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CSEC Physics Summary Notes -h3kz
Social Psychology (Regional Science High School Union)
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CSEC PHYSICS
MANUAL OF ESSENTIAL NOTES
Based purely on syllabus requirements.
Worked example questions and practice
questions at the back.
Complete list of formulae and laws at back.
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PHYSICS, SECTION A (1/2) : MEASUREMENTS AND STATICS
QUANTITIES AND UNITS
The SI (Standard International) unit system is the most widely used system in measurement
and comprises seven fundamental units.
A fundamental quantity, also called a base quantity, is known as one that is independent from
the others and usually cannot be expressed using other quantities. A derived quantity is one that
is a combined product of different fundamental ones, e.g. ‘speed’ is derived from distance
(length) and time, two base quantities. ‘Area’ and ‘volume’ are derived from multiple lengths.
The table below shows units the seven“fundamental quantities”.
Quantity
Symbol
Unit Name
Measuring Instrument
Length
l
Metre (m)
Metre rule
Measuring tape
Vernier caliper
Micrometer screw gauge
Mass
M
Kilogram (kg)
Scale balance / Triple beam balance
Time
T
Second (s)
Stopwatch
Electronic Current
I
Ampere (A)
Ammeter
Temperature
T or ϴ
Kelvin (K)
Thermometer
Amount of a Substance
n
Mole (mol)
---------
Luminous Intensity
L
Candela (cd)
---------
This table shows a few derived quantities.
Quantity
Unit
Unit Breakdown
Measuring Instrument
Volume
m3
mxmxm
Measuring cylinder / Burette
Force
N
kg m/s2
Force-metre / Spring balance
Speed
m/s
m÷s
Ticker tape timer
Pressure
Pa
(kg m/s2)/m2
Barometer / Manometer
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ENSURING ACCURACY WHEN TAKING MEASUREMENTS
1. Avoiding parallax errors – These occur when the experimenter is not viewing the readings at
eye level. Not doing this can cause inaccurate data to be recorded. When possible, equipment
should always be placed on a level surface. Sometimes perpendicular aids must be constructed
from set squares in order to read instruments accurately.
2. Avoiding zero errors – Before using an
instrument, it is important that it is
calibrated to read zero at the start of the
3. Human response time – When taking
readings with stopwatches, for example, the
experiment. Scales and stopwatches have an
option to reset to zero while the gauges on
ammeters and voltmeters must be checked
beforehand.
actual time for the experimenter to start and
stop the stopwatch causes a delay and
accounts for a slight error in measurement.
This is why it is important to repeat an
experiment multiple times.
Accuracy and precision are two different things.
•
•
Accuracy refers to how correct the data is.
Precision refers to how consistent the data
is when reproduced between trials.
The table below shows a list of some unit prefixes that denote the magnitude (size) of the unit.
Prefix
Symbol
Power
SI Unit Conversion Example
Mega
M
10+6
5.0MJ = 5.0 x 106 J = 5000000 J
Kilo
k
10+3
4.52km = 4.52 x 103 m = 4520 m
Centi
c
10-2
300cm = 3 x 10-2 m = 3 m
Milli
m
10-3
6.8 ms = 6.8 x 10-3 s = 0.0068 s
Micro
µ
10-6
4500 μA = 4500 x 10-6 A = 0.0045 A
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STANDARD FORM & UNIT CONVERSION
Standard form is a means of expressing large numbers in simple ways using integer powers and
usually three significant figures. Note that the decimal point goes after the first significant figure.
For e.g. 54880N in standard form (to 3 s.f.) will be written as 5.49 x 104 N.
0.006483J in standard form (to 3 s.f.) will be 6.48 x 10-3 J.
How to convert km/h to m/s
How to convert m/s to km/h
Convert 108km/h to m/s
Convert 18m/s to km/h
THE SCIENTIFIC METHOD
The scientific method is a process for creating setups of situations to examine factors of the real
world and gather data from testing. This data can then be analyzed and replicated by other
scientists to further study the models and draw reasoning from them. It was first used by scientists
such as Isaac Newton and Galilei Galileo.
The scientific method has FOUR main steps:
1. OBSERVATION - Which can be made visually or through apparatus.
2. HYPOTHESIS - A statement made that has to be proven true or false. It has to be
testable.
3. METHODOLOGY - Formulating a method to test the hypothesis and gather data. May
have to be repeated several times to validate results under various conditions.
4. ANALYSIS - Determining whether or not the results conform to the hypothesis and
formulating a theory based on them.
PERIOD OF A PENDULUM
One of the first major experiments in Physics was Galileo’s determination for the acceleration
due to gravity on Earth, also known as g. This was done using a pendulum with strings of varying
lengths.
•
The period is defined as the THE TIME TAKEN TO COMPLETE A FULL OSCILLATION.
•
The only factor that affects the period of the pendulum is LENGTH. The mass of the bob and the
angle of displacement the bob is held at does not affect the time for one swing.
•
Usually 10-20 oscillations are taken because the human response time would create too large of
a delay and error if just testing for 1 oscillation.
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Example question: Complete the table and plot a graph of T2 vs. L.
Length, L (m)
Time for 20 oscillations, t(s)
Period, T (s)
Period Squared, T2 (s2)
0.10
12.96
0.65
0.42
0.20
18.00
0.90
0.81
0.30
22.00
1.10
1.21
0.50
28.28
1.41
1.99
0.60
31.10
1.56
2.43
Using the graph, find the T2 value
when the length is 0.40m:
1.60m
Calculate the gradient:
y2 – y1 = 2.43 – 0 = 4.05 s2/m
x2 – x1 0.60 – 0
(The unit for the gradient is always
the y-axis unit divided by the x-axis
unit)
Now calculate the acceleration due to gravity, g, using this formula.
Put the unit for your answer as m/s2 as that is the unit for acceleration.
(π = 3.14)
g = 4 x (3.14)2 x (1 ÷ 4.05)
= 4 x 9.86 x 0.25
= 9.86 m/s2
(very close to the actual value for ‘g’,
which is 9.81 m/s2)
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SCALARS AND VECTORS
Quantity
Definition
Examples
Scalar
A quantity that has magnitude but NO
direction.
Distance, speed, area, volume, density
Vector
A quantity that has BOTH magnitude
and direction.
Displacement, velocity, acceleration, force,
momentum
Parallel and antiparallel vectors: We just add the vectors to form a single vector called a
RESULTANT. A single vector may also be the resultant of two other vectors, e.g. an airplane’s
overall flight direction is a combination of the engines’ thrust, gravity and the wind.
Opposite direction vectors (antiparallel) are viewed as negative. Draw the resultant vectors for the
two examples below.
NON-PARALLEL VECTORS
Draw and measure the resultant forces for both diagrams below.
Question: An airplane is flying east in still air at 92m/s. A heavy north-east wind starts to blow at
36m/s at 45o. Using a scale of 1cm:10m/s, draw a vector diagram to show the resultant velocity of
the plane. Measure the angle the plane deviated from its original path.
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MASS AND WEIGHT
Quantity
Definition
Example
Mass
The amount of matter contained in an
object. It is a measure of an object’s
INERTIA or resistance to change in
motion.
A truck has more mass than a car and thus,
would resist a change in motion more than a
car would. It would take longer to speed up
and require more force on its brakes.
Weight
The force exerted on a body’s mass by
gravity.
An astronaut on the Moon would have the
same mass on Earth but less weight, because
the Moon’s gravitational field is weaker.
Note the formula for weight:
Since inertia is defined as an
object’s resistance to change, the
greater the mass, the more force is
required to change its motion.
CENTRE OF GRAVITY AND STABILITY
Objects balance at a point called the centre of
gravity. The centre of gravity of an object can be
defined as THE POINT AT WHICH THE
WEIGHT OF A BODY ACTS.
The force of weight acts downward from the
centre of gravity. Imagine it as a straight line
vector pointing down from that position.
Objects or systems that are stable tend to have most of their mass deposited much LOWER than
unstable ones. They are said to have a low centre of gravity. Observe the shapes below.
An irregular lamina’s centre of gravity can be found by boring
holes and hanging a plumbline from each hole
The purpose of the plumbline is to see which points are
vertically below the hole. By marking the lines,
an intersection will be noticed. This is the lamina’s
centre of gravity.
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FORCES
Forces enable masses to overcome inertia, i.e. they are able to cause a change in an object’s
acceleration, deceleration or direction (even shape and size, but NOT mass)
Forces are measured in Newtons (N) which can be derived as 1N = 1 kg m/s2.
Type of Force
Description
GRAVITY
Pulls objects towards the centre of the Earth.
WEIGHT
The effect of gravity on an object’s mass.
FRICTION
The resistance an object experiences when rubbing a surface.
BUOYANCY / UPTHRUST
The upward force exerted by a fluid.
ELECTROSTATIC
Attraction due to charged particles called electrons stored in an object.
MAGNETIC
An attraction or repulsion caused by north and south poles.
REACTION
The force that always acts opposite to another, e.g. the forward push
from swimming while pushing the water backward.
TENSION
An upward force exerted on a string or rope attached to a load.
CENTRIPETAL
The pull towards a central point for an object moving in a circle.
NUCLEAR
The attraction holding the nucleus of an atom together.
•
Forces may be CONTACT or NON-CONTACT. They may also be ABSORBED, such as
by kneepads worn by athletes, cyclist helmets, bubblewrap packaging and cellphone
cases. When a force is absorbed, its impact is decreased.
•
All moving objects on Earth experience some form of resistance, whether from the
surface they are on (friction) or the medium that they are in, such as the atmosphere
(called air resistance or drag).
In this example, the two “resistant forces”
are equal to the applied forward thrust of the
car. This will give an overall resultant or net
force of 0 Newtons.
This doesn’t mean the car will stop. This means that the object is in EQUILIBRIUM and is
moving at a constant velocity. Therefore, we can say that if a force is absent, there will be no
change in motion or direction.
NOTE: The car does not require a force to keep moving forward. It only requires a force to
accelerate or to overcome the friction of the road. If the resistant forces are greater than the
forward thrust, the car will DECELERATE and then stop.
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AIR RESISTANCE & TERMINAL VELOCITY
Observe the panels below:
1. As he falls, GRAVITY initially pulls him down.
2. AIR RESISTANCE acts upwards, making his ACCELERATION DECREASE (NOT
decelerate).
3.
Eventually, the air resistance will be equal to his weight. He will then be held at
EQUILIBRIUM and fall at a CONSTANT SPEED. Acceleration stops at this point. This
balanced velocity is referred to as TERMINAL VELOCITY.
4. When he opens the parachute, he decelerates (velocity decreases) as the parachute has a wide
surface area that increases his air resistance.
5. As his velocity decreases, his air resistance also decreases until the forces are balanced again.
He falls at a safe terminal velocity, no longer accelerating.
6. When he hits the ground, the ground causes a sudden deceleration that brings him to rest. The
ground hits him back with a REACTION FORCE to stop him.
NOTE: An area that has no air or atmosphere is known as a VACUUM. If there is no air, then there is no
air resistance. All objects fall or accelerate at the same rate in a vacuum, since only gravity is pulling
them down.
FREEFALL
When an object is accelerating due to gravity only, it
is said to be in freefall. If on Earth, this is to be taken as
10 m/s2 (rounded off from 9.81m/s2) this means that
.
with each second, the velocity increases by 10 m/s. So,
after 5s in freefall, the velocity would be 50 m/s.
NOTE: The value for ‘g’, 10m/s2, may also be
written as 10N/kg.
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LEVERS
A lever is a type of simple machine. Machines are designed to make work easier, which means that they can
either:
1. Modify or transmit forces and motion
2. Convert different types of energy into mechanical energy
All machines have an input and an output. The input force is usually referred to as the EFFORT and the output
as the LOAD. Levers have a point of rotation that these forces will turn about. This point of rotation is referred
to as the PIVOT or FULCRUM.
The greater the distance from the fulcrum, the greater magnitude of turning force the effort would have. This
turning force is sometimes referred to as a MOMENT or a TORQUE.
There are THREE classes of levers. On the diagrams below, label the effort, load and fulcrum and determine
which class of lever each is.
Class
Placement
First
Fulcrum between effort and load.
Second
Load between effort and fulcrum.
Third
Effort between load and fulcrum.
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PRINCIPLE OF MOMENTS
The drawing depicts Odie trying to balance Garfield, whom is heavier. Let’s also say that the two of them
are at a balance or equilibrium. How far would Odie have to be from the pivot to balance Garfield?
Each above is creating a turning force or MOMENT. Moments are determined about the turning point or
fulcrum, so any distances used in calculation must be measured from the fulcrum.
Note the formula for calculating a moment: Moment = Force x Distance
Unit = Nm
The Principle of Moments states that THE SUM OF CLOCKWISE AND ANTICLOCKWISE
MOMENTS ABOUT THE SAME PIVOT ARE EQUAL AT EQUILIBRIUM.
Using the figures shown, what is the force
applied to the effort end of the wheelbarrow?
F1D1 (load) =
F2D2 (effort)
600 x 1.2
=
F2 x (1.8 + 1.2)
Remember the
convert mass to a
force (weight)
720
F2
w = mg
= 60 x 10 = 600N
=
=
3 F2
720 ÷ 3 = 240 N
Reena, Mark and Sharon, sit on a seesaw fashioned from a log resting on a pivot. Each of them has the
same weight of 500N. Mark sits 0.4m away from the pivot and Sharon sits 0.8m away from the pivot. For
the seesaw to be in equilibrium, calculate the distance Reena has to sit to balance Mark and Sharon.
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This relationship is denoted by Hooke’s Law,
which states that:
THE EXTENSION OF A SPRING IS DIRECTLY
PROPORTIONAL TO THE FORCE ACTING ON
HOOKE’S LAW
IT, WITHIN ITS ELASTIC LIMIT.
Formula:
F = kx
The term directly proportional means the
variables increase/decrease at the same rate.
If one quantity increases while the other decreases,
this is called inversely proportional.
When an object changes shape due to the action
of a force upon it, the object is said to
experience DEFORMATION. On the diagram,
the initial length of the spring is noted as L0.
This is when no weight is attached.
However, when a load (F) is attached, the spring
extends. This extension is noted as x. The total
length of the spring is now given as (L0 + x).
As the weight of the load is increased, the
extension will increase. If the weight is doubled
to 2F, the extension will double to 2x.
The constant (k) can be obtained by finding the gradient of an extension-force graph. To put it simply, k
represents the “stiffness” of the spring. A bigger ‘k’ value would require more force to extend the spring.
HOWEVER, there is a point where the proportionality will stop if too much weight or force is applied to
the spring. This is called the LIMIT OF PROPORTIONALITY. Beyond this point is the ELASTIC
LIMIT, where further extension can cause permanent deformation of the spring.
Example question: The initial length of a spring is 10mm. A 20N weight is attached and it has a
length of 14mm. What is the extension and length of the spring if 50N were attached?
Extension: 14 – 10 = 4mm
Find ‘k’ first
F = kx
k = F ÷ x
= 20 ÷ 4 = 5N/mm
Now find ‘x’ for 50N
F = kx
x = F ÷ k
= 50 ÷ 5 = 10mm
Length = 10 + 10 = 20mm
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DENSITY AND ARCHIMEDES’ PRINCIPLE
Density is defined as MASS PER UNIT VOLUME.
However, Cube A is considered denser
because it has more MASS.
Cube A has twice as much mass in it than
Cube B. Therefore, we can say that Cube A
is twice as dense than B.
Cube B can be made denser by:
Note these two objects. They are both cube
containers of the same size and volume.
1. Adding more mass.
2. Decreasing its volume (compacting it).
Note the formula and units for density:
Archimedes’ Principle states that:
THE UPWARD FORCE THAT IS EXERTED ON AN OBJECT IMMERSED IN A FLUID IS
EQUAL TO THE WEIGHT OF FLUID DISPLACED.
To find the volume, fill a measuring cylinder with an initial
volume of water. Place the rock gently to avoid splashing. Next,
measure the final volume of the water.
The volume of the rock is equal to the change of volume of the
water (given that the rock has been fully submerged).
NOTE: If the rock were only partially submerged, the water level
would rise by the volume partially submerged and the weight of
water displaced would only be the weight partially submerged.
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RELATIVE DENSITY
Relative density is a given ratio of the density of a substance in reference to the density of
another substance (usually the medium it is kept in). It is one of few quantities with NO UNIT.
For e.g. if the block below had a mass of 6000kg and was kept in a container of mercury, what
would be its relative density is mercury had a density of 13,600kg/m3?
SINKING AND FLOATING
Whether or not an object sinks or floats depends on two things: the density of the object, and the
density of the medium the object is held in. There are usually two forces that act on the object at
this point: a downward force (WEIGHT) and an upward force known as UPTHRUST.
A large boat of great weight is able to float because of two main reasons:
1. It has a HOLLOW interior, which decreases its overall density. Only the hull is made of
material denser than water, such as steel or zinc.
2. It has a WIDE SURFACE AREA, which increases the UPTHRUST acting on it.
NOTE: The density of pure water is given as 1000 kg/m3 or 1 g/cm3. Since seawater has salt and
other substances, its density would be slightly higher.
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PHYSICS. SECTION A (2/2): DYNAMICS AND ENERGETICS
DISTANCE AND DISPLACEMENT
Distance is the HOW MUCH GROUND AN OBJECT HAS COVERED. The magnitude is of
importance, not the direction, therefore distance is noted as a SCALAR quantity.
Displacement is the OVERALL CHANGE IN POSITION OF AN OBJECT IN A STRAIGHT
LINE BETWEEN ITS ORIGIN AND DESTINATION.
