?
E=?
I = V/R
= 1.0 V/5 Ω
= 0.2 A
THEN E = I(R + r)
= 0.2 A(5 Ω + 2 Ω)
= 1.4 Ω
#2. A battery of e.m.f 4.0 V and internal resistance of 5 Ω is connected to a resistor of 1.5 Ω. Calculate the
terminal p.d.
Answ
Data
E = 4.0 V
r=5Ω
R = 1.5 Ω
V=?
I = E/(R + r) = 4.0/(1.5 + 5) = 0.6 A
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V = E – Ir
= 4.0 – 0.6(5)
= 1.0
16.2.5
I/V GRAPHS – Graphs showing the relationship of current and voltage drop across a
conductor.
1) Ohmic conductors
The current through the conductor is directly proportional to the voltage across the ends of the conductor
provided the temperature and other physical properties are constant – OHM’S LAW
The graph is a straight line.
The inverse of the graph here is equal to the resistance of the conductor.
2) Non – ohmic conductors
They are conductors which do not obey the ohm’s law
a)
Diode
Voltage is not proportional to current
Curve getting steeper- therefore the resistance decrease with increase in current.
Note: if the voltage is increased in the other direction, the current will be almost zero since a
diode allows the current to flow only in one direction. This means a diode has a small resistance
when connected in one way but a very large resistance when the voltage is reversed.
b) Filament lamp
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Filament lamps or light bulbs are designed to produce light and therefore heat. Any current
passing through the filament will make it hot and increase its resistance. A light bulb is therefore
non-ohmic for the whole range of possible currents
The graph bends over as V and I increase. Then this means the gradient (I/V) decrease and hence
the resistance (V/I) increases and makes the filament hotter.
c)
Thermistor
A thermistor is an electrical component which is used in temperature-operated circuits such as
the circuits used to control air conditioning units. It is a non-ohmic resistor, its resistance
decreases as the current increases.
The graph bends up, this means the inverse of the resistance (I/V) increase and therefore the resistance (V/I)
decreases.
LIMITATIONS OF THE OHM’S LAW
Under normal working conditions a resistor is ohmic, its resistance does not depend on the current or voltage
applied to it. If too much current flows through the resistor, it will become hot and its resistance will start to
increase. This resistor has become non-ohmic
Therefore, in general, when the temperature increase the resistance of metals will also increase. The
resistance of some conductors will also change when they are bent or placed under pressure.
16.2.6
QUESTIONS
a). What is the resistance of its element?
b) Why does the element need to have resistance?
Q4. A 6 V supply is applied to 1000 Ω resistor. What current will flow?
Q5. Use ohm’s law to calculate the following:
a)
The voltage required to produce a current of 2 A in a 12 Ω resistor.
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b)
c)
d)
e)
f)
The voltage required to produce a current of 0.1 A in a 200 Ω resistor.
The current produced when a voltage of 12 V is applied to a 100 Ω.
The current produced when a voltage of 230 V is applied to a 10 Ω resistor.
The resistance of a wire which under a potential difference of 6 V allows a current of 0.1 A to flow.
The resistance of a heater which under a potential difference of 230 V allows a current of 10 A to
flow.
Q6. Explain clearly the difference between electromotive force of a cell and potential difference across a lamp.
Q7.a) If the current through a floodlamp is 5 A, what charge passes in i) 1 s ii) 10 s iii) 5 minutes?
b) What is the current in a circuit if the charge passing in each point is i) 10 C in 2 s, ii) 20 C in 40 s iii) 200 C
in 2 minutes?
Q8. The p.d across the lamp is 12 V. How many joules of electrical energy are changed into light and heat
when:
i). A charge of 1 C passes through it
ii). A charge of 5 C passes through it
iii). A current of 2 A flows through it for 10 s?
16.2.7
ELECTRIC CIRCUIT
Some circuit symbols used for different components:
Series circuit
Components are in series when they are connected into a continuous line, end to end such that the same
current flows through each component
i)
The current that flows through components in series is the same and equal at each and every
point.
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ii)
All the components will share the e.m.f. according to their resistances. The largest voltage drop
will be across a component with the largest resistance. The sum of the potential difference in
series circuit is equal to the terminal potential difference across the source.
VE = V1 + V2 + V3........ ------------> (1)
V1 = IR1
V2 = IR2
VE = IRTOTAL
iii) Resistance in series
From ohm’s law: V =IR
Then equation (1) above can be modified:
VE = V1 + V2 + V3
IRT = IR1 + IR2 + IR3
IRT = I(R1 + R2 + R3)
Divide by I
IRT/I = I(R1 + R2 + R3)/I
RT = R1 + R2 + R3 ---------------> Total/combined/effective resistance for resistors in series
PARALLEL CIRCUIT
Components are in parallel when they are displayed side by side and their corresponding ends joined.
i)
The branches will share the main current I according to the resistance of each branch. The largest
current will flow through a branch with the smallest resistance. The sum of the current through
the branches is equal to the main current.
I = I1 + I2 + ........ ----------> (2)
ii)
The potential difference across the components connected in parallel is equal and also the same
as the terminal difference across the source.
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iii) Resistance in parallel resistors
Equation can be modified:
I = I1 + I2 + I3
From ohm’s law
VE/RT = V1/R1 + V2/R2 + V3/R3;
V/RT = V/R1 + V/R2 + V/R3
Remember:
VE = V1 = V2 = V3
Factorise and then divide by V
V/RT = V(1/R1 +1/R2 + 1/R3)
1/RT = 1/R1 + 1/R2 + 1/R3
-------> effective/total/combined resistance for parallel resistors
*For two parallel resistors:
1/RT = 1/R1 + 1/R2
1/RT = R1 + R2/R1R2
RT = R1R2/R1 + R2
RT = Product of resistance/sum of resistance
16.2.8
ELECTRICAL ENERGY
When electrons flow through any component, some of their stored electrical energy is released in (converted
to) different forms:
e.g



light bulb: electrical energy ------------> light and heat
kettle: electrical energy --------> heat
resistor: electrical energy -------> heat
How to calculate the amount electrical energy converted to other forms (or consumed) by an electrical
appliance:
Recall: The amount of electrical energy being transferred to other form(s) when a unit charge flows through a
component (appliance) in a circuit is called the potential difference (voltage).
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From the definition it follows;
Voltage (p.d) = Energy transferred/Charge
Energy = Voltage x Charge
E=VxQ
Remember that Q = It ----------> ohm’s law
Then
E = VIt
SI unit of electrical energy: joule (J)
Other equations;
i.
ii.
iii.
16.2.9
E = I2Rt
E = (V2/R)t
E = Pt
ELECTRICAL POWER
The amount of electrical energy a component converts into other forms every second is called its (electrical)
power
Or
Electrical power is defined as the rate at which electrical energy is converted into other forms.
Power = Energy converted/time taken
P = E/t
P = VIt/t
P =VI
SI unit of electrical power: watt (W)
1 W = 1 J/s
Other equations that can be used to calculate electrical power:
Recall the ohm’s law; V = IR
i)
THEN
I = V/R
P = V(V/R)
P = V2/R
We can have
ii) V = IR
P = (IR)R
P = I2R
Examples
#1: A 240 V, 5 A kettle takes 5 minutes to boil 1 L of water.
a) What energy change occurs in the kettle?
b) What is the electrical power of the kettle?
c) How much electrical energy is converted into heat by the kettle in 5 minutes?
ANS:
a)
Electrical energy --------> heat energy
b) Data; V = 240 V,
I =5 A,
P=?
P =VI
= 240 V x 5 A
= 1200 W
c)
Data; V = 240 V,
© SPANAPODI 2010
I = 5 A,
t = 5 minutes =330 s,
P = 1200 W,
E =?
Page 183
E = VIt
= 240 V x 5 A x 330 s
= 396 000 J
E = Pt
= 1200 W x 330 s
= 396 000 J
OR
#2: A 220 V, 10 A electric motor takes 20 seconds to lift aload of bricks to the top of a building 15 m above the
ground. Each brick has a mass 0f 1.5 kg.
a) What energy changes occur as the bricks are lifted?
b) How much electrical energy is supplied to the motor in 20 seconds?
c) Assuming the motor is 100 % efficient, how many bricks can be lifted in a single load?
Ans:
a)
Electrical energy ----------> gravitational potential energy
b)
Data; E =?,
I = 10 A,
V = 220 V,
t = 20 s
E = VIt
= 220 V x 10 A x 20 s
= 44 000 J
c)
Total electrical energy converted = total GPE
44 000 J = mgh
44 000 J = 15 m x 10 N/kg x total mass m of bricks
m = 44 000 J/15 m x 10 N/kg
m = 293 kg
number of bricks = m/mass of a single brick = 293 kg/1.5 kg
= 195 bricks
16.2.9
DOMESTIC ELECTRICITY
Electricity available in household circuits originates from a generator in a power station. Electricity is supplied
to our homes through two cables (wires); Live and neutral. The current flowing through these cables is
alternating current (a.c) with a frequency of 50 Hz. This means that the current in which the current flows
reverses 50 times every second. The electricity cables are connected to the terminals in wall sockets.
1.
Live wire (brown or red) – carries the alternating current to the appliance. It supply supplies
electricity at a voltage 240 V. Since the supply is a.c. at 50 Hz, the voltage varies between positive and
negative (+240 V and -240 V) 50 times a second. This causes the current to flow to and fro through
the circuit.
2.
Neutral wire (blue or black)- completes the circuit by providing the return path to the supply (or
mains). The neutral wire is earthed at the electricity substation, therefore it is at 0 V
*Although the neutral wire carries electric charge there is no danger of electric shock if it is touched
since it is at the same potential as a person who stands on the floor.
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3. Earth wire (green and yellow) or (green)- this wire is for safety purposes. One end of the Earth wire is
connected to the metal case of the appliance. The other end is connected via the wall sockets and metal
pipe to Earth box outside the house.
The earth wire provides a path of almost zero resistance from the case of the appliance to the earth. If the
live wire accidentally touches the metal case of the appliance, a large current will flow through the earth
wire and the fuse melts, isolating the appliance.
Without an earth wire, the case would become live anyone touching it would receive a dangerous shock.
FUSES (& CIRCUIT BREAKERS)
Function: to prevent excessive current to flow through an appliance. Too high current may cause some electric
fire or accident.
Fuse is a wire made from a metal with a low melting point. If a fuse is part of a circuit, it will eventually melt if
the current is too excessive and the circuit will break. But excessive current may flow through an appliance
even if a fuse there if a short circuit is present.
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*Fuses must be connected into the live wire. This ensures that when the fuse melts, the appliance is no longer
“live”.
Fusing Rating
Fuses are rated according to the amount of current required to melt/blow it. E.g. 1 A fuse will melt if a current
of 1 A flows through it, a 5 A fuse will melt if a current of 5 A flows through it, etc. Fuse rating are always whole
number integers. The plugs are usually fitted with either 3 A, 5 A or 13 A.
It is vital that the correct fuse is installed into an appliance. The fuse rating should be greater than the normal
operating current of appliance, but as close to it as possible- so that the fuse will be blown as soon as the
current gets too high.
Example
An electrical kettle is labelled 230 V 2300 W. Work out whether a 3 A, 5 A or 13 A fuse is needed.
Ans: First, calculate the normal operating current
P = 2300 W
V = 230 V
I=?
P = VI
I =2300 W/230 V
= 10 A
If the normal operating current is 10 A, a 13 A fuse should be fitted.
#2 DVD PLAYER: 100 W, 240 V
I = 100 W/240 V
= 0.4 A
So a 3 A fuse is ideal.
*Note: 1) The DVD player would still work with a fuse of 13 A. But if a fault develops, the current will continue
to flow without the fuse blowing and this might cause the appliance to overheat and catch fire.
2) For currents higher than 13 A, circuit breakers are used instead of fuses. Circuit breakers operate
electromagnetically and can be reset by flicking a switch (they do not have to be replaced like fuses)
THREE-PIN PLUG
Three-pin plug
power point/socket
The three wires in an electrical cable of appliances are connected to a three-pin electrical plug. In such plugs
the live wire from the cable is connected to the live pin, the neutral wire is connected to the neutral pin and
the earth wire is connected to the earth pin. When the plug is inserted into a power, each pin on the plug
connects with the corresponding wire in the power point.
*It is important to ensure that wires are correctly connected in both plugs and the sockets. The power point
switch is placed in the live side of the circuit
*The sheath of the cable (not the wires themselves) is clamped to keep the connections safe (intact) if ever the
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cable is pulled or tugged.
*The fuse is chosen to suit the circuit which it protects.
DOUBLE INSULATION
Some household appliances, e.g. radios, have plastic cases and their cables do not have an earth wire. They
have only the live and neutral wires. There is no risk getting an electrical shock from a plastic case since plastic
is an electrical insulator. This is described as double insulation because:


The live and neutral wires are covered in an insulated sheath,
The appliance itself is covered by an insulated case.
FEATURES OF A HOUSE CIRCUIT
a)
PARALLEL CIRCUITS:- House circuits e.g. lights are connected in parallel so that appliances receive the
full mains supply of 240 V and also that they can operate independently (e.g each bulb can have its
own switch and also if one bulb breaks, the others will remain on unlike in a series circuit where all
would turn off).
b) SWITCHES AND FUSES:- are always connected in the live wire. If they were connected in the neutral
wire, the appliance would remain ‘live’ even when the switch is off or the fuse is blown
c)
STAIRCASE CIRCUIT:- The light is controlled from two places by the two-way switches.
d) RING MAIN CIRCUIT:- the wiring system in which the live and neutral wires run in two complete
rings/loops round the house and the power sockets each rated at 13 A, are tapped off from them
USES OF ELECRICITY
1.
Lighting