Both magnitude and direction are importance. It is therefore a VECTOR.
Looking at the example to the left, if a
person ran from A to B and then B to C,
they would have travelled a distance of 7m
but a displacement of 5m.
DISPLACEMENT-TIME GRAPHS
Displacement-time graph simply show an object’s position as time passes. Observe the graph
below. It shows that after 5 seconds, the object is 25m away from the starting position. From 5s to
10s, the object has not moved since its position is still 25m away. For the last 2.5s, the object has
returned to its starting position.
Calculating the gradient of a line in the graph gives the object’s VELOCITY.
Gradient of upward
slope:
y2 – y1
x2 – x1
=
25 - 0
5 – 0
= 5 m/s
(velocity)
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SPEED AND VELOCITY
Quantity
Definition
Formula
Speed (s)
Distance travelled per unit time time. s = d
Unit
Category
m/s or ms-1
SCALAR
m/s or ms-1
VECTOR
t
Velocity (v)
Displacement travelled per unit time.
v=x
t
ACCELERATION
When the velocity of an object is changing, it has an acceleration. It can either speed up or slow
down or change direction. A positive acceleration denotes that the velocity has increased over
time. A negative acceleration (or deceleration) denotes that velocity has decreased over time.
Acceleration is therefore defined as the CHANGE IN VELOCITY OVER TIME. It is a
VECTOR quantity.
Note the formula and unit for acceleration below:
VELOCITY-TIME GRAPHS
These graphs above represent an object’s change in velocity as time passes. HOWEVER, note
that the lines are straight for the left figure and curved for the right figure. The acceleration in
graph A is said to be UNIFORM while graph B is said to be NON-UNIFORM. Since the line is
getting less and less steep in the right figure, the acceleration can be said to be at a decreasing
rate.
Observe the LEFT figure for now. Aside from the appearance of the graph and general idea of
motion, other quantities can also be deduced and calculated from the graph:
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•
The ACCELERATION can be obtained by calculating the gradient of the slope.
•
The DISPLACEMENT can be obtained by calculating the area under the required portion
of the graph. If the displacement for the entire journey is required, we need to find the
area of a trapezium in this case, which is given by the following formula:
Example Question (Graphwork)
Area = ½ (a + b) x h
1. Calculate the gradients of B and D, and the displacement of BCD.
Gradient B
y2 – y1 = 8 – 2 = 2 m/s2
x2 – x1
4 – 1
Gradient B
y2 – y1 = 0 – 8 =
x2 – x1
10 – 7
-2.67m/s2
Displacement:
½ (a+b) x h
½ (3+10) x 8
6.5 x 8 = 52m
Example question: Plot the events on the graph. Label the points.
A – The driver begins at 10m/s and keeps going at constant velocity for 20 seconds.
B – He takes 10 seconds to decelerate uniformly until he comes to rest.
C – He remains at rest for 10 seconds.
D – He accelerates in reverse for 10 seconds until he is at -10m/s.
E – He reverses at a constant velocity of -10m/s for 20 seconds.
F – He decelerates for 10 seconds until he is at rest again.
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NEWTON’S THREE LAWS OF MOTION
Before Isaac Newton’s laws of motion were made known, many people ascribed to Aristotle’s
Law of Motion, which basically stated that “Nothing moves unless you push it. An object’s
speed is proportional to the force applied to it.”
We learned previously that this is not true because: A force is not required to keep an object
moving. If there was no friction, an object would keep moving forever.
Newton’s Three Laws are stated below:
Law
What the Law States
Example
1st
An object at rest remains at rest, or an
object in motion remains in motion at a
constant velocity, unless an unbalanced
force acts upon it.
A trolley will stay where it is unless
someone pulls or pushes it. It cannot
move unless a force is applied to it.
The force on a body is directly
proportional to its acceleration.
A trolley with more mass will need a
greater force to get it to accelerate at the
same rate as a trolley with less mass.
2nd
(F = ma)
3rd
Similarly, if a trolley is moving, a force
will be needed to stop it. This force
could be friction, air resistance or the
reaction force from a collision.
Every action force has an equal and
In order to swim forward, a person must
opposite reaction force.
push the water backwards. Pushing the
water back is the “action” while the
water pushing the body forward is the
“reaction”.
If a Body A acts on Body B, then B
exerts an equal and opposite force on A.
Think about how Newton’s Laws apply to the following situations:
1. A rocket or airplane being able to propel itself upward or forward.
2. A child jumping on a trampoline.
3. Why an astronaut would need to tie themselves to an object while doing repairs in space.
4. Why a loaded truck is harder to stop than an empty one
5. Why seatbelts or deployable airbags are necessary in cars
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LINEAR MOMENTUM AND IMPULSE
Linear momentum is defined as THE PRODUCT OF AN OBJECT’S MASS AND
VELOCITY. Momentum is a VECTOR quantity, since it has a direction. The force that produces
a change in momentum of a body is called an IMPULSE.
Note the formulas and units
for momentum and impulse:
Scenario A: The white ball hits the 8-ball,
transferring all its momentum to it, and comes to
a stop. The 8-ball then moves at the same
velocity as the white ball.
Scenario B: The two balls move at a combined
mass. Since the combined mass is exactly twice
as large, the resultant velocity will be halved,.
The law of conservation of linear momentum states that:
IN A CLOSED SYSTEM, THE TOTAL MOMENTUM BEFORE COLLISION IS EQUAL TO THE
TOTAL MOMENTUM AFTER COLLISION.
Use the law of conservation of linear
momentum to calculate the velocity of the
trolleys if they collide and move together:
p (before)
m1v1
=
4 x 3
=
12
=
v
=
=
= p (after)
m2v2
(4+6) x v
10v
12 ÷ 10
1.2 m/s
Question: A footballer’s boot is in
contact with a ball for 0.05s. The force
on the ball is 180N. The ball leaves his
foot at 20m/s. Calculate:
(i) p = F x t
= 180 x 0.05 = 9 Ns
(i) the impulse of the force on the ball
(ii) the ball’s change in momentum
(iii) the mass of the ball
(iii) p = mv
m = p ÷ v
= 9 ÷ 20 = 0.45 kg
(ii) 9 Ns
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LINEAR MOMENTUM AND COLLISION
The previous examples dealt with one moving object colliding with a stationary object. However, what
would happen if we had a question like this:
PROBLEM 1: A car, heading east at 24m/s, of mass 1200kg collides with a 4000kg truck, heading west
at 5m/s. If the wreckage moves as a combined mass, what is the velocity and direction it moves at?
First, calculate the total momentum in the system before collision. This momentum should be equal
to the momentum of the wreckage after collision. The wreckage’s mass is the sum of both vehicles.
(Recall that one of the values for velocity must be negative, since it is in an opposing direction)
The direction of the wreckage will move at will be in the direction of whichever vehicle had a higher
momentum. In this case, it will be EAST.
PROBLEM 2: Two American football players collide into each other. Calculate the velocity the first
player will push the second.
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FORMS OF ENERGY
Energy is simply defined as the CAPACITY FOR DOING WORK. The unit for energy is Joule (J).
A Joule is defined as the work needed to move 1N by a 1m distance, so 1J = 1Nm.
The principle of conservation of energy states that
.
ENERGY
CAN NEITHER BE CREATED NOR DESTROYED, BUT CAN ONLY BE CONVERTED
FROM ONE FORM TO ANOTHER.
The table below describes some of the many different types of energy:
Type of Energy
Description
Example
CHEMICAL
Released during chemical reactions or
transformation.
Batteries, food, fossil fuels,
metabolism.
ELECTRICAL
The flow and movement of electrons.
Power lines, lightning.
KINETIC or
MECHANICAL
Occurs during physical collisions and
movement.
A rolling ball. A falling
object.
GRAVITATIONAL
POTENTIAL (GPE)
The energy possessed by a body by virtue of its
position, such as its height.
An airplane in mid-air. A car
on a cliff.
ELASTIC
POTENTIAL
Energy that is stored within an object
experiencing deformation.
Compressed spring.
Slingshot. Catapult.
ELECTROMAGNETIC
Held in waves such as light, X-rays and radio.
Transmitters, TV screens.
NUCLEAR
Released during the splitting (fission) of an
atom or the combining (fusion) or two atoms.
Splitting of Uranium in
nuclear reactors.
SOUND
Associated with the vibrations of matter to
produce various pitches and tones.
Vocal cords. Music. Tyres
screeching.
THERMAL
Energy that can be stored or transferred across
molecules through kinetic energy.
Heat from friction. Wasted
energy from appliances.
Note the energy transfers in the following: (i) a car being driven on a straight road (ii) burning match
(iii) slingshot (iv) object falling from shelf (v) radio (vi) in a football being kicked (vii) acoustic guitar
(viii) wheels after brakes are applied (ix) lithium-ion batteries (x) a sprinter racing up a hill
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ENERGY AND POWER
NOTE: Even though a Joule can be broken down to be a Newton-metre (Nm),
J and Nm should not be used interchangeably. Nm is reserved for moments
or turning forces, while J is reserved for energy.
Energy can either be released or stored. Energy that is used or released to produce some type of change
is termed WORK DONE. Work has the same unit as energy. HOWEVER, even though energy can be
stored, work cannot, so these terms should not be used interchangeably.
Note the formula for work below:
POWER refers to THE RATE OF ENERGY CONVERSION, OR WORK DONE OVER TIME.
For example, if there are two sprinters of the same mass (70kg) who run the same 100m dash, but sprinter
A completes the race in 1 minute, while sprinter B completes it in 1.5 minutes, BOTH sprinters did the
same work, but sprinter A had more power than B, since he did the work in less time.
Note the formula and unit for power below:
INPUT, OUTPUT & EFFICIENCY
EFFICIENCY refers to THE PERCENTAGE OF USEFUL OUTPUT COMPARED TO TOTAL
SUPPLIED INPUT.
Most objects will not convert 100% of one type of energy to another type. A fraction of the energy is
always lost due to heat, for example. When these energy losses are reduced, machines are said to be more
energy-efficient. For example, fluorescent lights tend to lose much less heat than filament lights, which
heat up very quickly. As a result, fluorescent lights are more efficient and last much longer.
Note the formula for efficiency below:
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ENERGY IN A PENDULUM
When the pendulum swings from positions 1 to
5, it is converting kinetic to GPE. Note what
happens at:
1 – Maximum GPE, minimum KE
2 – GPE converting to KE
3 – Minimum GPE, maximum KE
4 – KE converting to GPE
5 – Maximum GPE, minimum KE
KINETIC ENERGY (KE)
This is the energy possessed by an object IN MOTION OR DURING COLLISION. Note its formula:
GRAVITATIONAL POTENTIAL ENERGY (GPE)
This is the energy possessed by an object BY VIRTUE OF ITS POSITION OR HEIGHT.
Note its formula:
KE AND GPE CONVERSION
When an object is falling (assuming no air resistance) or sliding down a slope, the following is noted:
GPE LOST = KE GAINED
For situations that account for resistance or friction, energy loss is accounted for, e.g. A cyclist and his
cycle have a mass of 70kg. They descend a slope from the 2100m point to the 1600m point. Assuming
that 75% is lost to friction, what is the velocity of the cyclist as he travels down?
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ALTERNATIVE & RENEWABLE ENERGY SOURCES
Fossil fuels are formed from the remains of decayed microscopic organisms, animals and plants from
millions of years ago that have been pressed and subjected to hot temperatures over long periods of time.
They mainly come in the forms of coal, crude oil or natural gas. Fossil fuels are finite resources that
cannot be replaced and are said to be NON-RENEWABLE.
In addition, the combustion of fossil fuels has, however, had negative effects on the environment, such as
the GREENHOUSE EFFECT (due to the release of carbon dioxide by combustion) and ACID RAIN (due
to the release of sulphur dioxide into the atmosphere).
Energy sources that are infinite and can be replaced are termed RENEWABLE and can be used as viable
alternatives to fossil fuels. Note that the Sun is the main source of energy for all of these, except
GEOTHERMAL and NUCLEAR.
Some examples of alternative energy sources include:
Source
Explanation
SOLAR
Energy obtained from the Sun are stored in photovoltaic cells in solar
panels and converted to electricity.
WIND
Winds turn the blades that spin a shaft that powers a generator.
HYDROELECTRIC
The gravitational potential and kinetic energy of water flowing down a
conduit helps power a generator.
TIDAL
The kinetic energy from the moving tides helps generate a current.
GEOTHERMAL
Heat generated by converting hot water from deep beneath the earth’s
surface can be used as a source of power.
NUCLEAR
The fission (splitting) of Uranium atoms release energy from their nuclei,
which can be harnessed. This is non-renewable but very efficient.
BIOFUELS
On a smaller scale, some farmers use the remainder of their harvest to
produce ethanol that would act as fuel for their machinery.
Other things can be done to help conserve fossil fuels or reduce our usage of them, such as carpooling,
switching off appliances when not in use, using fuel-based transport less often (bicycles for short
distances, for e.g.) and switching to more energy-efficient fluorescent lights in the household.
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PRESSURE
Pressure is simply defined as FORCE ACTING PER UNIT AREA.
Note the formula and unit:
Question: Why does
your body exert more
pressure on the ground if
you stand on one foot?
Both blocks are the same mass (60kg).
Block B is the same as A, but put to stand at
a different position. Even though the force
(weight) of both blocks would be the same,
the pressure will be different because that
force is acting down on two different surface
areas.
Calculate the pressure that blocks A and B exert.
w = mg = 60 x 10 = 600N
P (block A) = F / A = 600 / (5 x 2) = 60 Pa
P (block B) = F / A = 600 / (3 x 2) = 100 Pa
PRESSURE IN LIQUIDS AT DIFFERENT DEPTHS
Pressure in a fluid increases as DEPTH
increases.
This occurs because as the position gets
deeper, the more molecules lie above that
point and thus, they will exert a greater force
or weight downwards.
Note the formula for pressure in a fluid:
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Example question: An aquarium is filled with saltwater of density 1020kg/m3. It is 10m deep. The
bottom of the aquarium is to be fitted with a glass window of measurements 2m x 1.5m. The
atmosphere above the water surface is 101kPa. Calculate
(i) the pressure of the water acting against the base of the glass
(ii) the TOTAL pressure, in kPa, acting against the base of the glass
(iii) the maximum force, in kN, the glass should be able to withstand.
(i)
P = ρgh
= 1020 x 10 x 10
= 102 000 Pa
(ii)
P (total) = 102,000 + 101,000 (atm)
= 203 000 Pa
(iii)
P=F/A
F=PxA
= 203,000 x (2 x 1.5) = 609 000 N
= 609 kN
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GAS PRESSURE MEASUREMENT
[g = 10 ms-2] [ρ of mercury = 13,600 kg/m3]
1. BAROMETER
The mercury is pushed up the bore in the
middle and forms a column. The higher the
column has, the higher the pressure.
Mercury is used instead of water because of
its high density. Mercury is 13.6x denser
than water. This means that if water was
used instead, the column would be 13.6x
taller.
The atmospheric pressure acts on the
mercury (Hg) in the reservoir container,
applying a downward force to it.
Atmospheric pressure is given as 760
mmHg, but what is this value in Pascals?
(iv)
P = ρgh
= 13600 x 10 x 0.76m
= 103,360 Pa
2. MANOMETER
Manometers are used to find pressures of
fluids of interest. It does this by making a
comparison to atmospheric pressure (which
is already known). Atmospheric pressure is
given as either 760mmHg or 101kPa.
The difference in height (Δh) of the
column is used to calculate the pressure of
the gas.
(i) If the difference in height of both columns is 30mm, what is the unknown pressure in mmHg?
Pressure = 760 + 30 = 790 mmHg
(ii) What is the unknown pressure of the gas, in Pascals?
P = ρgh
= 13600 x 10 x 0.79 = 107 440 Pa
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HYDRAULIC LIFTS
The diagram above illustrates a hydraulic press model demonstrating the relationship between the
pressures of a plunger/piston, liquid and ram. When the plunger is pushed down with a pressure at
P1, it exerts the SAME PRESSURE in P2.
This is denoted by Pascal’s Law, which states:
THE PRESSURE APPLIED TO A POINT IN AN INCOMPRESSIBLE FLUID IS EVENLY
DISTRIBUTED TO ALL POINTS IN THAT FLUID.
Devices following this model act as force multipliers and can be used for lifting heavy objects
by applying small amounts of force. This also explains why a force as small as a foot on a pedal
could stop a moving car.
Example Question: If a 20N force is applied to the piston:
(i)
(ii)
(iii)
Calculate the pressure exerted on the liquid by the small piston.
Determine the pressure on the large piston.
Calculate the force exerted by the large piston on the load:
(i)
P=F/A
= 20 / 2 = 10 Pa
(ii)
10 Pa (due to Pascal’s Law)
(iii)
P=F/A
F = P x A = 10 x 10 = 100 N
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HYDRAULIC BRAKES:
1. A force is applied on the brake pedal. This acts as a lever to exert a force against the master
cylinder.
2. The master cylinder has a small surface area, so its pressure is large. Pascal’s Law ensures
this large pressure is distributed to the brake oil and to the four wheel cylinders.
3. The four wheel cylinders fill with brake oil and expand evenly.
4. The wheel cylinders push against the brake shoes, which press against the brake drum. The
friction from this eventually decelerates or stops the automobile.
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PHYSICS, SECTION B (1/2) – STUDY AND NATURE OF HEAT
Heat is a form of energy that is transferred from areas of higher temperature to lower
temperature until the objects and their surroundings are at equilibrium, the same temperature.
CALORIC THEORY
Heat was once believed to be a weightless
HOW WAS THIS DISPROVED?