Filament lamp – has a small coil of tungsten wire which becomes hot when current flows
through it.
Fluorescent lamp – current is passed through mercury vapour which emits ultraviolet light
which in turn makes the powder on the glass give out visible light.
2.
Heating:- heating elements are made from nichrome wire which has a high resistance. Heating
elements are used in electric fires, kettles, irons, cookers, ovens, etc.
3.
Machines:- electric machines such as drills, saws, lawn-mowers, cassette recorders, fans, washing
machines, etc all use electric motor which is operated by electricity.
4.
Communications:- there are various electric powered communication devices, e.g. telephone, cellphone, fax, radio, television, telex, computer, etc.
5.
Security: many security systems such as smoke sensors, automatic gates, remote controlled locks,
burglar alarm, etc operate on electricity.
COST OF ELECTRICITY
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Electrical metres (joule-meter) are included in our houses to measure the amount of electrical energy
consumed by the household. The household is charged for the electrical energy they consumed. Electricity
supply companies (e.g. B.P.C) measure electrical energy consumed in kilowatt-hours (kWh) or simply ‘units’.
1 kWh = 1 unit
1 kWh is the measure of the amount of the electrical energy consumed for 1 hour (3600 s) at the rate of 1 kW
(1000 W) or the energy used by an appliance rated 1 kW in 1 hour.
i.e. 1 kWh = 1000 W x 3600 s
= 1000 J/s x 3600 s
= 3 600 000 J
1 kWh = 3.6 MJ
Then;
cost of electricity = total electrical energy consumed in kWh x cost per kWh
Example:
a)
How much energy is used by a 3 500 W heater which is on for 30 minutes
b) How much will it cost to run the heater if one unit of electricity costs 5 thebe
Ans:
a)
P = 3500 W (3.5 kW),
t = 30 minutes (1/2 h),
E=?
E = Pt
= 3.5 kW x ½ h
= 1.75 kW or 1.75 units
b) E = 1.75 kW,
cost per kW = 5 thebe
Total cost = E x cost per kW
= 1.75 kW x 5 thebe/kW
= 8.75 thebe
= P0.09
ELECTRICAL HAZARDS AND DANGERS
1.
DAMP CONDITIONS: Water can conduct current. And also our bodies’ resistance is lower if it is wet
and hence a great amount of current will flow through it. Therefore if electrical equipment gets wet
or touched with wet hands, there is a risk someone being electrocuted (getting an electric shock).
2.
OLD, FRAYED WIRING AND DAMAGED INSULATION:- broken strands mean a wire will have a higher
resistance at one point. When current flows through it, there might be more heat produced, enough
to melt the insulation and cause a fire.
Damaged insulation can cause ;i) an electrical shock to a person touching the exposed ‘live’ wire, and
ii) a short circuit if the bare wires touch.
SHORT CIRCUIT: results if the ‘Live’ wire touches the neutral wire. The current by-passes the
appliance and the current can increase to such a high value that it can cause an electric fire especially
if there is no fuse.
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To prevent this, always inspect your cords more frequently and replace worn or damaged cables.
3.
OVERHEATING OF CABLES: caused by passing a high current on a wire designed for a low current.
Overheating can cause the insulation to melt or burn and can cause fires.
4.
OVERLOADING OF SOCKETS: connecting many appliances in one socket can lead to overheating of
cables and hence cause electric fires.
FINDING A FAULT
When an appliance stops working it may be due to a fault that is easy to rectify. Before calling a technician it is
wise to try to diagnose the fault.
You may follow the steps below;
1.
2.
3.
4.
5.
6.
Check that the appliance is switched on.
Check that the power is on. Do other appliances work?
Check the fuse. If it is blown, replace it. If the new fuse blows, check for a short circuit.
Check that the plug is correctly connected, with no loose wires or untidy strands of wire sticking out.
Check that the cable connection to the appliance is firm.
Check that the insulation is in good condition. If it looks worn or torn replace it with a similar cable.
*NB:- If after checking all the above, the appliance is still not working, engage a trained technician.
16.2.11
QUESTIONS
Q1. What is meant by the statement ‘the e.m.f. of a battery is 12 V’? When the battery is in use, the
p.d. between the terminals is found to be 11.5 V. What reasons might there be for that?
Q2. An electric heater has a label attached to it, as shown below.
Explain the meaning of the following terms used on the label; (i) 240 V (ii) 50 Hz (iii) power: 2 kW.
Q3. You have a selection of fuses available: 1 A, 2 A, 3 A, 5 A, 7 A, 10 A, 13 A. Which would be the most suitable
fuse for (i) a TV set labelled 230 V, 140 W, (ii) an electric fire labelled 230 V, 2 kW, (iii) a kettle labelled V,
750 W?
Q4. An electric motor is raising a load of weight 5000 N at a steady speed of 0.5 m/s. The motor works from a
250 V supply. How much work is done in 1 second?
Q5. A 720 W kettle boils some water in 10 minutes. How much will this cost if 1 unit of electricity is charged at
10 thebe? How long will a 60 W lamp run for the same cost?
Q6. a)Why should wires with damaged insulation be replaced?
b) Often, the plug used to connect an appliance to a wall socket has a fuse fitted inside it. Explain the
reason for this.
c) An appliance which has metal parts, for example an electric kettle, should be earthed. Explain why this
should be done.
d) In some countries it is illegal to have power sockets in a bathroom, to stop you using hairdryers. Why
would it be foolish to use a hairdryer near to a washbasin?
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Q7. The diagram below shows the inside of a three-pin plug.
a). What is the name of pin A?
b) What is the name of pin B?
c) What is the colour of the wire connected to the Earth pin?
d)What is D?
Q8. If electrical energy costs 7 thebe per kWh, calculate the cost of the following:
a) a 3 kW fire turned on for 6 hours
b) a 1.2 kW hair drier for 30 mins
c) a 100 W bulb for 10 hours.
Q9. A student using the circuit shown below investigates the relationship between the current flowing through
a resistor and the p.d. across it.
a)
b)
c)
d)
What is A?
What is B?
What is C?
What is D?
The student’s results are shown in the table below.
e)
f)
g)
p.d./V
0
2
4
6
8
10
12
current/A
0
0.25
0.50
0.80
1.00
1.25
1.50
Plot a graph of p.d. against current.
Which result appears to have been measured incorrectly?
What is the resistance of the resistor R?
Q10. A number of 8 Ω resistors are available. Draw diagrams to show how you could connect a suitable
number of these resistors to give an effective resistance of (a) 24 Ω (b) 4 Ω (c) 18 Ω
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Q11. An electric lamp is marked 250 V, 100 W and an immersion heater is marked 250 V, 2 kW.
a) Calculate the current in each device when operating normally.
b) Explain why the filament of the lamp is made to have a larger resistance than the heating element of
the immersion heater.
c) Suggest a reason why the filament is made of a metal with a much higher melting point than that of
the element.
d) The heat capacity of the filament of the lamp is very small. State one reason why this is an advantage.
e) Explain why the wire connecting the immersion heater to the supply remains cool even when the
heater has been in use for some time.
16.3.0
ELECTROMAGNETIC EFFECTS
Electricity can be produced in two ways:
1) Chemical reactions: produce flow of electricity from batteries and cells. The current of the electricity
produced in this way is quite small.
2) Electromagnetic induction: this is a process of producing electricity in generators and dynamos using
magnetic fields.
16.3.1
ELECTROMAGNETIC INDUCTION.
Current is created in a wire when:
 The wire is moved through a magnetic field (cutting the field lines)
 The magnetic field is moved past the wire
 The magnetic field around the wire changes strength.
The current created in this way is said to be induced current.
1). Moving wire and a U-shaped magnet
When a wire is moved across a magnetic field, an E.M.F is induced between the ends of the wire. One end of
the wire becomes positively charged and the other end becomes negatively charged. If the wire forms part of a
complete circuit, the EMF makes (induced) current flow.
In the above diagram, first the wire is held at rest between the poles of the magnet and the galvanometer
observed. The wire is then moved in each of the six directions shown
Observations:
a.
b.
c.
There is deflection on the galvanometer only when the wire is moving upwards (direction 1) or
downwards (direction 2) indicating flow of current in the circuit.
No deflection on the galvanometer when the wire is moving in other directions (3, 4, 5 & 6), showing
that there is no current induced in those cases.
Explanation of observations
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

An EMF is induced in a conductor (e.g. wire) only when it crosses (cuts) magnetic field lines and this
cause a current to flow if the conductor is part of a complete circuit.
There is no induced EMF or current when the wire is not moving or is moving parallel to the lines.
Direction of induced current
The direction in which the current flows through the wire depends on the following factors
a.
b.
The direction of motion of the wire
The magnetic field direction.
Therefore reversing the direction of motion or polarity will reverse the current direction.
The direction can be predicted using fleming’s right hand rule
*Hold the thumb and the first two fingers of the right hand at the right angles to each other. Then according
to the fleming’s right hand rule the First finger points in the direction of the magnetic Field, the thuMb points
in the direction of the Motion and then the seCond finger shows the direction of the Current.
The induced EMF (and current) can be increased by:



Moving the wire faster
Using a stronger magnet
Increasing the length of wire in the magnetic field, e.g by looping or coiling the wire through the
several times.
The above facts are summed up by Faraday’s Law. The law states that:
‘The size of induced EMF (or current) is directly proportional to the rate at which the conductor cuts the
magnetic field lines’
2). Bar magnet and coil
An EMF can also be induced in the conductor when a bar magnet is pushed in and out of a coil. If the coil is
part of a complete circuit the induced EMF (VOLTAGE) drives a current round the circuit.
When the N pole is moved into the coil, the galvanometer register current, its needle is seen to be deflected to
the right.
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When the magnet is held still inside the coil, the needle returns to its zero position. This shows that no current
is flowing because there is no movement therefore no magnetic field lines are being cut.
When the bar is pulled out of the coil, the needle is deflected to the left. This shows that moving the magnet in
the opposite direction reverses the current direction.
*NB:- 1) the similar results as the above can be obtained by moving a coil of wire over a stationary magnet.
2) But if the S pole of a magnet, rather than the N pole, is used the direction of the current also reverses
and opposite results will be obtained for diagrams (a) and (b) above.
The size of the induced EMF (and hence of current) can be increased by:-
moving the coil or magnet faster
using a stronger magnet
increasing the number of turns on the coil (this increase the length of wire cutting through the
magnetic field).
LENZ’S LAW
The direction of the induced current through the coil can be found by using the Lenz’s law.
Lenz’s law states that:
‘The direction of the induced current is in such direction as to oppose the change producing it’.
According to the Lenz’s law, in (a) the induced current should flow in a direction which makes the coil behaves
like a magnet with its top as a N pole. Then the incoming magnet is repelled and the downward motion is
opposed.
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But when the magnet is removed, the top of the coil should be a S pole so that the removal of the magnet will
be opposed as the N pole is attracted and the current will thus flow in the opposite direction to that when the
magnet is pushed in.
16.3.2
A simple a.c. generator (alternator)
a). In a simple a.c. generator (alternator) the coil is rotated by the shaft.
b). the slip rings rotate with the coil. When the coil is rotated, it cuts magnetic field lines so a voltage is
generated. This makes a current flow. As the coil rotates, each side travels upwards, downwards,
upwards.... and so on through the field. So the current flows backwards, forwards..... etc. Therefore it is a.c.
c). the current passes to the outside circuit via carbon brushes which press against the side of each slip ring.
A typical graph that shows how voltage (or current) varies over one complete rotation
Note: . a). The current is greatest when the coil is horizontal because it will be cutting field lines most rapidly.
But current is zero when the coil is vertical since it will be along the field lines and no cutting
happens. Also the current will change the direction when in a vertical position.
b). increasing the speed of rotation increases the frequency of an a.c. generated. Frequency of an a.c. is
the number of complete cycles it makes in each second. For the mains supply a.c.’s frequency is 50
Hz.
The voltage (or current) from the generator can be increased by:
a). using a stronger magnet
b). increasing the number of turns in the coil.
c). winding the coil on a soft-iron armature and using a bigger coil
d). rotating the coil at a higher speed.
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16.3.3
A simple d.c. generator (dynamo)
An a.c. generator becomes a direct current one if the slip rings are replaced by a commutator (which contains
two half-rings known as split rings). The carbon brushes are arranged such that as the coil goes through the
vertical, changeover of contact occurs from one half of the split ring of the commutator to the other and the
commutator reverses the voltage induced and so one brush is always positive and the other negative. And this
ensures that current to the outside circuit always flows in the same direction.
Just like in an a.c. generator, when the coil rotates, a current is produced by electromagnetic induction and the
current passes to the external circuit through the brushes in contact with the commutator. Although the
induced is d.c. it varies in value unlike the d.c from the battery.
The current is maximum when the coil is horizontal and minimum (or zero) when the coil is vertical.
Bicycle dynamo
It uses the principles of electromagnetic induction to generate electricity in bicycles. The driving wheel of the
dynamo presses against the tyre of the bicycle. When the tyre rotates, it turns the driving wheel of the
dynamo and causes a cylindrical permanent magnet to turn as well. The turning permanent magnet reverses
the magnetism through the soft-iron core every time the coil is rotated by 180°. This change in the magnetic
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field through the core induces an a.c. in the coil wire (stator coil). The size of the current produced can be
increased by increasing the speed of the bicycle.
16.3.4
MUTUAL INDUCTION
This involves the induction of current in one circuit, whenever it cuts a magnetic field produced by another
circuit i.e current induced in a circuit due to the changing magnetic field of another circuit.
Observation:- when switch S is closed, the galvanometer needle deflects and returns to zero. When opening
the switch the needle deflects to the opposite direction and back to zero.
Explanation:- when closing the switch, the current in the primary coil (coil A)sets up a magnetic field which is
linked up to the secondary coil, inducing the current in it. The needle returns to zero as the current reaches a
constant value and the magnetic field is not changing. When opening the switch current is turned off. The
magnetic field changes as the magnetic field lines cutting coil B die, this induces current in B. A soft iron core
can be placed between the coils. It will trap the magnetic field lines so that all of them cut the coil B.
16.3.5
TRANSFORMERS
A transformer is a device which makes use of mutual induction to change voltages (and is frequently used in
home to step down the mains voltage of 230 V to 6 V or 12 V). It consists of two coils of insulated wire
wounded on an iron core. The coil connected to the a.c. input is called the primary coil and the coil that
provides the a.c. output is called secondary coil.
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If the alternating voltage is applied to the primary coil, the a.c. produces a changing field in the core. This
changing magnetic field induces an alternating current in the secondary coil.
*Note:- 1). The purpose of the iron core is to ensure that all the magnetic field lines generated in the primary
coil is made to pass through all the turns of the secondary coil.
2). A transformer can only operate on a varying voltage. A D.C. voltage in the primary coil will not
produce any change in the magnetic field so with D.C. no current is induced in the secondary coil.
Two types of transformers
1). Step-down transformer
2). Step-up transformer
1). Step-down transformer- has fewer turns on the secondary coil than on the primary coil. Therefore it
produces a smaller voltage in the secondary coil(less output voltage).