Count Rumford, during his cannon-boring
fluid called “caloric” that could flow from
experiments, was able to generate large
hotter to colder bodies. If a gas was
compressed, the concentration of caloric
would increase in the gas and the gas would
become hotter. This theory is now obsolete.
amounts of heat to boil water. This occurred
due to kinetic energy being converted to
heat energy by friction, as later proved by
James Joule. This showed that heat could be
developed due to the application of
mechanical energy and that it was indeed a
form of energy, not a fluid.
KINETIC THEORY
The theory used today is called the Kinetic Theory of Matter, which states that molecules in a
gas move freely and rapidly along straight lines. This random molecular bombardment can be
observed with light reflecting off dust or smoke particles (BROWNIAN MOTION).
Application of heat to molecules is able to add KINETIC energy, allowing the molecules to move
and collide more often. Heat is also able to break their intermolecular bonds and change state of
matter, e.g. adding heat to a solid weakens its bonds and turns it into liquid.
Quantity
Bond Strength
Density
Volume
Other Notes
Solid
Highest
Highest
Lowest
Molecules vibrate in place. Fixed shape.
Liquid
Gas
Takes shape of container, just like gases.
Lowest
Lowest
Highest
Most KE. Molecules in haphazard motion.
TEMPERATURE AND THE KELVIN UNIT
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Heat represents the total amount of energy (due to molecular vibrations) in a substance, the
temperature represents the average energy per molecule. A ‘cold’ substance such as an iceberg
contains more heat energy in it compared to a lit match, though the lit match’s temperature would
be higher.
The S.I. unit for temperature is given as KELVIN (K) To find the temperature in Kelvin, we
simply add 273 to the Celsius value. Calculate these:
Temperature
Kelvin (K)
Celsius (oC)
Equivalent to the temperature of…
Lower Fixed Point
-273
0
Pure melting ice at 1 atm
Upper Fixed Point
373
100
Pure dry steam at 1 atm
Absolute Zero
0
-273
Having no internal energy in system
It should be noted that absolute zero is the temperature at which there is no internal or thermal
energy in a state of matter. Put simply, it is the coldest possible temperature. Therefore, since
absolute zero is 0K, there are no negative Kelvin values.
THERMOMETERS AND TEMPERATURE MEASUREMENT
The main idea of constructing a thermometer is to find a physical property that changes steadily
with temperature and accurately link the fixed changes, e.g. when mercury is heated, it expands
proportionately and moves along the bore of the thermometer.
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COMPARING THE THREE THERMOMETERS
NOTE: Mercury is preferred to alcohol
because it has a much higher boiling point
(357oC) whereas alcohol’s is 78oC.
Thermometer
Response Factor
Range
Structural adaptation or advantages
Liquid-in-glass
Expansion of
mercury
-10 – 110 oC
Long stem for wide range of readings.
Clinical
Expansion of
mercury
35 – 45 oC
Large, thin bulb conducts heat quickly.
Small range. Constriction prevents
mercury from returning to bulb quickly.
Thermocouple
Voltage
-200 – 1250 oC
Quick, accurate readings. Can measure
from junctions of small masses.
FACTORS THAT AFFECT LIQUID-IN-GLASS THERMOMETER’S PERFORMANCE
Increase range
Increase sensitivity
Increase responsiveness
Longer stem.
Narrow bore.
More conductive fluid.
Less expansive liquid.
Larger bulb.
Thinner glass around bulb.
THERMAL EXPANSION
In a solid, the molecules are held closely together. When they are heated, kinetic energy is added
to the molecules, making them vibrate faster. This causes the molecules to move apart and
increase their volume. This is known as THERMAL EXPANSION.
This phenomenon can be observed in several everyday situations, such as creaking roofs, power
lines sagging on hot days (due to expansion), running warm water over a jar lid that is too hard
to open and even in carbonated beverages. When beverages get warm, the CO2 bubbles expand
and escape, leaving it with a ‘flat’ taste. In the cold, the bubbles contract and stay within the
drink.
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BIMETALLIC STRIPS
The bimetallic strip consists of 2 strips of different metals which expand at different rates as they
are heated, usually steel/iron and copper/brass. The different expansions force the flat strip to
bend one way if heated & in the opposite direction if cooled below its normal temperature.
In the circuit, the bimetallic strip (when
heated) would bend towards the contact to
allow electricity to flow. This effect is used
in a range of mechanical & electrical
devices, such as thermostats and fire alarms
THE GREENHOUSE EFFECT
Whether or not radiated heat can penetrate
glass depends on wavelength. Heat is
mostly carried by infra-red waves (and
some UV). Short wavelengths have higher
frequencies and higher amounts of energy,
and therefore more penetrative ability than
longer wavelengths.
Waves lose energy as they reflect off surfaces.
Therefore, the short wavelengths that were
able to penetrate the glass cannot escape once
they convert to long wavelengths when they
are reflected inside.
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EVAPORATION
Evaporation requires heat and is a cooling process. If you come out of a pool in a dry sunny day,
the water on your skin will use the heat energy from your body to evaporate. This produces the
"cooling effect".
At any temperature, the molecules of a liquid are in continuous random motion with different
speeds. Heat is absorbed by the liquid from the surroundings and thus gain KE and move
FASTER. At the surface, the more energetic molecules are able to escape into the atmosphere.
Since the molecules with the most heat energy escape, this cools the liquid.
It should be noted that evaporation only
occurs on the SURFACE of a liquid, so
DEPTH has no effect on rate of evaporation.
In what order would the vessels evaporate?
Other factors that affect evaporation include: HUMIDITY, AIR MOVEMENT,
PRESSURE, TEMPERATURE
HOW IS EVAPORATION DIFFERENT FROM BOILING?
Feature
Evaporation
Boiling
Temperature it occurs
Any temperature.
At boiling point.
Temperature change
Decreases.
Remains constant.
Location
At surface.
Throughout liquid.
Physical observation
Bubbles absent.
Bubbles present.
PERSPIRATION
When you perspire, heat is conducted into
your sweat and then moves out of the body
via the sweat gland and duct. The sweat,
with the heat, is then evaporated into the
atmosphere. This shows that evaporation is a
cooling process.
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THERMAL TRANSFER PROCESSES
Heat can be transferred from one place to
the next. When two objects of varying
temperatures are placed together, a transfer
of thermal energy occurs from HIGHER to
LOWER temperature in an attempt to get
both objects at the same temperature.
e.g. cold water left in a 30oC room will gain
heat from the room and eventually have a
temp. of 30oC. The room loses a little heat.
This transfer occurs via three processes:
Method
Definition
Example
CONDUCTION
The transfer of heat through the
vibrations of molecules to adjacent
molecules.
Heat moving along the
metallic frame of a frying pan.
CONVECTION
The transfer of heat through the
movement of the medium itself.
Smoke particles rising from a
fire. Water particles rising in a
boiling pot. Losing body heat
through sweating.
RADIATION
The transfer of heat through the flow
of electromagnetic waves. (can occur
in a vacuum)
Heat from the Sun reaching
the Earth. Heat leaving the
body after vigorous exercise.
THERMAL CONDUCTORS AND INSULATORS
•
Simply put, thermal conductors are materials that allow heat to pass easily. Conductors
are materials with free electrons (such as metals), which allow the efficient transfer of
heat.
•
Insulators do not have many free electrons and may have structural gaps or air spaces
that do not efficiently transfer heat, such as cloth or polystyrene. Air is a POOR
CONDUCTOR of heat..
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VACUUM FLASKS
A vacuum flask is a container that is designed to retain the heat in a liquid.
ABSORPTION AND REFLECTION OF THERMAL RADIATION
Materials of various textures and colour, absorb, emit and reflect different amounts of heat. Note
that good absorbers are also good emitters of heat. Would a Caribbean house roof be a good
reflector or emitter? What about a car radiator? Or a car windscreen shade?
Good absorbers
Good reflectors
Black colour
White colour
Dull / Matt
Shiny / Glossy
Rough texture
Smooth texture
Small surface area
Large surface area
SOLAR WATER HEATER
The purpose of a solar water heater is
convert solar energy into useable heat
energy. It consists of a solar panel, water
tank and an insulated frame.
The black copper pipes absorb any
radiated heat from the Sun and
conduct the heat into the flowing
water. The glass pane mimics the
Greenhouse effect and traps heat
inside.
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CONVECTION CURRENTS
1. How do the heated water molecules move?
They rise as they spread out and become less
dense.
2. When these molecules reach the surface,
what happens? The more energetic
molecules leave the surface.
The diagram above shows a metal pan
3. What happens to the temperature of the
placed on a hot plate. The objective is to
surface after? As heat is lost, the
illustrate the movement of water molecules
temperature of the surface decreases.
inside the pan.
4. How can one prevent heat from escaping
To determine this, we must answer the
following questions:
from the pan? Place a lid, which will
prevent convection from occurring.
ACTION OF SEA BREEZES
Sea breezes are another example of convection currents. Note the diagram below and compare it
to the heated metal pan above.
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PHYSICS, SECTION B PT. (2/2) – RELATIONSHIPS OF HEAT
SPECIFIC HEAT CAPACITY
Observe the diagrams above. The same mass, 1kg, of two different liquid samples are placed in
beakers A and B. Both samples had the same initial temperature (30oC). Both beakers are heated
for the same time (60s) with the burners set at the same power (70W). However, at the end, the
final temperatures differed.
Sample A required more heat to change its temperature. Sample A was thus said to be have a
HIGHER SPECIFIC HEAT CAPACITY.
The Specific Heat Capacity is defined as THE AMOUNT OF HEAT REQUIRED TO
CHANGE THE TEMPERATURE OF 1KG OF A SUBSTANCE BY 1K.
Note the formula and unit for Specific Heat Capacity:
NOTE: The specific heat capacity of water is given as 4200J/(kg K). What this means is that 1kg
of water would require 4200J of heat to increase its temperature by 1K. Similarly, it would have
to lose 4200J of heat to decrease its temperature by 1K.
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HEAT CAPACITY is defined as:
THE AMOUNT OF HEAT REQUIRED TO CHANGE THE TEMPERATURE OF A
BODY BY 1K.
Note the formula and unit for Heat Capacity:
While SPECIFIC HEAT CAPACITY is used for materials and is a constant that only accounts
per kg, HEAT CAPACITY is used for bodies and is dependent on the mass of that body.
For example, while the specific heat capacity of pure water is 4200 J/(kg K), the heat capacity of
a 10kg body of pure water is 42000 J/K (using C = mc). What this means is that 42000J of heat is
required to raise the temperature of that 10kg body of water by 1K.
TESTING FOR SPECIFIC HEAT CAPACITY, METHOD ONE (CALORIMETER)
The setup is called a CALORIMETER, an
apparatus used to measure specific heat
capacity. The following must be known to
calculate specific heat capacity.
- Mass of material
- Voltage and current (P = IV)
- Time
(E = IVt)
The metal aluminum block is heated for 3
minutes with a 5A, 10V supply. If the initial
and final temperatures of the 2kg block are
30oC and 35oC respectively, calculate its
specific heat capacity.
E = IVt = 5 x 10 x (3 x 60) = 9000 J
E = mcΔT
c = E ÷ (mΔT) = 9000 ÷ (2 x 5)
= 900 J/kg oC
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METHOD TWO (METHOD OF MIXTURES)
Since the specific heat capacity of pure
water is already known (4200J/(kg K) or
4.2 J/(g K)), this value could be used to
determine the SHC of another material. The
principle to remember is:
Heat gained by water = Heat lost by metal
By measuring the initial and final
temperatures of both the water and metal,
the following formula can be used:
mcΔT (water) = mcΔT (substance)
Example question: A 50g block is placed in 200g of water. The block was heated to 100oC. The
temperature of the block dropped to 30oC and the water rose from 30oC to 35oC.
Using 4.2J/(g K) as the SHC of water, calculate the SHC of the block, in J/(g K).
mcΔT (water) = mcΔT (block)
200 x 4.2 x 5 = 50 x c x (100 – 30)
4200
c
= 3500 c
= 4200 ÷ 3500 = 1.2 J/g K
Example question 2: A piece of iron of mass 21.5g at a temperature of 100.0oC is dropped into an
insulated container of water. The mass of the water is 132g and its temperature rose from 20.0oC
to 21.4oC. The iron’s final temperature is 19.6oC. Using 4.2J/(g K) as the specific heat capacity of
water, calculate the specific heat capacity of iron.
mcΔT (water) = mcΔT (iron)
132 x 4.2 x 1.4
= 21.5 x c x (100 – 19.6)
776.16
= 1728.6 c
c
= 776.16 ÷ 1728.6 = 0.45 J/g K
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SPECIFIC LATENT HEAT
Graph showing cooling curve of naphthalene
Observe the sections of the graph where there are no temperature changes. Heat is still being lost
at these points, but without temp. change. This type is heat is known as LATENT HEAT.
Latent heat is thermal energy being used to either reform intermolecular bonds or break them.
This type of heat is lost or gained only during changes in state of matter, i.e. freezing, melting,
condensation, boiling.
Quantity
Definition
Formula
Specific Latent Heat of
THE AMOUNT OF HEAT ENERGY
E = mLf
FUSION
REQUIRED TO CHANGE 1KG OF A
SOLID TO A LIQUID WITHOUT A
TEMPERATURE CHANGE.
E = Energy (J)
m = mass (kg)
L = Latent heat (J/kg)
Specific Latent Heat of
VAPOURIZATION
THE AMOUNT OF HEAT ENERGY
REQUIRED TO CHANGE 1KG OF A
LIQUID TO A GAS WITHOUT A
TEMPERATURE CHANGE.
E = mLv
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EXAMPLE QUESTION
A student heats 200g of ice at 0oC until it turns to steam at 100oC. How much energy was needed
to do this?
[specific heat capacity of water = 4200 J/(kg K)]
[specific latent heat of fusion of ice = 3.36 x 105 J/kg]
[specific latent heat of vapourization of water = 2.25 x 106 J/kg]
E = mLf
= 0.2 x (3.36 x 105)
= 67200 J
E = mcΔT
= 0.2 x 4200 x 100
= 84000 J
E = mLv
= 0.2 x (2.25 x 106) = 450 000 J
E (total) = mLf + mcΔT + mLv = 601 200 J
TESTING FOR SPECIFIC LATENT HEAT OF FUSION OF ICE
(Heat Lost by Water) = (Heat Used to Melt Ice) + (Heat Gained by Melted Ice)
Calculate, in order, the following: [SHC of water = 4.2 J/(g K)]
(i)
The heat energy lost by the water
(iii) The heat used to melt the ice
(i)
(ii)
(iii)
E = mcΔT = 100 x 4.2 x 10 = 4200 J
E = mcΔT = 10 x 4.2 x 20 = 840 J
ΔE = 4200 – 840 = 3360 J
(iv)
E = mLv
Lv = E ÷ m = 3360 / 10 = 336 J/g
(ii) The heat energy gained by the melted ice
(iv) The specific latent heat of fusion of ice
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AIR PRESSURE AND THE THREE GAS LAWS
First, it is important to understand what exactly creates air pressure. Air pressure is caused by the
random motion of gas molecules (Kinetic Theory of Matter) and their collisions with the
surfaces of objects (not the molecules hitting each other!)
The greater the frequency of collisions or the greater the force the air molecules collide with
the surfaces, the greater the pressure.
There are three quantities that are examined with each of the gas laws: Pressure, Volume and
Temperature. For each law, two of these quantities vary while one is kept constant.
Boyle’s Law states that FOR A FIXED MASS OF GAS AT CONSTANT
TEMPERATURE, PRESSURE AND VOLUME ARE DIRECTLY PROPORTIONAL.
It can be represented by the equation: P1V1 = P2V2 or PV = k
The lower the volume, the less
space the molecules have when
they are moving. Due to this, they
collide more often, increasing the
pressure.
Calculate the pressure in the 20cm and 10cm cylinders, in kPa.
For 20cm3 cylinder:
For 10cm3 cylinder:
P1V1 = P2V2
P1V1 = P2V2
2 x 30 = P2 x 20
2 x 30 = P2 x 10
P2
P2
= 60 ÷ 20 = 3 kPa
= 60 ÷ 10 = 6 kPa
Boyle’s Law can be graphed as shown below.
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Charles’ Law states that FOR A FIXED MASS OF GAS AT CONSTANT PRESSURE,
VOLUME IS DIRECTLY PROPORTIONAL TO TEMPERATURE.
It can be represented by the equation:
The pressure is made constant by increasing volume. This means that as heat increases, there is
more space for the molecules to move, so they don’t collide against the surfaces as often,
despite moving faster and hitting with greater force.
(i) A gas at 27oC was heated, which
caused the gas to expand and push
the syringe upwards. Pressure
remained constant. If the volume
increased from 30cm3 to 50cm3, what
is the final temperature?
(ii) What would be the temperature to raise the volume to 60cm3?
Answer = 600 K
There are two graphs used to represent Charles’ Law, depending whether or not the Kelvin or
Celcius scale is used as the unit for temperature.
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Pressure Law states that FOR A FIXED MASS OF GAS AT CONSTANT VOLUME,
PRESSURE AND TEMPERATURE ARE DIRECTLY PROPORTIONAL.
It can be represented by the equation:
Why does pressure increase with
At absolute zero, there will be in the
temperature? This is because as the
substance. This is because at this
molecules are heated, they gain more kinetic
temperature, the molecules have no internal
energy and collide against the walls at a
or kinetic energy and do not move, thus they
greater rate and with greater force.
cannot collide against the walls and create
pressure.
Two graphs may represent the Pressure Law, depending on whether Kelvin or Celcius is used as
the unit for temperature.
COMBINED GAS LAW / GENERAL GAS LAW
All three gas laws can be combined to form one formula called the General Gas Law. This is
employed when no quantity remains constant. The formula for it is a combination of all three
gas laws and is stated as:
NOTE: Not to be confused with the IDEAL GAS LAW, which will be learned at A’ Level.
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PHYSICS, SECTION C (1/1) : WAVES AND OPTICS
WAVE FEATURES
Waves carry energy without carrying matter. Some waves must propagate through a medium.
They involve oscillations, where there can be just one oscillation (called a PULSE) or a series or
succession of oscillations (called a PROGRESSING WAVE).
Waves that require a medium to be transferred are termed MECHANICAL waves, while those
that can travel through a vacuum are classed as ELECTROMAGNETIC.
Feature of Wave
Definition
IN PHASE
Points on successive waves that lie on the same position
WAVELENGTH
Distance between two successive crests, troughs or points in phase
AMPLITUDE
Height of a wave, indicating its maximum displacement
FREQUENCY
Number of waves passing a point per second (measured in Hz)
PERIOD
Time taken for a wave’s complete oscillation (measured in s)
3 waves = 6m
1 wave = 2m
3 waves = 1 second
1 wave = 1/3 second
(period)
The VELOCITY of the wave can
be found by the following formula:
v = fλ
Question: Calculate the wavelength and velocity of the waveform above. Other formulas:
Wavelength => 6m ÷ 3 = 2m
Velocity ➔ v = fλ = 3 x 2 = 6 m/s
Frequency = No. of waves
Time
Period (T) = 1 ÷ Frequency
Frequency = 1 ÷ T
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Wave Phenomenon
Description
REFLECTION
All waves can bounce off a surface.
REFRACTION
All waves bend or change direction when entering another medium.
DIFFRACTION
All waves can curve or bend through narrow openings and edges.
INTERFERENCE
All waves can fuse, increasing or decreasing their amplitude.
DISPERSION
Light can split into different colours. Note that light waves with
only one frequency (MONOCHROMATIC) cannot do this.
TRANSVERSE and LONGITUDINAL WAVES
Transverse
Longitudinal
Has CRESTS and TROUGHS.
Has COMPRESSIONS and RAREFACTIONS.
Displacement of particles is
PERPENDICULAR to propagation of wave.
Displacement of particles is PARALLEL to
propagation of wave.
Examples: Any wave from the e.m. spectrum
(radio, visible light, microwaves, gamma rays)
Examples: Sound and some seismic waves.
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SOUND WAVES
Sound is transferred by LONGITUDINAL waves that are MECHANICAL in nature, meaning
that they require molecules or a medium for their transfer. They are unable to travel through a
vacuum such as in space.
The presence of more molecules enables
sound to increase its speed. This means that
sound will travel faster in denser states of
matter, e.g.
State
Medium
Approx. Speed of Sound in m/s
Gas
Air
330
Liquid
Water
1500
Solid
Steel
5000
Sounds can have different pitches or
volumes. The PITCH of a sound is
dependent on its FREQUENCY while its
LOUDNESS is dependent on its
AMPLITUDE for e.g. a mouse’s squeak has
The human audible range is
high-freq, low-amp. A loudspeaker’s bass
has low-freq, high-amp.
Ultrasound has numerous practical
applications, including the observation of
fetuses in their pre-natal stages, ultrasonic
cleaning (dental scalers, jewelry cleaning)
and probing materials for internal flaws.
20Hz - 20000Hz. Any wave with a
frequency higher than that range is termed
an ULTRASOUND wave.
ECHOES AND SONAR
SONAR (Sound Navigation and Ranging) is
a technology that uses ultrasound pulses to
determine distances.
It does this by measuring the time it takes
for a fired sound pulse of known speed to be
emitted from a transducer, echo from a
surface and be received by a detector. The
formula for calculation is given as: s = 2d
t
Question: If the speed of sound in sea water is 1600 m/s and the time taken for the sound pulse to
hit the sea bed and return to the detector is 400 ms, calculate the depth of the sea bed, in km.
s = 2d ➔ 2d = s x t
t
2d = 1600 x 0.4s = 640m
d = 640 ÷ 2 = 320m = 0.32km
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REMEMBER THE ORDER:
Rich Men in Vegas Use Xpensive Gadgets
THE ELECTROMAGNETIC (E.M.) SPECTRUM
This is from lowest to highest frequency.
The electromagnetic spectrum refers to the range of wavelengths or frequencies of
electromagnetic radiation. All of them are transverse and all travel at 3 x 108 m/s in a vacuum.
ORDER FROM SHORTEST TO LONGEST WAVELENGTH
NAME
SOURCE
APPLICATIONS
Gamma-rays
Radioactive decay
- Penetrates matter.
X-rays
Electron bombardment
against an anode
Ultra-violet
Ultra-heated bodies (such
as the Sun)
- Causes fluorescence.
- Gamma-rays are useful in killing cancer cells.
- Tanning beds
- Fluorescent lights
- Used to sterilize medical equipment.
Visible light
Emission of excited
electrons.
- Detected by stimulating nerve endings of human
retina.
Incandescent bodies.
- Used in optical fibres in telecommunications, as
well as in medicine.
Infra-red
Heated bodies.
- Our bodies emit this type of wave.
- Detection of bodies and matter.
Microwaves
Magnetron circuits.
- Radar and telephone communication
Radiowaves
Transmitters.
- Radio broadcasting or telescopes.
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DIFFRACTION
Diffraction occurs when a wave passes through a narrow aperture (opening) and thus spread out
over a large area as it continues to progress. All waves can undergo diffraction.
NOTE: It is difficult to observe diffraction of light because of its SMALL WAVELENGTH.
Special equipment would be needed for proper observation.
THEORIES OF LIGHT
Many notable scientists had differing theories of lights over the eras.
Scientist
Isaac Newton
Christiaan Huygens
Thomas Young
Albert Einstein
Theory
Light is a stream of particles called corpuscles.
Light is a transverse wave, not particles.
Light is a wave that can undergo interference.
Light behaves as both a wave and a particle. (Quantum Theory)
Einstein also came up with the photoelectric effect (for which he won the Nobel Prize). The
photoelectric effect is a phenomenon that produces electrons when light is shone on a metal plate.
Ideal examples of this are DIGITAL CAMERAS and SOLAR PANELS.
In digital cameras, the photons are of different strengths, which produces variations of brightness
and colour to translate the photograph image.
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INTERFERENCE
Interference occurs when two waves superpose with each other to form a resultant wave that
might either raise or lower the amplitude. There are two types of interference:
Destructive
interference has the
1. CONSTRUCTIVE Interference
2. DESTRUCTIVE Interference
waves being out of
phase by exactly ½ λ
The concept of interference proved that light experienced properties of a wave. The diagram
below shows Thomas Young’s double-slit experiment.
Where the waves are in phase
(CONSTRUCTIVE interference), the
crests and troughs are aligned and result
in bright fringes (called MAXIMAS).
Where the waves are out of phase
(DESTRUCTIVE interference), they
result in dark fringes (called MINIMAS).
Troughs of one wave ‘cancel’ out the
crests of another.
SHADOWS
Shadows are considered proof that LIGHT
TRAVELS IN STRAIGHT LINES.
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REFLECTION OF LIGHT
A NORMAL is an imaginary 90o line to any boundary or
surface. All angles are measured from the normal.
Reflection occurs when a wave bounces off a surface. Complete the diagrams below.
The ray would
be reflected
straight up at an
angle of 0o.
ϴi = angle
of incidence
ϴr = angle
of reflection
TWO LAWS OF REFLECTION
Law
States
First
The incident ray, normal and reflected ray all lie on the same plane.
Second
The angle of incidence is always equal to the angle of reflection. (ϴi = ϴr)
Example of a Plane Mirror Ray Diagram
The image that is formed in a mirror is called a VIRTUAL image and typically has the following
characteristics:
They are always LATERALLY INVERTED, UPRIGHT, THE SAME HEIGHT AS THE
OBJECT and THE SAME DISTANCE FROM THE MIRROR AS THE OBJECT.
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REFRACTION
Refraction occurs when a wave passes through a MEDIUM OF DIFFERING DENSITY
for example: sunlight entering a piece of glass from the air, or light exiting water.
In the diagram, the light is reflected off the
fish and enters the person’s eye.
However, because the light has to move
across a different medium (water to air), it
refracts and the image of the fish seems
closer than it really is.
Characteristic of Wave
Denser medium
Less dense medium
Change in direction
TOWARDS NORMAL
AWAY FROM NORMAL
Speed
DECREASES
INCREASES
Wavelength
DECREASES
INCREASES
Frequency
NO CHANGE
NO CHANGE
The diagrams below show refraction of light in two prisms.
As the ray enters the block, it bends
TOWARDS the normal. It bends AWAY
from the normal as it leaves.
White light undergoes DISPERSION in a
prism and splits into the colours of the
rainbow as it refracts.
If the block was not there, the ray would not
refract. Its change in position as a result of
refraction is called its lateral displacement.
Red has a longer wavelength than violet, so it
refracts less.
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NOTE: A wavefront is
defined as a point of
connection for molecules
that are all in phase.
WAVEFRONT DIAGRAMS
e.g. straight waves on
water or circular ripples.
Wavelength decreases.
Speed decreases.
Wave bends towards normal.
Wavelength increases.
Speed increases.
Wave bends AWAY from
normal.
Wavelength decreases.
Speed decreases.
Wave is UNDEVIATED,
meaning it does not change
direction, as it cannot bend any
more towards the normal.
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MIRAGES
Mirages occur mostly in hot places. This is
because heated air is less dense than cooler
air (which is why heated air rises).
The difference in density is important to
note, as heated air and cooler air would be
considered two separate mediums. As a
result, light would refract or bend as it
moves from one to the other.
As a result, it is as if the ground acts a
mirror, showing a reflection of the sky.
GLARE
Upon hitting a surface, light is said to be
POLARIZED. Direct light sources are
unpolarized. If both a polarized and
unpolarized light source enter the eye
simultaneously, this results in a blurry visual
called glare.
LAWS OF REFRACTION
Law
States
First
The incident ray, normal and refracted ray all lie on the same plane.
Second
The refractive index is equal to the ratio of the sines of the angles of incidence and
refraction.
(also called
Snell’s Law)
Represented as the formula: n = sin i
sin r
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CRITICAL ANGLE AND TOTAL INTERNAL REFLECTION
The critical angle can be defined as:
an angle of incidence that produces an
angle of refraction of 90o.
We have now understood the concept that light refracts away from the normal when entering a
less dense medium. However, if the angle of incidence is too LARGE, it will be unable to be
refracted in such a way to escape.
The point at which the angle of refraction is equal to 90o is called the CRITICAL ANGLE. The
angle of refraction cannot be more than 90o. Instead, TOTAL INTERNAL REFLECTION will
occur, keeping the light inside the medium. In other words, the insides behave like a mirror.
APPLICATIONS OF TOTAL INTERNAL REFLECTION
Optical fibres are usually held in bundles to
carry data at high speeds. They may be used
as ENDOSCOPE, an instrument that is put
into the body to view the internal parts.
Light is shot into the fibre and it is reflected
back up to a detector with images.
Optical fibres are made of a core of high
refractive index and surrounded by cladding
that is LESS DENSE than the core.
The incident ray is shone
at an angle greater than the
critical angle so that it
keeps reflecting over and
over again in the fibre.
Another example of total internal reflection would be in the use of road reflectors, which are
usually right-angled prisms that reflect light back to a vehicle.
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REFRACTIVE INDEX
The refractive index of a material, put simply, tells how optically dense an object is. The higher
the refractive index, the slower the light will travel. For example, if a glass has a refractive index
of 1.5, this means light will travel 1.5x more slowly in glass than in a vacuum.
The refractive index (n) can be properly defined as THE RATIO OF THE SINES OF THE
ANGLES OF INCIDENCE AND REFRACTION OF A RAY PASSING FROM ONE
MEDIUM TO ANOTHER.
In order to calculate this refractive index, we may use either of these formulas:
Example question 1:
(i) Calculate the refractive index of light
passing from Medium A to B.
n = sinϴ1 ÷ sinϴ2
= sin60 ÷ sin45
= 1.22
(ii) If the angle of the ray in Medium A was increased to 45o, what would be the new angle of
refraction?
n = sinϴ1 ÷ sinϴ2
sinϴ2 = sinϴ1 ÷ n
= sin45 ÷ 1.22 = 0.58
Angle = sin-1 0.58 = 35.42o
(iii) What is the speed of light through Medium B?
n = speed (vacuum) ÷ speed (medium)
speed (med) = speed (vacuum) ÷ n
= (3 x 108) ÷ 1.22
= 2.46 x 108 m/s
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Example question 2: A manufacturer was asked to investigate the relationship between
angles of incidence, θi, and refraction, θr, for a certain type of fibre glass to build an
optical fibre. The results are shown below.
Θi / o
30.0
40.0
50.0
60.0
70.0
80.0
Θr / o
23.6
30.5
38.0
43.7
48.5
52.0
sin i
0.50
0.64
0.77
0.87
0.94
0.98
sin r
0.40
0.51
0.62
0.69
0.75
0.79
(a) (i) Complete the table above for both sin i and sin r.
(i)
Plot a graph of sin i vs. sin r below.
(b)(i) Calculate the gradient of the line.
Gradient = y2 – y1
x2 – x1
= 0.98 – 0.64
0.79 – 0.51
= 1.21
(This also represents the refractive
index.)
(ii) Calculate the critical angle of fibre glass.
n=1
sin c
sin c = 1 = 1
= 0.83
n
1.21
c = sin-1 0.83 = 56.1o
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LENSES
Type
Diagram
Example
CONVEX
(converging)
Magnifying glass,
microscope
CONCAVE
(diverging)
Flashlights, peepholes,
lenses for shortsighted
people
Example question: An object of 4cm height is placed 6cm distance from the optical center of a
lens. It produces a 20cm height image. Calculate:
(i) The magnification of the lens
M = hi ÷ ho
= 20 ÷ 4
=5
(iii) The focal length of the lens
1/f = 1/u + 1/v
1 = 1 + 1
f
20 + 30
3 + 2 =
60
(ii) The image distance
M = di ÷ do
di = M x do
=5x6
= 30cm
5
60
Invert => f = 60/5 = 12cm
(i) Principal axis – A horizontal line cutting across the optical centre.
(ii) Focal length – The distance between the lens’ centre and the focal point.
(iii) Principal focus – The point at which the light rays converge.
(iv) Focal plane – A vertical line cutting the focal point.
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Object between F and 2F
Object between F and optical centre
Object beyond 2F
Object at F
Concave Lens Diagram
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PHYSICS, SECTION D (1/2) – ELECTROSTATICS AND CIRCUITS
STATIC ELECTRICITY AND ATTRACTION
Electrostatics is the study of charges at rest. When two insulators are rubbed together, they can
produce electrostatic attraction. Matter is made of atoms which have negatively charged
particles called ELECTRONS orbiting around a small nucleus.
In the normal state, the atom has an equal number of electrons and protons, therefore we say that
it is electrically balanced or uncharged. At times, when rubbing a surface, electrons are removed
from the orbit and the object becomes POSITIVELY charged. The object that the electrons
rubbed off on then become NEGATIVELY charged.
It should be noted that only the electrons will move
because they are much lighter than protons. Protons are
also bound to the nucleus, which make them unlikely to
move due to friction.
If a plastic rod was used, it would gain electrons instead.
Note the formula for charge: Q = It
Q = Charge (C)
I = Current (A)
t = time (s)
Charge is measured in COULOMBS. One coulomb is equivalent to 6.25 x 1018 electrons. Devices
that store charge are called CAPACITORS. and gain current as time passes. It should be noted
that time plays a major factor in terms of charge.
Example questions: 1. During a certain lightning strike, a current of 5 x 104 A flows for a time
period of 0.15 ms. Calculate the quantity of charge of the lightning strike.
Q = It
= (5 x 104) x (0.15 x 10-3) = 7.5C
2. The makers of a cellphone have upgraded its battery capacity from 4320C to 9000C. If a
charger delivers 0.6A, how much more time will it take to charge the new battery than the old?
ΔQ = 9000 – 4320 = 4680 C
Δt = ΔQ ÷ I = 4680 ÷ 0.6
= 7800 s (or 130 mins)
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POTENTIAL DIFFERENCE
kinetic energy based on differences in height
(such as a river flowing downstream),
p.d. refers to the energy that generates an
e.m.f. (electromotive force), allowing
charges to flow to a component.
Potential difference (or p.d.) is simply
another term for voltage. Similar to how
gravitational potential may convert to
For e.g. the laptop has to have a lower p.d.
than the solar cell for the charges to flow
from the solar cell to the laptop. If the laptop
had a higher p.d. than the solar cell, the
laptop would charge the solar cell instead.
CHARGING BY INDUCTION
Objects can also be charged by placing them next to each other and using a charged rod within
proximity. This method is called charging by INDUCTION.
Examples of technology that employ electrostatic forces are: PHOTOCOPYING MACHINES,
ELECTROSTATIC PAINTING, ELECTROSTATIC SMOKE PRECIPITATORS.
ELECTRIC FIELDS
An electric field is defined as a region around a charged particle or object within which a force
would be exerted on other charged particles or objects.
Electric fields flow outward from
+ve charges and inward from –ve
charges.
So they always flow from positive
to negative.
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CIRCUIT COMPONENTS
Component
Circuit Symbol
Note
Dry cell / Battery
Converts chemical to electrical energy.