2). Step-up transformers- have more turns on the secondary coil than on the primary coil, so their
output/secondary voltage is greater than the input voltage.
The relationship between the number of turns and voltage in the secondary and primary coils can be given by
the equation:Primary coil voltage/secondary coil voltage = number of primary turns/number of secondary turns
VP/VS = NP/NS
TRANSFORMER EQUATION
If no energy is wasted in a transformer, the power (energy per second) delivered by the output coil will be the
same as the power supplied to the input.
Then, since P =VI, we can have the transformer equation as;
Input voltage x input current = output voltage x output current
V1I1 = V2I2
Note: V α 1/I
This follows that a transformer which increases the voltage will reduce the current in the same propotion, and
vice versa.
ENERGY LOSSES IN A TRANSFORMER
All transformers waste some energy because of the following factors
1). Resistance of the copper coils.
Copper coils are not perfect electrical conductors. Whenever some current flow through them, some
electrical power/energy is used to overcome their resistance and this energy will then be given out as
useless heat to the surrounding. Therefore, their resistance need to be kept low, so thick copper wire
should be used where possible.
2). Eddy currents
The core is itself a conductor, so the changing field induces current called eddy current in it. The eddy
currents also cause heating effects. To reduce this, core is laminated i.e. it is made of thin sheets of iron (or
mumetal) instead of a solid block, which are insulated from each other to have a high resistance.
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3). Leakage of field lines
All the lines produced by the primary coil may not cut the secondary coil, especially if the core has an air
gap or badly designed.
*Large transformers have to be oil-cooled to prevent overheating.
TRANSMISSION OF ELECTRICAL POWER
1). Power for the a.c. mains is generated in power stations and then transmitted through long –distance
cables. A network of overhead cables, supported on pylons, which connect power station/s to consumers is
called a National Grid. Power from the grid is distributed by a series of substations. These contain stepdown transformers which reduce voltage in stages to level needed by consumers.
2). A.C or D.C?
Electric power is generally transmitted as a.c. This is so because a.c. can be easily and cheaply stepped up
or down using a transformer. A transformer does not work with D.C.
3). High or Low voltage?
Transmission cables have significant resistance, especially when they are hundreds of kilometres long. This
means energy is wasted because of the heating effect of the current.
e.g. What is the power wasted in the cable when 10 kW is transmitted through a cable of resistance 0.5 Ω
at a) 200 V b) 200 000 V
NOTE:- Power loss, P = I2R
a). at 200 V
I = P/V = 10000/200 = 50 A
Then Power loss P = I2R = 502(0.5) = 1250 W
b). at 200 000 V
I = P/V = 10000/200000 = 0.05 A
THEN, P = I2R = 0.052(0.5) = 0.00125 W
From the calculations, it is demonstrated that less power is wasted from a cable if power is transmitted
at high voltage. Then a transformer can be used to increase the voltage, and reduce the current and this
means thinner, lighter and cheap cables can be used.
4). Overhead or underground?
Overhead cables are cheapest way of sending power long distances. Underground cables are more
expensive to lay. However, they are used in areas of outstanding natural beauty, where pylons would spoil
the landscape.
16.3.6
MAGNETIC EFFECT ON A CURRENT-CARRYING CONDUCTOR.
A wire carrying electric current generates a magnetic field around itself.
a) Magnetic field around a wire
If a current is passed through a straight wire, it produces a weak magnetic field as shown below.
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Rule for field direction: the right-hand screw rule- Imagine gripping the wire with your right hand so that your
thumb points in the direction of the current. Your fingers then point in the direction of the field.
NOTE:
i). The field lines are in circles.
ii) The field lines are shown closest together near to the wire, because the field is strongest there, and lines get
further apart away from the wire where the field is weaker.
iii). If the current is increased, the field is made stronger.
iv). If you reverse the current direction, this reverses the field.
b). Field due to a circular coil
The field lines pattern is as shown below;
c). Field due to solenoid
The magnetic field produced by a coil has these features:
a). The field is like that around a bar magnet, with magnetic poles at the ends of the coils.
b). If you increase the current, this makes the field stronger.
c). If you put more turns on the coil, the field is stronger
d). If you reverse the current direction, this reverses the field.
Rule for poles: Imagine gripping the coil with your right hand so that your fingers point the same way as the
current, your thumb then points towards the N pole of the coil.
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a). the current direction is from the + to the – (use the conventional current)
b). the magnetic field direction is the direction the N end of a compass needle would point.
16.4.0
MOTOR EFFECT
If a wire that is carrying an electric current is put in a magnetic field, the wire experiences a sideways force and
moves. This effect is used to make the electric motor work in devices such as loudspeakers, electric drill, etc
Demonstration
A flexible wire is supported in the strong magnetic field of a C-shaped magnet. When the switch is pressed,
current flows in the wire which jumps upwards.
Explanation: when a current flows through the coil of wire, it creates a magnetic field, which interacts with the
field produced by the two permanent magnets. The two fields exert a force that pushes the wire at right angles
to the permanent magnetic field.
The field lines due to the wire are circles and their direction is as shown above. The dotted lines represent the
field lines of the magnet and their direction. The resultant field of the two fields is as shown in the diagram b.
There are more lines below than above the wire since both fields act in the same direction but in opposition
above. If you imagine that the lines are like stretched elastic, those below will try to straighten out and in so
doing will exert an upwards force on the wire.
To increase the strength of the force;
i). Increase the current
ii). Usea stronger magnet
iii). Increase the length of wire in the field.
If you reverse either the current or the field, the force is reversed
Fleming’s left hand rule:
This is the rule used to work out the direction of the force or thrust on the wire. It works like this:
Hold the thumb and the first two fingers of your left hand at right angles. The First finger is pointing in the
direction of the Field and the seCond finger in the direction of Current, then the Thumb points in the direction
of the Thrust(Motion).
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(When using this rule, remember that (i) the current direction is from + to – and the field lines run from N to
S.)
Examples:
1.
2.
3.
4.
5.
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6.
7.
8.
16.4.1
SIMPLE D.C ELECTRIC MOTOR
a). It works from the direct current (d.c.) and consists of a rectangular coil of wire mounted on an axle which
can rotate between the poles of a C-shaped magnet.
b). Each end of the coil is connected to a half of a split ring, called the commutator, which rotates with the coil.
c) Current passes into the coil via two brushes which are pressing against the split ring. When the current flows
through the coil, forces are set up on the two sides of the coil labelled ab and cd since they are at right
angles to the field. According to the Fleming’s left-hand rule, the two forces, equal in magnitude but
opposite direction, form a couple and produce a turning effect that causes the coil/loop to rotate.
d) When the coil reaches the vertical position, the brushes are in line with the gaps in the commutator and no
current flows for a moment. But the inertia keeps the coil rotating to overshoot the commutator halves and
change contact from one brush to the other. This reverses the current as well as the directions of the forces
on the two sides. This helps the coil to rotate in one direction (either clockwise or anticlockwise)
The turning effect on the coil can be increased by:
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a). increasing the current