Switch
Controls paths of electron flow.
Fixed Resistor
Decreases current, value is constant.
Variable Resistor (rheostat)
Decreases current, value can adjust.
Bulb / Lamp
Converts electricity to light + heat.
Voltmeter
Measures voltage. Connected in parallel.
Ammeter
Measures current. Connected in series.
Fuse
Breaks circuit path if current is too high
Semiconductor diode
Converts a.c. voltage to d.c. voltage.
a.c. Power Source
Typically a power outlet.
Motor
Converts electrical to mechanical energy.
Transformer
Alters voltage by altering current.
Galvanometer
Deflects needle due to small currents.
Heater
Generates thermal energy.
Bell
Releases sound energy.
Thermistor
Resistance reduces when temperature
increases.
Photoresistor / LDR
(Light-Dependent Resistor)
Resistance reduces when light intensity
increases.
LED (Light-Emitting
Semiconductor light source. Releases
Diode)
photons. Very efficient.
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WHAT IS THE DIFFERENCE BETWEEN CURRENT AND VOLTAGE?
Quantity
Definition
Unit
Derivation of Unit
Voltage
The amount of energy per unit charge.
Volt (V)
1V = 1 J/C
Current
The amount of coulombs passing a point per
second.
Ampere
(A)
1A = 1 C/s
Resistance
A measure in the opposition of the flow of
current.
Ohm
(Ω)
1Ω = 1 V/A
The general formula that links each quantity above is:
This is also called OHM’S LAW, which states that
THE CURRENT THROUGH A CONDUCTOR BETWEEN TWO POINTS IS DIRECTLY
PROPORTIONAL TO VOLTAGE AND INVERSELY PROPORTIONAL TO RESISTANCE.
Measuring Voltage and Current
Instrument
Measures
How it is hooked up
Why?
AMMETER
Current.
IN SERIES
It has a very low resistance, so as
to not affect the circuit.
VOLTMETER
Voltage.
GALVANOMETER Direction of small
amounts of
IN PARALLEL
It has a high resistance, which
could affect the circuit in series.
Same as ammeter.
Same as ammeter.
current.
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WIRES AND RESISTANCE
Factor
Explanation
LENGTH
Long wires have higher resistances than shorter ones. More power loss
tends to occur along far distances. Electrical energy converts to heat.
THICKNESS
Wires of thick diameter have more conducting material and thus can
transfer more current. The thicker the wire, the lower the resistance.
CONDUCTOR
Wires made of good conducting material, e.g. copper have low resistance.
DIRECT AND ALTERNATING CURRENT
Alternating current is specific type of
electric current in which the direction of the
current's flow is REVERSED on a regular
An a.c. voltage can be converted to d.c.
voltage using a SEMICONDUCTOR
DIODE or RECTIFIER.
basis. The magnitude of the voltage
produced FLUCTUATES a.c. voltages are
found in:
Power lines, transformers, power outlets
Direct current is simply when it flows in
ONE DIRECTION at all times. It has a
FIXED magnitude. d.c. voltages are found
in: Cell phone battery, laptop battery, simple
electromagnet, hybrid vehicles
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PRIMARY AND SECONDARY BATTERY CELLS
Batteries can be divided in two categories: primary cells and secondary cells.
Characteristic
Primary cell (Dry Cell)
Secondary cell (Wet Cell)
Rechargeability
Absent.
Present.
Portability
High (small size)
Low (usually larger size)
Terminal Voltage
Lower (e.g. AA = 1.5V)
Higher (e.g. Car = 12V)
Internal Resistance
Higher
Lower
Structure
Zinc anode, carbon cathode,
contains a powder or paste
of MnO2.
Sulphuric acid electrolyte
with lead plates. Or lithiumion batteries. Liquid
electrolyte.
RECHARGING A BATTERY CELL
Secondary batteries (which are d.c.) are
recharged when they are connected to a.c.
supplies (such as outlets).
A TRANSFORMER steps down the voltage
from the outlet and a RECTIFIER converts
the a.c. voltage to d.c to flow into the battery
and be stored.
VI-GRAPHS
Components that obey the relationship given by Ohm’s Law are said to be OHMIC while components
that don’t, such as filaments lamps and diodes are said to be NON-OHMIC.
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DETERMINING RESISTANCE OF AN UNKNOWN RESISTOR, R
The apparatus is set up as shown in both methods with the ammeter in series with the resistor and
the voltmeter in parallel. However, the methods differ when it comes to obtaining different values
of current. In Method 1, the length of the resistance wire ‘d’ is varied by connecting the contact at
different points (recall that longer wires have higher resistance). In Method 2, a rheostat is used to
vary the resistance to obtain different values.
Using the setup in Method 2, a student obtained the following results. Plot a graph of V vs. I, and
find the gradient. What does the gradient represent?
V/V
2.00
3.00
4.00
5.00
6.00
I/A
0.42
0.60
0.84
1.02
1.18
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SERIES & PARALLEL CIRCUITS
Let’s analyse the simple series circuit below to state its characteristics:
If one component stops
working in a series circuit,
the circuit breaks and
current cannot travel to the
other parts in the circuit.
This is due to there being
only one pathway.
RESISTANCE IN A SERIES CIRCUIT – The total resistance in series is the sum of all
resistors in the circuit. For example, find the total resistance of a circuit which has two resistors of
10Ω and 15Ω.
FORMULA: RS = R1 + R2 ...
CALCULATION: RS = 10 + 15 = 25 Ω
CURRENT IN A SERIES CIRCUIT – The current flowing into each component in a series
circuit is equal to the current flowing out of each component. This means that each ammeter (A 1,
A2 and A3) would have the same reading. Show the calculation:
I = V/R
= 6/25 = 0.24 A
Note: Ammeters are placed in series next to the component to be observed. They have very low
resistance, so as to avoid significant alteration of the current passing through it in series.
VOLTAGE IN A SERIES CIRCUIT – The sum of the voltages of the individual components
in the circuit should equal the voltage of the power source. This means that the sum of voltages in
R1 and R2 should be equal to 6V. What are the voltages in R1 and R2?
V (R1) => V = IR
V (R2) => V = IR
= 0.24 x 10 = 2.4V
= 0.24 x 15 = 3.6V
Now recall that total voltage = 2.4 + 3.6 = 6V
Note: Voltmeters are connected in parallel to the components. They have very high resistance, so
only very small amounts of current pass through it, since voltmeters are on separate wire paths.
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Now, let’s analyse a simple parallel circuit with the same components as before.
Houses are wired in parallel.
This is because the overall
resistance is lower than series.
Also, if one component ceases
to work, the circuit is not
broken like in series, due to
other electron pathways being
available.
RESISTANCE IN A PARALLEL CIRCUIT – The total resistance in a parallel circuit is smaller than
the value of the individual resistors.
FORMULA: 1/RP = 1/R1 + 1/R2 ...
CALCULATION:
VOLTAGE IN A PARALLEL CIRCUIT – The voltage in a parallel circuit is equal on each wire.
Therefore, on this circuit, the voltage on each wire would be 6V.
CURRENT IN A PARALLEL CIRCUIT – Since the wire splits at several junctions, so does the
conducting path for the electrons. This causes the current to decrease through these paths.
Therefore, since A1 and A4 are on the same pathway, their current will be equal.
However, A2 and A3 will have different currents. The sum of A2 and A3 = A1.
Calculate the currents through A2, A3 and then use those to find the current in A1.
For A1 → I = V/R = 6/10 = 0.6A
For A2 → I = V/R = 6/15 = 0.4A
Therefore, the total voltage → 0.6 + 0.4 = 1.0A
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COMBINING SERIES AND PARALLEL CIRCUITS
In the diagram, each resistor is 6Ω. A and B are in series with each other. C is parallel to both A and B.
And resistor D is series to A, B and C combined. To simplify the circuit, we need to reduce the number of
resistors by ‘fusing’ their values.
(a)(i) Calculate the total resistance of A and B.
RS = 6 + 6 = 12 Ω
(ii) Calculate the total resistance of A, B and C.
(iii) Calculate the total resistance of A, B, C and D.
RT = 4 + 6 = 10 Ω
(b) Calculate the total current in the circuit.
I = V/R
= 12/10 = 1.2A
(c) Calculate the voltage through C. (Keep in mind that resistor D draws voltage)
Finding voltage through D
V = IR
= 1.2 x 6 = 7.2V
Therefore Voltage through A, B and C would be:
V = 12 – 7.2 = 4.8V
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POTENTIAL DIVIDERS
From the diagram, calculate the value of Vout.
Rs = 1000 + 500 = 1500 Ω
I = V/R
= 12/1500 = 0.008A
Vout = IR = 0.008 x 500 = 4V
OR → 500/1500 x 12 = 4V
Potential dividers (or potentiometers) operate simply by splitting the voltage at various points
in a circuit. They usually involve some type of variable resistor or sensor-operated resistor. They
are widely used for adjusting voltages in appliance circuits. For e.g. a radio may only need 6V
from a 9V battery. The divider splits the voltage and allows 6V to flow as a Vout value.
ELECTRICAL HAZARDS, WIRING AND FUSES
Some metals melt easily at much lower temperatures than normal. These metals can be used to
make a SAFETY FUSE. If too much electricity flows through the fuse wire, it will get so heated
that it will melt. This will BREAK THE CIRCUIT and no more CURRENT can pass. If no fuse
is present and too much current passes, there can be a risk of an electrical fire.
Circuit breakers have the same purpose of a fuse. One main difference is that fuses must be
replaced, while circuit breakers don’t have to be. Fuses act faster than breakers, however.
If an 8A current is being delivered through the live wire, which fuse will be best? 2A, 5A or 10A?
There are three types of wires:
Type of Wire
Purpose
Colour
LIVE
Delivers electrical energy and high a.c. voltages to
appliances. Connects all switches and fuses.
BROWN (or red)
NEUTRAL
Carries current back to the supply. Has roughly zero
volts.
GREY (or blue)
EARTH or
GROUND
Deposits excess electrons from the circuit into the
ground. It is connected to the appliance frame or
casing, not mains.
GREENYELLOW
Three main electrical hazards are: 1. Damp wires 2. Broken insulation in wires 3. Short circuits
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Fuses and switches are always connected to
the live wire. There is a potential danger of
the live wire becoming loose and touching
the metal case of appliances.
Touching the metal casing can then result in
electrocution. However, the ground wire
will carry those excess electrons into the
ground, so the earth wire is always
connected to a case or frame.
ELECTRICITY GENERATION & CONSERVATION
1. BOILER – An external energy source (e.g. coal, biofuel, uranium) heats water into steam.
2. TURBINES – The steam provides mechanical energy for the turbines to spin.
3. GENERATOR – The turbines spin a generator, which is a large magnet that spins in a coil.
4. TRANSFORMER – Increases voltage for power line transmission, decreases for household.
Since we are dependent on non-renewable fossil fuels, we can do a number of things to
conserve them:
1. Switch off electrical appliances and lights when not in use.
2. Convert from incandescent to LED light bulbs.
3. Find alternative methods of transport (e.g. public transport, bicycles).
4. Employ alternative sources of energy (e.g. solar, wind, biofuels).
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PHYSICS, SECTION D (2/2) – ELECTROMAGNETIC COMPONENTS
MAGNETS
A magnet is a material that has a north and south pole that could either attract or repel other
magnets or magnetic materials. Magnetic materials, however, have no poles and cannot attract
others but can be attracted by a magnet.
Nature
Material
Application
Temporary Magnet
Permanent Magnet
Can be magnetized easily.
Retains its magnetism for a long time.
Iron, mu-metal
Steel, alnico
Electromagnets, transformers
Compass needles, décor magnets, metal detectors
Magnets create fields around them, as illustrated below.
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MAGNETIC INDUCTION
When a piece of unmagnetised magnetic material (such as IRON) touches or is brought near to
the pole of a permanent magnet, it is attracted to the magnet and becomes a magnet itself. In other
words, the material is said to have been magnetically induced. It should be noted that only 3
metals can be magnetized:
By wrapping a cylindrical coil or SOLENOID around an iron core and passing d.c. through it, the
iron core will become magnetized.
The electric field
creates a magnetic
field because they are
both part of the same
electromagnetic force.
They are 90o to each
other
DEMAGNETISING A MAGNET
Method
Explanation
HEATING
Molecules begin to vibrate so quickly that domains are rearranged and the
charges at the poles disappear.
HAMMERING
Physical force rearranges domains and polar charges disappear.
A.C. VOLTAGE
The a.c. causes some domains at the magnetic poles to switch directions.
If done long enough, the polar charges will be nullified.
RELAY CIRCUITS (ELECTRIC BELL)
A typical relay circuit contains a switch that is
electromagnetically operated.
1. When the current passes through the
electromagnets, they generate a magnetic field.
2. The soft iron armature is then attracted to the
electromagnet. It is pulled towards it, and the
hammer hits the gong.
3. At the same time, the contacts are broken in the
circuit, causing current flow to cease and the
magnetic field to be lost. This restarts the circuit,
causing the bell to ring in rapid successions.
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FLOW OF CHARGES & CONVENTIONAL CURRENT
Flow of charges is different from a metal
conductor and electrolyte. In an electrolyte
(a liquid conducting material), both positive
and negative ions can flow. It can also
occur in both directions.
However, in a metal conductor, only
negative charges flow (electron flow) and
only in one direction (-ve to +ve terminals).
There is one thing to note, however. While electrons indeed do move from –ve to +ve, tradition in
the field of Physics is to work the opposite way. Due to past limitations, we must assume that
flow is +ve to –ve instead. This system is called CONVENTIONAL CURRENT.
FORCES ON CURRENT-CARRYING WIRES
In the figure above, the thumb pointing
straight out represents the CURRENT
while the other four curved fingers
represent the MAGNETIC FIELD.
With this rule, the magnetic effect of a
current can be predicted.
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Fleming’s Left-Hand Rule is used to
predict the force (or thrust), magnetic field
and direction caused by a passing current. In
order for this interaction to occur, all three
must be perpendicular to each other.
First Finger = Field/Flux
SeCond Finger = Current
THumb = THrust
Force, magnetic field and current are linked
this way. If two are at a right angle, the third
can be produced.
•
Predict the direction of the wire in Fig 1. (downwards)
•
In Fig 2, the wire is being thrusted out of the page. Draw an arrow indicating the
conventional current direction, as well as the +ve and –ve terminals. (downwards)
APPLICATION OF LEFT HAND RULE TO A TURNING COIL
Predict whether the coil ABCD will have a clockwise or anticlockwise moment by determining
the forces on AB and CD.
Why would there be no force on BC?
In order to produce a thrust, the magnetic flux must be PERPENDICULAR to the current. At BC,
they are not perpendicular to each other, but parallel. There is no force as a result.
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D.C. MOTORS AND A.C. GENERATORS
Characteristics
d.c. motor
a.c. generator
Power source
Battery
External turning force
Energy conversion
Electrical → Mechanical
Mechanical → Electrical
Components
Split ring commutator
Slip rings
How to make the
Increase battery voltage.
motor spin faster or
Increase number of turns.
make the generator
create more power Use stronger magnets.
Increase turning force velocity.
Increase number of turns.
Use stronger magnets.
d.c. Motor: The purpose of the d.c. motor is to create a MOMENT on both sides of the wire
loops to create a turning force. This is due to Fleming’s Left Hand Rule, which says that in order
to create a force, a current must be PERPENDICULAR to the magnetic flux.
When the loop is turning, there is a chance the direction can reverse every half-rotation. A
SPLIT RING COMMUTATOR is used to BREAK THE CIRCUIT every half-turn to keep the
motor spinning in one constant direction. The direction of the turning force depends on the
orientation of the magnets and direction of conventional current.
a.c. Generator: It is noted that instead of a commutator, that SLIP RINGS are placed at the end
of the wire loop. The purpose of these is to allow the transfer of the alternating e.m.f. induced by
the rotating wire to the external circuit. Each one is connected to a contact brush, where it rotates
about the inner diameter. The faster the external rotator, more electrical energy can be converted.
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ELECTROMAGNETIC INDUCTION
Passing a magnet along a solenoid can allow electron flow and thus produce a VOLTAGE. This
is denoted by FARADAY’S LAW, which states that:
The voltage (or emf) induced in a coil is proportional to the rate of magnetic force
across it.
What this simply means is that the faster the magnet moves in and out of the coil, the more
voltage is obtained. If the magnetic field does not move, no voltage is induced.
Similarly, an alternating current constantly switches directions and by doing that, it inherently has
a changing magnetic field. An a.c. is therefore able to induce voltage across an adjacent coil.
A sensitive
galvanometer
is necessary to
detect very
small changes
in current.
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TRANSFORMERS
A transformer uses the concept of a constantly changing magnetic field to induce a voltage from a
primary to secondary coil. The more coils, the greater the electron flow and the higher the
voltage. However, if voltage is raised (step-up transformer), it trades by lowering the current.
Similarly, if voltage is lowered (step-down transformer), current is raised.
The following formulas are used in transformers:
Calculate the number of secondary coils and the secondary current in the primary coil.
Np/Vp = Ns/Vs
IpVp = IsVs
VsNp = VpNs
1000 x 5 = 200 x Ns
5000 = 200 Ns
Ns = 5000/200 = 25 turns
15 x 200 = Is x 1000
3000 = 1000 Is
Is = 3000/1000
= 3A
Due to the principle of conservation of energy, the power and energy output can never be more
than the input. In an IDEAL transformer, power input and output are said to be equal.