b). using a stronger magnet
c). increasing the number of turns on the coil
d). increasing the area of the coil.
16.4.2
Practical motors
- They have several coils with each set at a different angle and each with its own pair of commutator pieces.
This increases the turning effect and also gives a smoother running.
-The coils contain hundreds of turns of wire wounded on a iron core called armature. The armature gets
magnetised and increases the strength of magnetic field
-The poles of the magnet are curved to create a radial magnetic field. This keeps the turning effect at
maximum for most of the coil’s rotation.
16.4.3
Moving-coil loudspeaker
In the loudspeaker, the magnet is specially shaped so that the wire of the coil is at the right angle to its radical
field. The loudspeaker is connected to an amplifier which gives out an alternating current, this current flows
backwards, forwards, backwards, .......... and so on, causing a force on the coil which is also backwards,
forwards, backwards....... All these cause the cone to vibrate and creates sound waves.
16.4.4
Microphone
The moving-coil microphone contains a thin metal foil diaphragm. There is a small coil attached to the rear of
the diaphragm. This coil is situated in a magnetic field provided by a cylindrical permanent magnet. Sound
waves cause the diaphragm and coil to vibrate. As the coil moves in the magnetic field a current is induced in
it. This varying current can be amplified and heard in a loudspeaker.
16.4.5
Moving-coil meters
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Meters for measuring current and voltage frequently have a coil which is pivoted in a magnetic field.
a). Current enters and leaves the coil by hair springs above and below it.
b). When current flows, it produces a magnetic field that would interact with the field due to the permanent
magnet. This would produce a couple on the coil (as in an electric motor) and cause it rotate and turns
along with the pointer attached.
c). As the coil turns and twist the spring, the springs would try to stop the coil turning. The coil turns until the
turning effect of the forces due to the current balance the turning effect of the spring. The greater the
current in the coil, the coil would turn further and the greater the deflection shown by the pointer.
d). The soft-iron cylinder/drum produces a radial magnetic field which makes the coil deflection proportional
to the current and this gives a linear scale.
16.4.6
QUESTIONS
Q1. Give three examples of actions that cause an induced e.m.f to be set up in a coil of wire.
Q2. Fig. 2.1. shows a magnet being pushed into a coil of wire, which is connected to a galvanometer. Which of
the following statements is/are correct?
Fig. 2.1
a)
b)
c)
d)
The induced current will flow from A to B through the coil.
The induced current will flow from B to A through the coil.
No induced current will flow.
End B will become a north pole.
Q3. A magnet is used to induce a current in a coil of wire. List three things that could be done to increase the
current produced.
Q4. Fig. 4.1 shows a conductor AB in a magnetic field. Mark in the direction of the magnetic field. Which
direction will current be induced in the conductor AB when it is moved:
(a) Into the page
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(b) Out of the page?
Fig. 4.1.
Q5. i) The diagram below shows a bar magnet, and a coil of wire connected to a sensitive ammeter.
As the magnet was pushed slowly into the coil the ammeter pointer moved 10 divisions to the right.
What would you expected to happen
a) If the magnet is pulled slowly out of the coil?
b) The magnet is held stationary inside the coil?
c) The magnet is turned around so that its north pole is nearer the coil. The magnet is then pushed
quickly into the coil?
d) Explain in your own words why the ammeter deflects.
ii) The diagram shows the direction in which a galvanometer needle is deflected when a magnet is moved
towards a coil. The size of the arrow represents the speed at which the magnet is moved.
Show the position of the galvanometer needle in each of the following cases:
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Q6. Fig. 6.1. shows a structural diagram of bicycle dynamo. Study the diagram and answer the following
questions:
a)
b)
c)
d)
What turns the driving wheel of the dynamo?
What is connected to the output of the dynamo?
Briefly explain how the dynamo produces current.
How could the output of the dynamo be increased?
Q7. Draw a sketch graph to show how the EMF of a simple a.c. generator varies with time over two full
revolutions. Relate the positions of the coil to the values shown on your graph.
b) draw a second sketch graph showing what you would expect if the speed of rotation of the coil were
doubled.
c) i. Describe the main difference in the construction between a d.c dynamo and an a.c dynamo.
ii. Sketch a graph to show how the current generated by a d.c dynamo varies with time. How would the
output change if a coil with twice as many turns were used?
Q8. The filament of table lamp is connected to a 250 V, 50 Hz mains supply by two wires. One wire is the live
wire and the other is the neutral.
a)
Use the axes in Fig. 8.1 to sketch a graph which shows the variation with time of the voltage of the
live wire during one cycle. The zero of the voltage scale is earth voltage.
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Fig. 8.1
b)
On the axes in Fig. 8.2 show the corresponding variation of voltage of the neutral wire.
Fig. 8.2
Q9. Fig. 9.1 shows the essential parts of a moving-iron ammeter.
Fig. 9.1
a) Explain why the needle deflects when a steady current passes through the coil.
b) Explain why the direction of the deflection is unchanged when the direction of the current is reversed.
c) State and explain what would be observed when the steady current is replaced by an alternating
current with a frequency of 50 Hz.
The coil of an ammeter has a resistance of 0.5 Ω. A resistor of resistance 0.25 Ω is connected between the
terminals of the ammeter, and a current of 2 A passes as shown in fig. 9.2
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Fig. 9.2
d) Calculate the effective resistance of the coil and the resistor when connected as shown in f.g. 9.2.
e) Calculate the potential difference between the points A and B.
f) Calculate the current in the coil of the ammeter.
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17.0
ATOMIC PHYSICS
17.1.1
RADIOACTIVITY
Some materials (isotopes) contain atoms with unstable nuclei and these isotopes are said to be radioactive.
The nuclei can become stable by emitting tiny particles, energy or both. These particles and energy from the
nucleus are called radioactive emissions/radioactivity/nuclear radiation and the breaking-up process is called
radioactive decay.
There are three types of radioactive emissions, namely:a) Alpha radiation (α- radiation)
b) Beta radiation (β-radiation)
c) Gamma radiation (γ-radiation)
Summary of main properties of the alpha, beta and gamma radiation
Type of radiation
Nature
Charge
Mass
Ionizing effect
Penetrating effect
Effects of fields
Alpha particle (α)
2 protons + 2 neutrons
(identical to a nucleus of
helium-4)
+2
High, compared to β
strong
Not very penetrating: can
be stopped by a thick
sheet of paper or by the
skin. It can penetrate
through
a
few
centimetres of air
Deflected by magnetic
and electric fields
Beta particle(β)
An electron
Gamma rays (γ)
Electromagnetic waves
-1
low
weak
Penetrating:
it
can
penetrate
through
several metres of air but
stopped by a thin (e.g 2
mm) sheet of aluminium
or other metals
Deflected by magnetic
and electric fields
0
None
Very weak
Very
penetrating:
never
completely stopped, though
lead and thick concrete will
reduce intensity
Not deflected by magnetic or
electric fields
*Ionization occurs when a radioactive emission such alpha particle knocks electrons out of the surrounding
molecules or atoms leaving them as charged ions. Alpha particle is the most ionizing radiation because it has
the greatest size and mass.
*Penetration power: all the three radioactive emissions can penetrate materials because their sizes are much
smaller than the spaces separating the atoms in materials, even in solids. Beta particles are more penetrating
than alpha particles because they are much smaller. Gamma radiation is the most penetrating because it is an
electromagnetic wave without mass or size.
*Deflection in electric and magnetic field
Alpha and beta particles are deflected by electric fields because they are electrically charged. Alpha particles
are least deflected because of their larger mass and inertia.

Alpha particles will be attracted towards negatively charged plates because they are positively
charged.
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
Beta particles are attracted towards positively charged plates because they are negatively charged.


Gamma radiation has no charge and is not affected by charged plates.
Any electrically charged particle experiences a force when it moves through a magnetic field (motor effect).
Alpha and beta particles are electrically charged, therefore they will experience a force if they move through a
magnetic field and they will be deflected. Gamma rays have no mass or charge, this means they will pass
through a magnetic field without deflection.
The direction of deflection can be predicted using Fleming’s left hand rule.
17.1.2
RADIOACTIVE DECAY
Radioactive decay can be defined as a process in which a heavy nuclides (radioisotopes) spontaneously break
down/disintegrates to smaller more stable nuclides. This is a random process; it can never be predicted when
an individual nucleus will suddenly split up. It does not matter whether the substance is in its pure state or
combined with others. Also cooling or heating has no effect on the disintegration of the nucleus. Examples of
radioactive elements: carbon-14, uranium-235, uranium-238, cobalt-60, caesium-137, polonium-213, iodine131, barium-143
The number of nuclei that disintegrate per second is called the activity of the radioactive material. The unit of
the activity is called the Becquerel, Bq
activity = number of nuclei which decayed/time taken in seconds
1 Bq = 1 disintegration (decay) per second
(a) Alpha (α) decay
During alpha decay, an unstable nucleus emits 2 protons and 2 neutrons as single particle , known as alpha
particle, that travels at high speed. Therefore an alpha particle is a nucleus of a helium atom. When an atom
decays by α emission, its mass number decreases by 4 and its atomic number decreases by 2.
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Z
A
X
A-4
Z-2 Y
------------------------->
(parent nuclide)
226
Ra
88
e.g.
(daughter nuclide)
-------------------> 86222Rn +
238
92 U
4
2 He
+
α-particle
4
2 He
------------------> 90234Th +
4
2 He
*Note: when an element decays by emission of an alpha particle it turns into an element with chemical
properties similar to those of an element two places earlier in the periodic table.
(b) Beta (β) decay
In a beta decay, a neutron changes to a proton and an electron. The proton remains in the nucleus but the
electron escapes at high speeds in form of a beta particle. The new nucleus has the same mass number but its
atomic number increases by one.
X ------------------------------> Z+1AY
+
(parent nuclide)
(daughter nuclide)
Z
e.g.
A
14
6 C
---------------------------->
40
19 K
------------------------>
14
7 N
20
40
Ar
+
+
0
-1 e
(β-particle)
0
-1 e
0
-1 e
*Note: When an element disintegrates by emission of β-particle it turns into an element with properties
similar to those of an element one place later in the periodic table.
(c) Gamma radiation
After emitting α-particle or β-particle, some nuclei are left still in an excited state, i.e. has surplus energy and
therefore unstable. So such nucleus emits this energy as γ-radiation/rays. When a nucleus undergoes gamma
decay, it keeps the same atomic number Z and the same mass number A. The gamma radiation only carries
away energy so that the nucleus becomes more stable.
Note: Cobalt-60 and Radium-226 are common gamma emitting nuclides.
Detection of radioactive emissions
Most methods of detection depend on the fact that all three radiations can ionize air molecules.
a)
Photographic paper or film: Radiation can affect photographic film in much the same way as light or
X-rays.
b) The gold-leaf electroscope: a charged electroscope discharges if a radioactive isotope is moved to the
cap. The radioactive emissions ionize the surrounding air molecules. If the electroscope is negatively
charged, the positively charged ions are attracted to the cap and the charge on the electroscope is
neutralized. If the electroscope is positively charged the electrons which were removed from the air
molecules are attracted to the electroscope.
c)
Geiger-Muller tube
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G.M tube contains argon gas that ionizes when radiation passes through, thereby creating ions and
electrons. The positive ions move towards the cathode and negative electrons move to the anode.
This produces some electric current which will be fed to a scaler or ratemeter.
Scaler- counts pulses and shows total received in a certain time.
Ratemeter – gives counts per seconds. Some have a loudspeaker which would give a ‘click’ per each
count.
Other detectors are i) spark counter, ii) ionization detector and iii) cloud chamber
17.1.3
HALF-LIFE
Some isotopes decay much more rapidly than others. Scientists measure the decay rate of an isotope in the
form of half-lives.
Half-life is defined as the time taken for half the original number of radioactive nuclides to decay or the time
taken for the activity of a radioactive isotope to fall to half its original value. This time is the same no matter
what the original activity is.
Example: Thoron gas is radioactive and has a half-life of 52 s. the table shows how the amount of thoron is
halved every 52 s.
Time/s
Mass
thoron/g
Fraction
remaining
of
0
52
104
156
208
120
60
30
15
7.5
1/2
1/4
1/8
1/16
*very unstable nuclides decays quickly than one with greater stability but in every case the rate of radioactive
decay is proportional to number of nuclei present.
Rate of decay α N
Rate of decay = λN
where N = number of nuclei present
λ = is a constant
EXAMPLES
Isotope
Type of emission
Half-life
Uranium-235
α
700 million years
Carbon-14
β
5 700 years
Cobalt-60
β, γ
5 years
Sodium-24
β
15 hours
Strontium-93
β, γ
8 minutes
Barium-143
β
12 seconds
Polonium-123
α
4 x 10-6 seconds
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A graph for radioactive decay (Decay curve)
The graph is known as exponential curve. Even though the curve falls, it never quite reaches x-axis. The graph
shows that activity reduces by the same fraction in successive equal time. E.g.
If the curve falls from 80 counts/s to 40 counts/s in 10 min, then from 40 counts/s to 20 counts/s in the next 10
min, from 20 to 10 counts/s in the 3rd 10 min and so on, half-life is then 10 min.
*If count rate is N at time t1 and has fallen to N/2 at time t 2 then half-life t1/2 is t2 – t1. Similarly, if the count
rate has fallen to N/4 at time t3, the half-life is t3 – t2.
If at the beginning there are N undecayed nuclei, after 1 half-life there will be N/2, after a second half-life
there will be ½ x N/2 = N/4, after third half-life there will be ½ x N/4 = N/8 undecayed nuclei, etc.
17.1.4
1.
Uses of radioactivity
Thickness gauges: Radioactive isotopes help manufacturers to check and carefully control the
thickness of product like duplicating machines paper.


a radioactive isotope is placed on one side of the material and a detector on the other side.
The amount of particles (radiation) reaching the detector is monitored closely by the
machine operator or control unit. If the thickness of the material (paper) increases, fewer
particles will reach the detector and visa versa
*The isotope has to be chosen to suit the requirements of the manufacturer. For example, an alpha
emitting isotope would be suitable choice for a paper factory and a beta source would be more
suitable for a steel mill. Gamma sources are not suitable since gamma is a very penetrating radiation.
2. Sterilization of surgical equipment: Surgical equipment is placed in sealed bags and then exposed to short
bursts of gamma radiation. The gamma rays kill any microbes inside the bag and the contents will remain
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sterile until the bag is opened.

Penetrating gamma rays from cobalt-60 are used to kill cancer cells in the body.
3. Long-life fruits and vegetables: Many fruits are also exposed to short bursts of gamma radiation. The
gamma rays kill any micro-organisms which may be inside the fruit, reducing the chances of the fruit rotting
whilst on the shop shelves.
4. Medical tracers- some isotopes are used as tracers to see the performance of specific organs in the body
such as kidneys or the thyroid gland. The patient will be given a liquid containing iodine-123, a gamma
emitter and a detector would then be used to measure the activity of the tracer to find out how quickly
iodine becomes concentrated in the gland.
5. Radioactive isotopes can be used as tracers to detect leaks in underground pipes for gas, water and sewage.
A small amount of gamma radiation source is injected into the pipe and the leak can later be detected with
Geiger-Muller tube.
6. In Agriculture isotopes can be used:- i) as tracers to find how fertilisers and other nutrients are used in
plants. ii) to alter genes in seeds to produce genetically modified plants with superior qualities to natural
plants.
7. Carbon dating: this technique is used by historians and archaeologists to estimate age of historic artefacts
and also it is used by geologists to estimate the age of rocks and fossils.
17.1.5



Dangers of Radiation
The danger from alpha particles is slight.
Large doses of beta and gamma rays can cause radiation burn
Beta and Gamma rays can penetrate deep into the body and destroy cells inside the body or cause
cells to multiply uncontrollably forming cancer or damage chromosomes causing genetic defects
(mutation).
17.1.6
Safety handling and storage of radioactive isotopes
Even when a radioactive material emits low levels of radiation, (e.g. materials used in school laboratories), it
must be handed with extreme care.
Handling:



Always handle isotopes using forceps or special gloves
Keep away from eyes. Do not point the source towards any person.
Always wash hands after handling.
Storage


Keep the samples in special boxes lined with lead
Store the boxes in a locked cupboard
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Disposal of radioactive waste


17.1.7
Burn low-level waste or bury it in the ground or release it into the sea
High-level waste in steel drums are buried in disused mines or granite caves or bedded in concrete
and dumped in deep oceans. Or stored at special factories for re-processing.
Background Radiation
It is low level radiation that is always present around, mainly because of radioactive materials in the ground
and air. Every person on Earth is exposed to this form of radiation. Major sources are:






17.1.8
Rocks
Soils and underground water
Cosmic and solar rays
Food and drinks
Man-made radiation
Buildings
DETECTING ALPHA, BETA PARTICLES AND GAMMA RAYS BY INVESTIGATING
PENETRATING ABILITY - EXAMPLE
The source is a piece of radium which emits all the three types of radiation.
X
Y





Switch on the meter and record the background radiation.
Set the source at position X and take a reading all the three radiation.
Put a sheet of paper at Y (between the source and the G. M tube)and take a reading for beta gamma
rays.
Put a 3 mm sheet of aluminium at Y and take the reading for gamma rays only.
In each case subtract the background radiation from the meter reading
A typical set of results is shown below on the table
Material at Y
Meter reading
Background
Radiation detected
Reading
without
background
None
186
6
α, β, γ
180
Paper
126
6
Β, γ
120
Aluminium (3 mm)
87
6
γ
81
Using these results:
The alpha radiation is
180 – 120 = 60
The beta radiation is
120 – 81 = 39
The gamma radiation is
= 81
17.2.0 NUCLEAR REACTION
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17.2.1
Nuclear fission
Nuclear fission is the splitting of a heavy nucleus (such as U-235) by hitting it with a neutron into two nearly
equal smaller nuclei and two or three neutrons. The lost mass appears as energy.
A beam of neutrons is directed at the uranium atom. If a neutron strikes a nucleus of U-235, this splits into two
roughly equal parts, and shoots out two or three neutrons as well. If these neutrons hit other U-235 nuclei,
they make them split and give out more neutrons. And so on. This process is known as a chain reaction.
235
U
92
+ 01n -------> 56144Ba + 3690Kr + 2 01n
If the chain reaction is uncontrolled, huge numbers of nuclei are split in a very short time. The heat builds up
so rapidly that the material bursts apart into an explosion. This happens in a nuclear (atomic) bomb. If the
chain reaction is controlled, there is a steady output of heat. This happens in a nuclear reactor.
A NUCLEAR REACTOR
In nuclear reactors, fission is carried out in a controlled way. Reactors use naturally occurring uranium, U-235
and U-238 but only U-235 undergoes fission with slow neutrons. Neutrons from the fuel rods go into graphite
core, where they collide with graphite atoms and lose K.E. The graphite is called a moderator because it slows
down the neutrons. The neutrons then pass into fuel rod (which consists of uranium) and cause fission. The
boron steel rods control the rate of fission by absorbing some neutrons. The heat generated by nuclear fission
warms a coolant fluid which circulates through the moderator. The coolant may be water or gas CO 2 . The heat
is used to turn water into steam. The steam drives the turbines and generates electricity.
17.2.2
Nuclear fusion
In fission a heavy nucleus split in two to release energy. On the other hand in nuclear fusion the opposite is
done to produce large amounts of energy.
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Nuclear fusion is the combination of two light nuclei to form a heavier nucleus, e.g. two nuclei of hydrogen-2
(deuterium) can be combined to form a nucleus of helium-3.
2
1 H
+
2
1 H
-------------->
3
2 He
+
1
0 n
For two nuclei to fuse, they must be brought sufficiently close to each other. But it is difficult to do this as they
repel each other with large electrical force. To overcome this repulsion, the nuclei have to be heated to high
temperature (e.g. 108 K) so that they gain enough K.E.


17.2.3
The sun obtains its energy from nuclear fusion. In the sun the temperature is about 10 million °C and
the hydrogen-2 atoms have enough energy to fuse.
Uncontrolled fusion on Earth can result with hydrogen bomb. Initial high temperature required is
obtained by using an atomic (nuclear) bomb to trigger off fusion. A hydrogen bomb releases much
more energy than an atomic bomb.
Nuclear energy
In radioactive changes (or nuclear reaction), a little bit of mass disappears (this is called mass defect), and
equivalent amount of energy appears as kinetic energy of the formed particles.
The relationship between these mass and energy can be given by the following equation (formulated by Albert
Einstein)
E = mc2
where c2 = speed of light, 3 x 108 m/s
E.G:- When radium decays into radon, about 1/40 000 0f the mass of each decaying atom disappears. Calculate
the energy released from 1 g (1/1000 kg) when it decays to radon.
Data: m = mass disappearing = (1/400 000) x (1/1000 kg) = 1/(4 x 10 7) = 2.5 x 10-8 kg
c = 3 x 108 m/s
E = mc2
= 2.5 x 10-8 x (3 x 108)2
= 2.25 x 109 J
QUESTIONS
1. Use a diagram below to answer questions that follow.
Radioactive source
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lead block
GM-tube
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Count rate (average)
Counts per second
With source in place
28
With source + block
18
With source + block removed
2
a) What is the count rate due to the background radiation?
b) What is the count rate due to the source alone?
c) If the source emits one type of radiation only, what type is it? Give reasons to your answer.
2. A figure below show the arrangement of equipment in paper industry. A radioactive source is used to
monitor the thickness of the paper.
GM-tube
rollers
paper
Radioactive source
a) What is the GM-tube used for?
b)State which radioactive emission is the most suitable to use. Give a reason for your answer.
c)Briefly explain how the equipment can keep the paper at constant thickness.
3. The half life of iodine 128 is 25minutes. If the activity of a sample is 800Bq, what would you expect the
activity to be after,
a)25minutes
b)50minutes
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c)100minutes
4. In an experiment to find the half life of radioactiveiodine,the countrate falls from 200Bq to 25Bq in
75minutes. What is its half life.
5. If the half life of a radioactive gas is 2minutes. After 8minutes the activity would have fallen to a fraction of
its initial value. What is this fraction.
6. A radioactive isotope has original nuclei Ro. The half life of radioactive isotope is 5 hours. Sketch a curve for
the isotope.
7. The high temperatures deep underground are caused by decay of radioactive isotopes in the rocks. Why
does radioactive decay cause high rise in temperatures?
8. What is meant by,
a) fission
b) fusion
c) chain reaction
9. Give an example of
a) a controlled chain reaction
b) an uncontrolled chain reaction
10. In a typical fission process, Uranium 235 absorbs a neutron, creating a nucleus which splits to form Barium
141, Krypton 92 and 3 neutrons.
Neutron = 1.674x 10-27kg
Uranium 235 = nucleus 390.250x10-27kg
Barium 141 nucleus = 233.964x10-27kg
Krypton 92 nucleus = 152.628x10-27kg
a) Using the data above, calculate the total mass of the uranium nucleus and the neutron.
b) Calculate the total mass of the barium and krypton nuclei and the three neutrons.
c) Use E = mc2 to calculate the energy released per decay by the fission process.
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