However, power loss does occur in transformers in real-world. To minimize power loss across a
wire, electrical energy is transferred with HIGH VOLTAGES and low currents. There are
numerous ways in which power loss can occur in a transformer, stated below:
Cause of Power Loss
Prevention Method
Line loss (heating)
Using wires of greater diameter.
Eddy currents
Laminating the soft iron core.
Hysteresis (delay during magnetization)
Using a perm-alloy core.
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LOGIC GATES
GATE
SYMBOL
NOT
AND
OR
GATE
NAND
NOR
SYMBOL
TRUTH TABLE
EXAMPLE USE
Input
Output
1
0
0
1
Also called an inverter. It
may be used in circuits that
regulate factors, e.g. turning
on flash in cameras when
the environment is dark.
Input 1
Input 2
Output
0
0
0
0
1
0
1
0
0
1
1
1
Input 1
Input 2
Output
0
0
0
0
1
1
1
0
1
1
1
1
TRUTH TABLE
An ATM will only allow a
user to access his account if
they swipe the correct card
and enters the correct PIN.
Doing one alone will deny
access.
If a machine is meant to
shut off if the temperature
OR pressure is too high, this
gate can allow the machine
to shut off if at least one
exceeds a certain limit.
EXPLANATION
Input 1
Input 2
Output
NAND = Opposite of AND
0
0
1
0
1
1
1
0
1
Also called the “universal
gate”, where the only zero
output is when there are two
zero inputs.
1
1
0
Input 1
Input 2
Output
NOR = Opposite of OR
0
0
1
The only positive output
0
1
1
0
0
0
occurs when there are two
1
1
0
zero inputs.
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Solve the following logic gate problems:
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An electric kettle is connected to an alarm that sounds whenever the kettle is switched on
and the lid is left open or the water level is below the heating element. The figure below
shows the circuit that controls the electric kettle’s alarm.
(a) Draw the appropriate logic gates in A, B and C to perform the electric kettle’s
alarm function. (A = AND, B = AND, C = OR)
(b) Complete the table below to show in which scenarios the alarm will go off or not.
Input
Output
L
M
N
X
Y
Z
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
1
1
1
1
1
1
1
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PHYSICS, SECTION E (1/1) : ATOMIC PHYSICS & RADIOACTIVITY
HISTORY OF THE ATOM
J.J. Thomson theorised and discovered the
electron. However, he believed the atom to
be a cluster of positive and negative charges
that he termed the “plum pudding model”.
However, scientists named Ernest
Rutherford and Niels Bohr later theorised
(and proved) that the atom had to have a
centre of positive charge. James Chadwick
discovered the neutron.
Two scientists named Hans Geiger and
Ernest Marsden assisted Rutherford in
developing the structure of the atom that we
know today. They performed an experiment
known today as the Geiger-Marsden
experiment or “gold foil” experiment.
NOTE: Gold was used because of its
malleability. It could have been cut thinner
than paper to allow alpha particles to
penetrate it.
The experiment involved setting up a radioactive source that emitted alpha-particles across a thin
piece of gold foil. A ring-like detector was placed around the foil. It was observed that the
majority of particles went straight through. However, a few were deflected.
The ones that were deflected had to have hit the nucleus, or were repelled by its positive charge.
This proved that the atom several things about the atom:
The atom has a small central positive mass at its nucleus. Most of the atom is empty space.
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SUBATOMIC PARTICLES
In the atom, there are THREE types of particles:
Particle
Atomic mass
Charge
Founder
Proton
1
+1
Ernest Rutherford
Neutron
1
0
James Chadwick
Electron
0
-1
J.J. Thompson
Definitions:
ATOMIC NUMBER - The number of PROTONS in an atom.
MASS NUMBER / ATOMIC MASS - The number of PROTONS and NEUTRONS in an atom.
For example, if a carbon atom has 6 protons and 6 neutrons, its atomic number will be 6 and its
mass number (or atomic mass) will be 12.
The electrons are arranged in SHELLS
rotating around the atomic nucleus.
When the number of protons and
electrons are equal, the atom is said to
be ELECTRICALLY NEUTRAL.
ISOTOPES
An isotope is defined as FORMS OF THE SAME ELEMENT THAT CONTAIN THE SAME
NUMBERS OF PROTONS BUT DIFFERENT NUMBERS OF NEUTRONS.
An atom has a nucleon number and an atomic number. Using an example of Uranium (U), which
has 92 protons and 143 neutrons, we represent it as:
Each atom is assigned its own atomic number. An atomic number of 7 is always nitrogen, for
example, while an atomic number of 8 is always oxygen. So if one proton was added to nitrogen,
the element will change to oxygen.
However, the number of NEUTRONS can differ. For example, Uranium (U) could have various
numbers of neutrons and thus have various isotopes.
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THE THREE TYPES OF RADIATION
For an atom to be stable, it must have A NUCLEAR RATIO OF 1 PROTON: 1 NEUTRON.
Unstable atoms are far removed from that ratio and lose energy by continuously emit differing
forms of energy known as radiation. This overall process is called radioactive decay. These three
types of radiation are represented as:
Type of radiation
α particles
β particles
γ rays
Nature
A helium nucleus.
A fast-moving electron.
A high-frequency e.m.
wave.
Ionising effect
Strongest
Intermediate
Weakest
Penetration strength
Weakest (stopped by
paper)
Intermediate (stopped
by aluminium)
Strongest (stopped by
thick lead)
Range
Shortest (2-10cm)
Intermediate (~1m)
Longest ( > 1m)
Deflection in
magnetic fields
Attracted to negative.
Attracted to positive.
Undeflected.
An instrument known as a G-M TUBE OR GEIGER COUNTER is used to test for the presence
of radioactive emissions. There is a margin of error in using this instrument, as sometimes the
number will exceed slightly. This occurs due to BACKGROUND RADIATION, which is due to
radiation already present in the room or contamination of the detector tube itself. This value is
simply subtracted from the total.
The G-M tube may also be used to gauge the penetrating power of the three different types of
radiation.
If the Geiger counter was
placed behind the paper, no
alpha radiation would be
detected. However, beta and
gamma would be.
If it was placed behind
aluminium, only gamma
radiation would be detected
as beta particles are stopped
by a sheet of aluminium.
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CLOUD CHAMBERS
A cloud chamber can be created by setting up a petri-dish filled with dry ice and isopropyl
alcohol. When a radioactive source is placed on the alcohol and dry ice, lines can be seen as
particles are emitted. These lines represent the ionic trails of the particles. The density and shape
of these lines determine the type of radiation being emitted.
DEFLECTION OF RADIATION ALONG ELECTRIC AND MAGNETIC FIELDS
Alpha particles are described as positive while beta particles are described as negative. Gamma
rays do not have a charge and are thus unaffected by any magnetic fields. In the diagram below,
draw how the three different types of radiation will interact.
SAFETY
Radioactivity was founded by MARIE CURIE. who studied elements such as Uranium and
Thorium. Unfortunately, she died of radiation-induced anaemia. Awareness increased by
scientists who have to work with ionising radiation, since it can break apart molecules in the
body, kill cells and cause cancer. They have since been taking the following precautions:
1. Using protective gloves and forceps when handling materials
2. Using protective screens and Hazmat suits
3. Storing radioactive materials in lead containers
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RADIOACTIVE DECAY
Alpha-Decay: When an element loses an alpha particle, it loses
E.g.
Beta-Decay: When an element loses a beta particle, the nucleon number is unchanged while the
atomic number increases by 1, .e.g.
Gamma-Decay: During alpha and beta-decay, the nucleus gathers spare energy. This energy is
released as gamma-rays This does not affect the atomic or nucleon numbers.
Decay Chains and Formulas
Isotope
Atomic No.
Nucleon No.
U-238
92
238
Th-234
90
234
Pa-234
91
234
Pb-210 (unstable)
82
210
Pb-206 (stable)
82
206
Bismuth (Bi)
83
210
Polonium (Po)
84
210
Using the table above, write the decay equations that
(i)
Show the process to turn U-238 into Pa-234. [2 equations]
(ii)
Show the process of unstable lead turning into stable lead. [3 equations]
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HALF-LIFE
Radioactive decay, explained before, represents the emission of particles due to unstable nuclei.
The decay process is independent of conditions external to the nucleus. Since radioactive decay is
a random process, half-life is only an estimate (though a very good one).
The half-life of a substance is defined as: THE TIME TAKEN FOR A RADIOACTIVE
SUBSTANCE TO DECAY BY HALF, OR FOR ITS ACTIVITY TO REDUCE TO HALF.
Calculating half-life of a substance after plotting a curve:
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Half-life Example Questions
1. The half-life of C-14 is 5700 years. A plant, upon death, experiences 8 disintegrations per
minute. Calculate how much time has passed since its death if the plant now experiences
1 disintegration per minute.
8 → 4 → 2 → 1
(each arrow represents one half life, t½)
1 half-life = 5700 years
∴ 3 half-lives = 5700 x 3 = 17100 years
2. A 800mg sample of radon decays over a period of 20 days until only 25mg remains.
What is the half-life of radon, in days?
800 → 400 → 200 → 100 → 50 → 25
5 half-lives = 20 days
(800mg decaying to 25mg)
∴ 1 half-life = 20/5 = 4 days
Background radiation and determining half-life
Remember that background radiation is radiation that is recorded despite not being placed close
to the radioactive source or after the source has completely decayed. It must be subtracted in
order to determine accurate radiation readings.
Example question 1: A Geiger counter is used to measure the radiation counts of a substance, X.
At the start of the experiment, the reading is 520 counts/s. After one hour, the reading is 70
counts/s. The background radiation was found to be 40 counts/s. Calculate the half-life of X.
Actual readings = 480 (520 – 40) and 30 (70 – 40)
480 → 240 → 120 → 60 → 30
4 half-lives = 1 hour = 60 mins
∴ 1 half-life = 60/4 = 15 mins
Example question 2: A radioactive source is tested over a number of hours with a radiation
detector. The readings are shown in the table.
Use the readings to:
(i)
(ii)
suggest a value for the background count rate during the test (Ans = 20 /s)
determine the half-life of the sample. (Ans = 30 mins)
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USES OF RADIOACTIVE ISOTOPES
Field
Isotope(s)
Use
Medical
Cobalt-60 and gamma rays
Killing cancer cells
Nitrogen-13, Oxygen-15,
Iodine-123
Used as radioactive tracers to detect
tumours and abnormalities
Archaelogical and
Scientific Research
Carbon-14
Carbon-dating fossils and older
materials
Power Generation
Uranium-235, Thorium-232
Nuclear fission plants
Industrial and
Commercial
Bromine-82, Iodine-125
Detecting leaks in pipes
Americium-242
Smoke alarms
Strontium-90
Used in thickness gauges.
NUCLEAR ENERGY
Albert Einstein suggested the relation between energy (E) and mass (m) in his famous formula
ΔE = Δmc2, where c = speed of light (3 x 108 m/s) c2 = (9 x 1016)
Reaction
Description
Example
NUCLEAR
FISSION
One nucleus splits to form smaller nuclei, releasing
massive amounts of energy as gamma rays.
Splitting of Uranium in
nuclear power plants
NUCLEAR
FUSION
Two smaller nuclei combine to form a larger
nucleus, giving off energy as it does.
Two H isotopes forming
helium (He) in the Sun.
Nuclear energy is efficient and does not contribute to air pollution. However, nuclear waste is
difficult to dispose of. Also, there is a risk of MELTDOWN. (e.g. Chernobyl and Fukushima).
Example question: The mass of the sun is lost at the rate of 2.0 x 109 kg every second. If the
speed of light in a vacuum is 3.0 x 108 ms-1, calculate the energy output of the sun in 1 second.
Convert to kilojoules.
ΔE = Δmc2
= (2 x 109) x (9 x 1016) = 1.8 x 1026 J
To kJ (÷ 1000) = 1.8 x 1023 kJ
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Calculating energy released in a nuclear reaction
The equation below represents nuclear fusion in the Sun. When calculating the masses before and
after the reaction, it will be noticed that there is a small difference. This small difference in mass
was converted to energy, according to Einstein. To calculate the energy, observe the table.
Nuclide
Atomic
mass / u
H-2
2.014
H-3
3.016
He
4.003
n
1.009
[u = 1.66 x 10-27 kg]
1. First, calculate the mass on the left side of the equation:
LHS = H-2 + H-3 = 2.014 + 3.016
= 5.03 u
2. Then the right side of the equation:
RHS = He + n = 4.003 + 1.009
= 5.012 u
3. Find the difference in masses, in u.
Δm = 5.03 – 5.012 = 0.018 u
4. Convert the ‘u’ value to kg by multiplying by 1.66 x 10 -27. This will be the value of Δm.
Δm (to kg) = 0.018 x (1.66 x 10-27)
= 2.988 x 10-29 kg
5. Lastly, apply Einstein’s formula (ΔE=Δmc2) to calculate how much energy, ΔE, was released.
ΔE = Δmc2
= (2.988 x 10-29) x (9 x 1016)
= 2.6892 x 10-12 J
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Nuclide
Mass / kg
Uranium-238
(U)
398.350 x 10-27
Krypton (Kr)
152.620 x 10-27
Barium-139
(Ba)
232.560 x 10-27
Neutron (n)
1.670 x 10-27
In the above case, the masses aren’t given in the unit ‘u’, so there is no need for conversion.
(i) Observe the diagram and write the equation of the fission reaction. Complete the missing numbers in
the Barium and Krypton isotopes.
EQUATION:
(ii) Calculate the difference in mass of the elements formed before and after the reaction.
Mass before (LHS) = U + n
= (398.350 + 1.670) x 10-27
= 400.02 x 10-27
Mass after (RHS) = Ba + Kr + 3n
= (232.560 + 152.620 + (3 x 1.670)) x 10-27
= 390.19 x 10-27
Difference (Δm) = LHS - RHS = 9.83 x 10-27 kg
(iii) Calculate the energy released in the reaction.
ΔE = Δmc2
= (9.83 x 10-27 kg) x (9 x 1016)
= 8.847 x 10-10 J
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WORKSHEET 1 – VECTORS, FORCES, DENSITY
1. Convert EACH reading below to its SI unit and determine which quantity is larger:
(a) 500cm or 0.5m
(d) 1 week or 600,000s
(b) 6.5km or 65,000cm
(e) 1800ms or 18s
(c) 0.018MW or 180kW
(f) 4500μm or 45mm
2. (a) The speed limit on Trinidad’s highways is 100km/h. Convert this value to m/s.
(b) A driver received a ticket while going 24m/s on a 80 km/h road. Did he exceed the speed
limit?
3. Convert the following to standard form scientific notation (to 3 s.f.)
(a) 4,200 J
(c) 300,000,000 m/s
(b) 101,325 Pa
(d) 0.03749 kg
(e) 0.000004599 m
(f) 0.009859 Hz
4. A light year is the distance it takes for light to travel in the span of one year (365 days). The speed
of light is estimated as 3.0 x 108 m/s.
(i)
(ii)
Calculate the number of seconds in a 365-day year.
Using the formula distance = speed x time, calculate the distance (in m) light can travel
in one year. Put your answer in standard form to 3 s.f.
5. The two figures below show a plane
going north and being affected by a
wind blowing in different directions at a
magnitude of 30 km/h.
Figure 1 shows the wind blowing at a
right angle (90o) to the plane while
Figure 2 has the wind blowing at 120o.
Recreate both situations as vector diagrams using an appropriate scale, draw the resultants and
state the magnitudes of the resultants. Use a scale of 1cm : 10km/h for both.
6.
7.
A Boeing 747 jet experiences a lift
velocity of 125m/s while travelling
horizontally on the runway at 175m/s.
The angle between the lift and the
runway is 60o. Recreate the vector
diagram and calculate the resultant
velocity and state the angle of the
plane’s ascent to the runway.
The tensions of two cables are 10N
and 12N. The angles are depicted on
the diagram. Recreate it as a vector
diagram, draw and measure the
resultant force. Use an appropriate
scale.
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8. The acceleration due to gravity on the Earth’s moon is 1.6 ms-2. If a 75kg astronaut walks on its
surface, determine his (i) mass (ii) weight
9. The acceleration due to gravity on Earth is 9.8 ms-2. A trailer has a mass of 3000 kg. Each wheel
of the trailer is able to exert a maximum of 5000N of reaction force. Calculate the minimum
number of wheels the trailer should have.
10.
(a)
(b)
(c)
Draw the following diagrams and show forces represented as arrows. Name the forces as well:
A car on a bumpy road decelerating.
(d) A basketball hitting the floor.
A rocket taking off from Earth.
(e) Clothes spinning in a washing machine.
A submarine sinking deeper into the sea.
(f) A parachuter falling at a constant speed
11. Relating to the concept of density, describe the mechanisms that allow a submarine to be able to both
sink and float in seawater. Draw a simple diagram to back up your explanation.
12. Explain why hot air rises. Draw a simple diagram comparing the spread of molecules in hot air and in
cold air.
13. A spring has an initial length of 2.5cm. When an 8N weight is attached to it, it extends by 0.25cm.
[use g = 10N/kg]
(a) Calculate the constant, k, of the spring.
(b) Calculate the extension and total length of the spring when a 24N weight is attached.
(c) Calculate the extension and total length of the spring when a 5.6kg mass is attached.
14. Complete the table below and plot the graph showing Weight vs. Extension. [use g = 10N/kg]
Mass/kg
0.0
1.0
2.5
3.0
4.5
6.0
Weight/N
0.0
10.0
Length/cm
4.0
4.4
5.0
5.3
y
6.4
Extension/cm 0.0
0.4
x
(a) Calculate the gradient, k. (b) Use the graph to find the value, x and thus y.
(c) Use the value, k, to determine the extension and total length of the spring when a 12.5kg mass is
attached.
15. (a) If 500kg of gasoline has a volume of 0.7m3, calculate the density of gasoline.
(b) Calculate the relative density of gasoline if its placed in sea water, which has a density of
1050kg/m3. Using your answers, state and explain whether or not gasoline sinks in seawater.
16. The water in a pool has a density of 1000kg/m3. If the pool has a length of 24m, width of 8m and a
depth of 6m, calculate the mass of water needed to fill the entire pool.
17. A block of pine wood has a volume of 40cm3. The density of pine wood is 0.65g/cm3.
(a) If its length is 2.5cm and its height is 8cm, how wide is it?
(b) Calculate the mass of the block.
18. A sheet of aluminum foil that is 11cm wide and 12cm long has a mass of 8.9g. If aluminum has a
density of 2.7g/cm3, what is the thickness of the foil? Convert your answer to mm.
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WORKSHEET 2 - PRINCIPLE OF MOMENTS
To achieve ____________________, the
1. In the figure below, Raj and Keon are sitting
on opposite ends of a seesaw. They are currently
balancing each other. Two distances are labelled.
________________________ moment
created by Keon must be equal to the
____________________ moment
created by Raj.
If Raj has a weight of 450N, calculate Keon’s
weight if the seesaw is balanced.
2. A metre ruler is suspended on a spring balance as shown. Calculate the reading of the tension on the
spring balance.
3. The figure below shows a student doing a
push-up. A force, F, acts upwards on his hands
as he presses against the ground. A force also
acts on his toes. The student has a weight of
600N. Calculate the force, F.
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4. A uniform rod, P, is supported at its centre and held in a horizontal position. The length of PQ is
1.00m. A force of 12N acts at a distance of 0.30m from the support. A spring, S, is fixed at the lower end.
Calculate the force exerted by the spring.
5. .The diagram shows several forces acting on a metre rule. If the system is in equilibrium, calculate the
value of W.
6. Two students, Patrick and Patricia, demonstrate their “magical balancing act” as depicted below. The
fulcrum is not located at the centre of the plank.
(a) Label the point where the weight of the plank acts.
(b) Using the Principle of Moments, calculate the weight of the plank.
(c) If Patricia were to move and Patrick were to sit alone on the plank, how far from the fulcrum
must he sit in order to balance the plank?
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WORKSHEET 3 – DYNAMICS AND MOTION
1. A taxi drives from Chaguanas to Port-of-Spain in a half hour. The distance between both places is
25km. Calculate the average speed of the taxi driver.
2. If the distance between Piarco International Airport and Grantley Adams Airport in Barbados is
340.0km and a CAL airplane cruises at an average of 125.9m/s, what is the expected time of arrival if the
flight leaves at 11:45pm? Round off to the nearest minute.
3. A truck driver steps on the brakes after seeing an emergency up ahead. The driver was going at 30m/s
and decelerates until he is going at 14m/s. This occurs over a span of 4 seconds. Calculate the driver’s
rate of deceleration.
4. (a) An airplane is travelling at 120.0m/s. It propels its forward using its jets and is able to accelerate at
a rate of 3m/s2. If it accelerates for 5 seconds, calculate its final velocity
(b) A similar airplane is travelling at 136.5m/s. Upon experiencing turbulence, the airplane experiences a
constant deceleration of 0.5m/s2 for a half minute. Calculate its final velocity.
5. A rollercoaster ride comes to a complete stop at the top of a ride. It suddenly begins a dive, accelerating
uniformly at the rate of gravity (10m/s2) downwards until it is travelling at a speed of 64.8km/h.
(a) Calculate the time it takes to get to its final speed.
(b) Sketch a velocity-time graph of the situation. Include the final speed and the time calculated in (a).
(b) Calculate the distance the rollercoaster travels during its dive.
6. The diagram below shows three forces acting
through the centre of mass of a 0.5kg object.
Calculate the object’s acceleration and state in
which direction.
7. Usain Bolt ran his record-breaking Olympic 100m dash in 9.58 seconds. During the first 60m, he ran
6.5 seconds before coasting at a constant maximum velocity towards the finish line.
(a) Calculate Bolt’s average velocity for the first 60m.
(b) Calculate the maximum velocity Bolt coasted at before the finish line.
8. A 4kg block is dropped from a building, 44m high. It hits the ground in 3s. If the block didn’t reach
terminal velocity before it hit the ground, calculate its (i) velocity upon hitting the ground and (ii)
momentum upon hitting the ground. [use g = 9.8ms-2]
9. (a) A bullet moving at 200 ms-1 hits a target, transferring all its momentum into it. As a result, the
target, which has a mass of 5kg, moves backwards. The bullet has a mass of 0.1kg. Assuming the bullet
does not stick to the target upon hitting it, calculate (i) the momentum of the bullet and (ii) the velocity of
the bullet.
(b) Calculate the velocity of the target in the same situation above, but assume the bullet was embedded
into the target upon hitting it.
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10. Two vehicles collide on the highway. A car, heading west, has a mass of 800kg and travels at 20m/s
collides head-on with a truck, heading east, of mass 2400kg travelling at 12m/s. Assuming that the
wreckage moves as a combined mass, calculate the velocity that wreckage will move at. Also, state its
direction.
11. A Boeing-747 jet has a mass of 3.4 x 105 kg. It is fitted with two identical thrusters that propel it
forward. It eventually travels at a velocity of 92 km/h after half of a minute.
(a) Calculate its rate of acceleration in m/s2.
(b) Calculate the force applied on each individual thruster.
(c) If more passengers boarded the plane, how would this affect (a) and (b)?
12. Using at least ONE of Newton’s Laws of Motion for each, explain how/why:
(a) seatbelts or airbags are essential (b) the haphazard movement of a quickly deflating balloon
(c) wet roads are dangerous to drive fast on (d) a loaded truck burns fuel at a faster rate than an empty one
13. When a car driver sees an emergency ahead, he applies the brakes. During his reaction time, the car
travels a steady speed and covers a distance known as the thinking distance. The braking distance is the
distance the car travelled after brakes are applied. Calculate:
(a) The thinking distance
(b) The braking distance
(c) The deceleration during braking
(d) The force provided by the brakes
14 (a) Calculate the displacement the sprinter
ran between reaching and leaving the hill.
(b) Calculate the displacement the sprinter ran
after leaving the hill.
(c) Calculate the force that allows the sprinter to
decelerate to rest after leaving the hill. The
sprinter has a mass of 75 kg.
15. A crash test dummy of 70 kg travelling at 26 m/s is subjected to a collision that lasts a duration of 0.1
seconds.
(a) Calculate the momentum of the dummy.
(b) Calculate the force upon impact experienced by the dummy.
(c) In another scenario, all protective gear is removed and the dummy is subjected to a lethal decelerating
force of 45,000 N. Calculate the duration of this collision.
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WORKSHEET 4 – ENERGY
[acceleration due to gravity, g = 10ms-2]
1. A student wishes to work out how much power she uses to lift her body when climbing a flight of
stairs. Her body mass is 60kg and the vertical height of the stairs is 3m. She takes 12s to walk up
the stairs. Calculate:
(i)
(ii)
the work done to raise her body mass up the stairs
the power she develops while climbing the stairs
2. Calculate the energy used by a 60W light bulb in one day.
3. The fastest recorded time at the Olympics was by Usain Bolt, at 12.4m/s. If Bolt has a mass of
94kg, calculate his kinetic energy while he was running his fastest speed.
4. How many minutes does it take a 240W heater to produce 43.2kJ of thermal energy?
5. A 70kg man climbs a 15-rung ladder in 20 seconds. Each ladder rung is 30cm apart. Calculate:
(a) The man’s weight
(b) The total power he developed while climbing the ladder
6. An electric pulley has a power rating of 0.25kW. It lifts a 50kg concrete block a height of 20m.
(a) Calculate the time taken to lift the block, assuming no loss.
(b) If the pulley was at a constant speed, calculate the speed the block was lifted.
(c) (i) State the main energy transformation in the block as it is lifted.
(ii) State the main energy transformation in the rope as the block hangs from it.
7. A student rubs her hands together. Each hand movement takes 1.2N of force and moves a
distance of 0.08m.
(a) Calculate how many movements would be needed to generate 1.92J.
(b) If one movement takes 0.2s to occur, how much power is generated?
8. A pole vaulter spends 6kJ to move his body upwards. If the pole vaulter had a mass of 80kg,
calculate the maximum height he carried himself.
9. A coal plant’s total output 120,000kJ per hour. However, a supply input of 200MJ per hour is
needed for this production rate to occur.
(a) Calculate the efficiency of the coal plant.
(b) Calculate the power output of the coal plant, using its total output.
10. A student has a mass of 60kg. Whenever he takes a step, he moves 0.2m in 1.2s.
(a) Calculate the student’s weight, in N.
(b) Calculate the work done by the student per step.
(c) Calculate the power developed per step.
11. One workman is measured as having a power of 528W. His weight is 800N. He can develop the
same power climbing a ladder, which rungs are 0.3m apart. How many rungs can he climb in 5s?
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12. A cyclist rides up and then back down a hill, as shown. The cyclist and her bicycle have a
combined mass of 90kg.
(a) Calculate the GPE of the cyclist and her bicycle at the top of the hill.
(b) Calculate the cyclist’s maximum velocity as she descends the hill, to the finishing point.
(c) Explain why her actual speed would be less than (b).
13. The diagram below represents a hydroelectric power plant. In order to generate electricity, water
flows from a high-level reservoir (600m above sea level) to a low-level reservoir (400m above
sea level). As it does, only 15% of the energy is converted to the energy needed to spin a turbine
at a station to generate electricity. 150kg of water flows through the station every second.
(a) Write a paragraph describing the various
energy transformations occurring in the
diagram.
(b) Explain how the water from the lowlevel reservoir eventually returns to the
high-level reservoir.
(c) Calculate the velocity of the turbine as
the water flows through it.
14. A mass of a falling rock is 75 kg. It accelerates due to gravity at 10 m/s2. The rock falls
for 2 seconds before hitting a pool of water.
(a) Calculate the kinetic energy of the rock just before it hits the water.
(b) Suggest THREE things that happen to the kinetic energy as it hits the water.
15. In the cylindrical wind generator, air passes in at 10 m/s. The generator has a circular
area of 1300 m2 and a length of 10 m. The density of air is given as 1.3 kg/m3.
(a) Calculate the volume of air passing the blades each second.
(b) Calculate the mass of this air.
(c) Calculate the kinetic energy of this air.
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WORKSHEET 5 – PRESSURE AND HEAT
[Take any instance of g = 10ms-2]
1. Explain why atmospheric pressure is less at the top of a mountain than at sea level.
2. A person presses his thumb against the pointed end of a nail with a force of 40N. The point has
a surface area of 2.52 x 10-5 m2. How much pressure is exerted on his thumb when he does this?
3. The diagram shows a person applying force on a brake pedal. The force applied is given as
75N. The brake pedal is connected to a hinge, H, which is then connected to a master cylinder.
The master cylinder has a cross-sectional area of 0.04m2.
(a) Calculate the force on the master
cylinder.
(b) Calculate the pressure against the
master cylinder.
4. The diagram shows a water reservoir and
dam with a conduit that ends with a valve.
The valve is closed.
The density of water is 1000kg/m3 and the
acceleration of gravity is 10m/s2. The
pressure at the valve is given as 200kPa.
(a) Calculate the depth of the dam, h, from the water surface to the exit pipe.
(b) The cross-sectional area of the exit pipe is 0.5m2. Calculate the force of the water on the valve.
5. (a) The pressure is taken along a vertical pipe of oil. If the pressure taken at a 60m depth is given as
4.8 x 105 Pa, calculate the density of oil.
(b) In an oil leak, the oil shoots in an upward direction. The force on the oil is 3600N and the leak has a
surface area of 0.05m2. Calculate the pressure of the oil and the maximum height of the jet of oil.
6. A large concrete block is depicted. Concrete
has a density of 2400kg/m3.
Calculate the (i)weight and (ii) pressure at the
base of the concrete block.(show both methods
of doing this)
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[specific heat capacity of water = 4200 J/kg K]
[Lv of water = 2.25 x 106 J/kg]
[Lf of water = 3.36 x 105 J/kg]
7. How much energy is required to heat 3kg of water from 30oC to its boiling point?
8. How much energy is required to heat 2500g of water, initially at 300K, to its boiling point and
turn it to steam?
9. How much energy is required to convert 1500g of ice at 0oC to steam at 100oC?
10. An experiment is carried out with 75g of water in an insulated beaker. The temperature of the
water increases from 20oC to 60oC in 210s. The heater’s power is 60W. Calculate the specific
heat capacity of water.
11. A person drinks 4kg of water per day. Assuming this entire volume of water, initially at 15oC,
is eventually excreted as urine at 37oC, calculate:
(a) the amount of heat removed each day.
(b) the mass of perspiration that would remove the same quantity of heat as the urine
when evaporated from the skin
12. A laboratory determination of the specific latent heat of vaporization of water uses a 120W
heater to keep water boiling at its boiling point. Water is turned into steam at a rate of 0.050g/s.
Calculate the specific latent heat of vaporization obtained from these experimental values.
13. A 1.2kW solar heater is designed to heat 0.3kg of water per minute. The initial temperature of
the water is 23oC.
(i) Convert 23oC to a Kelvin value.
(ii) Calculate the energy produced by the heater per minute.
(iii) Calculate the temperature of the water after one minute of heating.
14. The temperature of water at the top of a waterfall is 20oC, while the temperature at the base of
the waterfall is 20.5oC. If the waterfall is 210m high, use this information to prove that the
specific heat capacity of water is 4200J/kg oC. [g = 10N/kg]
15. In an experiment to determine the specific latent heat of fusion of ice using a container with
negligible heat capacity, a student obtained the following data.
Initial temp. of water = 30oC
Initial mass of water = 100g
(i)
(ii)
(iii)
|
Final temp of water + ice = 20oC
| Final mass of water + melted ice = 110g
Calculate the heat lost by the water.
Calculate the heat gained by the melted ice.
Calculate the specific latent heat of fusion of ice.
[specific heat capacity of water = 4.2 J g-1 K-1]
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WORKSHEET 6 – GAS LAWS
take all instances of atmospheric pressure as 1.0 x 105 Pa
| g = 10N/kg
1. Use the Kinetic Theory of Matter to explain how a balloon may pop when
(i) more air is put into it (ii) it is subjected to excess heat.
2. A contractible piston was used to pump gas into an air-bag. The volume of the piston is given
as 125cm3. Before pumping, the pressure gauge attached to it read 140Pa. After pumping, the
pressure gauge rose to 220Pa. Calculate the new volume of the piston.
3. A toilet flush is operated by the compression of air. The air inside the flush is at atmospheric
pressure (1.0 x 105 Pa) and a volume of 150cm3. When the flush is operated, the volume is
reduced to 50cm3. If the temperature remains constant, calculate the new pressure of the flush.
4. The diagram shows a diver.
She descends 24m below sea level.
Seawater has a density of 1050kg/m3. The
diver’s helmet has a small glass window that
is 0.32m long and 0.08m wide.
(a) Calculate the water pressure
exerted on the diver.
(b) Calculate the force the glass
window should be able to
withstand at that level.
5. A piston is fitted against a cylinder filled with
air. The volume of the piston is 860cm3 and the
initial pressure is 1.05 x 105 Pa. When the
weights are added, the volume decreases to
645cm3. The temperature remains constant.
(a) State what happens to the pressure when the
weights are added, and why.
(b) In the piston, draw a few air particles and
show their directions.
(c) Calculate the final pressure of the trapped air.
(d) Calculate the increase in pressure.
(e) The area of the piston is 5.0 x 10-3 m2.
Calculate the weight that was added to the piston
that caused the increase in pressure.
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6. On a cool day, a freshwater pond is 12m deep. Water has a density of 1000kg/m3.
(a) Calculate the pressure of the water at the base of the pond.
(b) Atmospheric pressure is given as 1.0 x 105 Pa. Calculate the total pressure at the bottom
of the pond.
(c) On a hot day, some of the water evaporates from the pond. State what effect this has on
the pressure at the base.
(d) A bubble of gas is released from the bottom of the pond and floats to the top. The initial
volume of the bubble is 0.5cm3. Ignoring any temperature differences, calculate the
volume of the bubble as it reaches the surface of the pond.
7. A car tyre is pumped to a pressure of 2 x 105 Nm-2 when the temperature is 23oC. Later in the
day, the temp. rises to 34oC. Calculate the new pressure in the tyre if the volume was constant.
8. Ms. Wilson drove her car across town. When she started off, the pressure in her tyres was
120kPa above atmospheric pressure and the temperature was 30oC. At the end of the drive, the
temperature rose to 70oC. If the volume of the tyre was not changed, what was the pressure inside
the tyre at the end?
9. Ms. Wilson decided to get new elastic tyres for her car. The volume adjusts with changes in
pressure and temperature. The pressure was the same at the start (120kPa above atm. pressure)
and the initial volume of the tyre was 0.8m3. After the drive, calculate the volume of the tyre if
the pressure increased by 10% and the temperature increased from 30oC to 70oC.
10. A hot air balloon must be filled with a certain amount of helium for it to float. When filled
with 24m3 of helium at a temperature of 32oC, the balloon is able to float. In order for it to float
higher, a rope must be tugged to light a fire beneath the balloon. The pressure and mass of helium
is constant when this happens.
(a) If the fire increases the temperature of the helium to 75oC, how much ADDITIONAL
volume was there in the balloon? Express this answer as a percentage increase of the
initial volume.
(b) Explain why the balloon floats higher when the fire is lit.
(c) Explain how the pressure of the balloon can remain constant despite being heated.
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WORKSHEET 7 - WAVES
[Speed of E.M. waves in air = 3 x 108 ms-1]
1. (a) Draw a series of four transverse waves. The final two waves should have approximately
half the amplitude of the first two.
(b) Redraw the above wavetrain but at double the frequency.
2. A wave of ultraviolet light travels through air and has a wavelength of 400 x 10-9 m. Calculate
its frequency.
3. A radio wave of 50kHz is sent from one signal tower to another.
(a) Calculate the period of the wave.
(b) Calculate the distance between the signal towers if only one wave oscillation was
sent.
4. In an experiment to determine the speed of sound in air, two scientists stand a certain distance
apart. One has a pistol and the other has a stopwatch. Explain how this setup can determine the
speed of sound in air. State a suitable distance between the scientists.
5. (a) In an experiment, Ravi and Chantal are trying to determine the speed of sound in air. Ravi
stands 60m away from a wall and claps two blocks together 20 times. Chantal records the time for
the 20 echoes as 7.2 seconds. Calculate the speed of sound from this data.
(b) In another experiment, there is a large vertical wall 50m in front of the loudspeaker. The wall
reflects the sound waves. If the speed of sound in air was found to be 340 m/s, calculate the
time taken for the waves to travel to the wall and return to the speaker.
6. A lightning strike occurs in the distance at 00:09:55 on a stopwatch. At 00:10:07, thunder is
heard. If the speed of sound in air is 330m/s, how far away was the source of the thunder?
7. A boat uses a SONAR pulse to determine the depth of an oil spill. The pulse takes 200ms to
travel to the spill and echo back up to the boat’s transmitter. If the oil spill is found to be 150m
deep, what is the speed of the sound pulse?
8. Differentiate between the terms ELECTROMAGNETIC radiation and NUCLEAR radiation.
9. The wave shown has a speed of 340m/s
and a frequency of 200Hz. Using this data,
calculate the distance PX on the diagram.
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10. (a) On the diagram, draw two arrows
showing the displacement of particles.
(b) If the speed of the wave is 3.2m/s,
calculate the frequency of the wave.
(c) Calculate the period of the wave.
11. A tsunami is a giant water wave. It may be caused by an earthquake below the ocean. Waves
from a certain tsunami have a wavelength of 1.9 × 105 m and a speed of 240 m/s. The shockwave
from the earthquake travels at 2.5 × 103 m/s. The centre of the earthquake is 60km from the coast
of a country.
(a) Calculate the frequency of the tsunami waves.
(b) (i) Calculate the time it takes for the earthquake shockwave to reach the coast.
(ii) The time between the arrival of the shockwave and the arrival of the tsunami is known as the
“warning time”. Calculate how much warning time the people along the coast have.
12.The figure shows a white ray incident to a prism and a red refracted ray, PQ.
(b) The angle of incidence for the white
light is 40o. If the prism’s refractive
index is 1.52, calculate the angle of
refraction for the red light.
(c) Calculate the speed of the red light
in the prism.
(a) On the figure, complete the red ray
and draw the path for a violet ray.
(d) Comment on changes in
wavelength, speed and frequency
when a light ray passes into glass.
13. The diagram below shows a glass block ABCD. Recreate the diagram in your book.
(a) On the recreated diagram, draw the paths of the
refracted and emergent rays.
(b) Use a protractor to draw the reflected ray.
(c) If the angle of refraction is 43o, calculate the
refractive index of the glass block.
(d) Calculate the critical angle of the glass block
14. An object is placed 30cm away from a convex lens of 15cm focal length. Calculate:
(a) the distance of the image from the lens
(b) the magnification of the image
15. A 5cm wide object is placed 10cm from a convex lens. The image is 40cm wide. Calculate:
(a) the image’s magnification (b) the image distance (c) the focal length of the lens
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WORKSHEET 8 - CIRCUITS
1. (a) Calculate the reading on the:
(i) ammeter
(ii) voltmeter
2. Calculate the readings on both ammeters.
3. Calculate the readings on both ammeters.
4. The circuit below shows a 6V battery, rheostat
and light bulb of rating 4.8V, 15W. Calculate:
(i) the current used by the bulb.
(ii) the energy used by the bulb after 1 hour
(iii) the resistance of the rheostat.
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5. Calculate the reading on the ammeter, in mA, when the switch, S, is (i) open (ii) closed
6. Calculate the reading on the voltmeter.
7. The circuit below shows three resistors. The resistor, Rx, has an unknown value. The ammeter has a
reading of 3mA. Calculate the value of Rx.
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WORKSHEET 9 – ELECTRICITY & ELECTRICAL COMPONENTS
1. (a) A Playstation Dualshock controller battery has a rating of 3600C. It uses a 0.5A USB charger. How
long would it take to fully charge, in hours?
(b) If an iPad battery has a charge capacity of 43200 C and it takes 6 hours to fully charge, what is the
current rating of the charger?
2. A lamp is marked 12V, 36W. Calculate the current and resistance of the lamp.
3. A solenoid (coil of wire) is connected to a circuit with a variable resistor and battery. The variable
resistor is set to 4Ω while the current across the circuit is 0.45A.
(i) Calculate the potential difference across the circuit.
(ii) Calculate the thermal energy released in the coil in 9 minutes.
4. A water heater has a power rating of 2.4kW. If it is connected to a 120V power supply, calculate the
current supplied to the heater. Calculate the energy produced if the heater is left on for an hour.
5. In a household with 200V a.c., a 100W lamp is switched on. Calculate
(i) the current in the lamp
(ii) the charge passing through the lamp in one minute.
6. Three 60W filament lamps are replaced by three fluorescent lamps, which give the same light output
but are rated at 15W each. Calculate:
(i) the total reduction in power
(ii) the energy saved when the fluorescent lamps are lit for one hour
7. A 24 V d.c. motor was used to lift a small appliance of mass 25kg from the ground to the second floor
of a building. The second floor is 30m above the ground. The motor operates at 100% efficiency and
works at a steady rate. It takes 5s to complete the activity.
(i)
(ii)
(iii)
(iv)
Calculate the gravitational potential energy needed to lift the appliance.
Calculate the power of the motor, in kW.
Calculate the current drawn from the d.c. supply, in mA.
If the the appliance had a greater mass, what effect would this have on the value of the
current?
[g = 10N/kg]
8. A lightning strike occurs and, in 2.0 × 10–4 s, a charge of 560 C passes from the cloud to the tree..
Calculate the current of the lightning strike
9. One cathode-ray tube has 5000 V between the accelerating anode and the cathode.
The beam of electrons carries a total charge of 0.0095 C in 5.0 s.
(i)
(ii)
(iii)
Calculate the current caused by the beam.
Calculate the power of the beam.
Calculate the energy produced every 20 seconds by the beam.
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10. The diagram shows the current from a power outlet passing through a resistor of 0.6kΩ.
(a) Calculate the peak voltage, from the diagram shown.
(b) Calculate the frequency of the current.
11. A transformer “steps down” 1800V to 200V. If the primary side has 360 coils, how many coils would
the secondary side have?
12. The primary side of a transformer has 120 coils and produces 500V. Calculate the secondary voltage
if there are 300 coils on the secondary side.
13. Explain why an a.c. voltage must be used as the input for a transformer instead of a d.c. input.
14. The diagram shows a step-up transformer.
(i) Calculate the secondary voltage.
(ii) Calculate the secondary current.
(iii) Assuming the transformer is 80% efficient, calculate the power
on the secondary side.
15. On the primary side of a transformer, there are 6 turns and 8V A.C.
(a) Calculate how many turns there must be on the secondary side to produce a 180V D.C. output.
(b) If 100A is produced on the primary side, calculate how much current will be on the secondary side.
(c) The transformer is said to be 82% efficient. Calculate how much power is developed on the secondary
side as a result.
16. Electrical power produced by Powergen in Trinidad is stepped up from 11,000V at 8000A to
110,000V for transmission to Tobago.
(a) If the number of turns in the secondary coil is 900, calculate the number of turns in the primary
coil for an ideal transformer.
(b) Calculate the transmission current for the ideal transformer in (a).
(c) Calculate the transmission power if the transformer is only 70% efficient.
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WORKSHEET 10 – ATOMIC PHYSICS
[speed of light in a vacuum (c) = 3.0 x 108 ms-1]
1. Write the chemical symbols for the following:
(a) Radium (Ra), atomic no. = 88, nucleon no. = 226
(b) Carbon (C), having 6 protons and 8 neutrons
(c) Lead (Pb), having 82 protons and 127 neutrons
(d) Uranium (U), having 92 protons and 146 neutrons
2. Write the chemical symbol for any possible isotope for Carbon or Uranium.
3. Calculate the number of neutrons in an isotope of Polonium, which has an atomic number of 84 and
nucleon number of 209.
4. The diagram below represents three α-particles moving towards thin gold foil.
Particle A is moving directly towards a gold nucleus.
Particle B is moving along a line which passes close to a gold nucleus.
Particle C is moving along a line which does not pass close to a gold nucleus.
(a) Complete the paths of the α-particles.
(b) Write a paragraph stating how observations
seen in A, B and C, using large numbers of αparticles, provides information that helped
scientists determine the structure of an atom.
5. State what makes an atom (i) unstable (ii) electrically neutral (iii) electrically positive.
6. Uranium (U) has a nucleon number of 233 and atomic no. of 92. It undergoes α –decay to
become Thorium (Th). Write the equation.
7. Uranium is formed when Proctacinium (Pa) undergoes β –decay. Write the equation. Use the
same nucleon and atomic nos. above for Uranium.
8. Fill in the missing numbers for the radioactive decay equations below.
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9. Radium (Ra) has a nucleon number of 226 and atomic no. of 88.
- Radium undergoes α -decay to become Radon (Rn)
- Radon undergoes α -decay to become Polonium (Po).
- Polonium undergoes α -decay to become Lead (Pb).
- Lead undergoes β -decay to become Bismuth (Bi).
Write a radioactive decay formula for each of the above.
10. (a) The half life of iodine-131 is 8 days. What percentage of an iodine-131 sample will remain
after 40 days?
(b) Os-182 has a half-life of 21.5 hours. How many grams of a 10.0 gram sample would have
decayed after 64.5 hours?
(c) U-238 has a half-life of 4.5 x 109 (4.5 billion) years. How many years would have to pass for a
sample of U-238 to decay to 1/32 of its original amount?
11. The table below shows readings from a Geiger counter over a 1.5-hour periods. The
background radiation has already been subtracted. Use the readings to determine the substance’s
half life.
Time/mins
Radiation count (counts/s)
0.0
2400
90.0
300
180.0
37
270.0
5
12. The energy released in a reaction is 1.8 x 10-12 J. Calculate the change in mass in the reaction.
13. The equation below represents the fission of U-233:
Nuclide
Atomic mass / u
U
233.03964
Sb
132.91525
Nb
97.91033
n
1.00867
[u = 1.66 x 10-27 kg]
(i)
Fill in the missing numbers in the equation.
(ii)
Calculate the energy released during the fission.
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KINEMATICS & DYNAMICS
STATICS& HYDROSTATICS
QUANTITY / LAW
FORMULA / WORDING
UNIT
QUANTITY / LAW
FORMULA / WORDING
UNIT
Speed (s)
s=d/t
w = mg
N or
v=x/t
m/s or
ms-1
Weight (w)
Velocity (v)
Acceleration (a)
a = Δv / t
m/s2or
ms-2
Density (ρ)
ρ=m/v
kg/m3 or
g/cm3
Relative density
(RD)
RD = ρ(substance)
No unit.
The weight of fluid displaced by an
immersed objectis equal to the fluid’s
buoyant force.
a=v–u
t
a = F/m
kg ms-2
y2 – y1
x2 – x1
y-unit
x-unit
Displacement
(inv-t graph)
Area of shape under
required portion of given
v-t graph.
m
Archimedes’
Principle
Displacement (if
trapezium)
½ (a + b) x h
m
Moment of a force
(M)
M = Fd
Newton’s 1st Law
(Law of Inertia)
An object at rest remains at rest, or
an object in motion remains in
motion at constant velocity, unless
acted upon by an unbalanced force.
Principle of
Moments
For a system in equilibrium, the sum of
clockwise and anticlockwise moments
about the same point are equal.(F1D1 =
F2D2)
Newton’s 2nd Law
Acceleration is directly proportional
to the net force applied to an object
and inversely proportional to its
mass.(F = ma or a = F/m)
Hooke’s Law
Newton’s 3rd Law
For every action force, there is an
equal and opposite reaction force.
The extension of a spring is directly
proportional to the force applied to it
until it reaches its limit of
proportionality.
F = kx (F = Force, k = spring constant,
x = extension)
Momentum (p)
p = mv
Impulse (Δp)
Δp = Ft
Law of
Conservation of
Linear Momentum
The total momentum in a closed
systemis the same before and after
collision.
Gradient/Slopeof a
Graph
kg m/s
or Ns
Ft = mΔv
(mv)before= (mv)after
ENERGETICS
QUANTITY / LAW
FORMULA / WORDING
UNIT
Work done (W)
W=Fxd
J or Nm
Power (P)
P = E/t or P = W/t
W or J/s
Kinetic Energy (KE)
KE = ½ mv2
J
Gravitational
Potential Energy
(GPE)
∆GPE = mg∆h
J
Law of
Conservation of
Energy
Energy can neither be created nor
destroyed, but can only be converted
into different forms.
Efficiency
Useful energy (Output)
Totalenergy (Input)
Velocity (during
GPE→ KE
conversion)
%
ρ(reference)
Nm
PRESSURE MECHANICS
QUANTITY / LAW
FORMULA / WORDING
UNIT
Pressure against a
surface (P)
P=F/A
Pa or
N/m2
Pressure in fluid
(P)
P =ρhg
Pa or
N/m2
Pascal’s Law
The pressure exerted at a given point
in an incompressible fluid is
distributed equally through all points
in the fluid.
Boyle’s Law
The volume of a gas is inversely
proportional to the pressure, given
that temperature is constant.
(P1V1 = P2V2) or PV = k
Charles’ Law
The volume of a gas is directly
proportional to its temperature, given
that pressure is constant.
(V1 / T1 = V2 / T2) or V/T = k
Pressure Law
The temperature of a gas is directly
proportional to its pressure, given that
volume is constant.
(P1 / T1 = P2 / T2) or P/T = k
Complete Gas
Equation
P1V1 = P2V2(if P, V or T aren’t constant)
T1
T2
m/s
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ELECTROMAGNETISM& ELECTRONICS
THERMODYNAMICS
QUANTITY / LAW
Specific Heat
Capacity (c)
Heat Capacity (C)
Specific Latent
Heat of Fusion (Lf)
Specific Latent
Heat of
Vapourization (Lv)
Kinetic Theory of
Matter
UNIT
QUANTITY / LAW
FORMULA / WORDING
The amount of heat 1kg of
a substance required to
change its temperature by
1K.(E = mcΔӨ)
J/kg K
or
J kg-1 K-1
Conv. current
Flow of +ve charge from +ve to –ve.
Electron Flow
Flow of –ve charge from -ve to +ve
Derivations
1V = 1 J/C
1A = 1 C/s
C = mc
J/K
V and I in Series
VT = V1 + V2...
I in = I out
The amount of heat 1kg of
a substance required to
convert it from a solid to
liquid without changing its
temperature.(E = mLf)
J/kg
or J kg-1
Voltage (V)
V = IR
V = E/Q
V
Power (P)
P = IV
P = E/t
W
Energy (E)
E = IVt
E=Pxt
J
Rs = R1 + R2...
Ω
The amount of heat 1kg of
a substance requiresto
convert it from a liquid to
gas without changing its
temperature.(E = mLv)
J/kg
or J kg-1
Resistance (series)
(Rs)
Resistance
(parallel) (Rp)
1 = 1 + 1…
RpR1R2
Ω
Charge (Q)
Q = It
C
Ohm’s Law
The current through a conductorof constant
temperature is directly proportional to itsp.d.
and inversely proportional toresistance. (V = IR)
Faraday’s Law
The emf in a coil is proportional to the rate of
change of magnetic flux.
FORMULA / WORDING
Matter is made up of particles in
random motion. Adding energy makes
particles move farther apart.
WAVES &OPTICS
QUANTITY / LAW
FORMULA / WORDING
UNIT
Wave velocity (v)
v=fλ
m/s
Echo speed (s)
s = 2d / t
m/s
Frequency (f)
f =no. waves
time elapsed
f = 1_
T
Fleming’s Left
Hand Rule
UNIT
1 Ω=1VA-1
All three must be 90o
to each other to
generate a turning
force in a motor or
current in a
generator.
Hz or s1
Equations for ideal
transformers
T = 1/f
Two Laws of
Reflection
1. The incident ray, reflected ray and
normal all lie on the same plane.
2. The angle of incidence is equal to the
angle of reflection.(Өi = Өr)
Two Laws of
Refraction
1. The incident ray, refracted ray and
normal all lie on the same plane.
2. The refractive index (n) is equal to the
ratio of the sines of angles of incidence
and refraction. (Snell’s Law)
Atomic no. (Z)
No. of Protons
Nucleon no. (A)
A = Z + N (protons + neutrons)
Nuclear stability
n = Speed of lightin air (c)__
Speed of light in medium (v)
n = __ λ in air____
λ in medium
n = sinӨ1 / sinӨ2
When N : Z = 1 : 1
(same no. of protons and neutrons)
Radiation Particles
Alpha =42He Beta = o-1e
Isotope
An element with the same atomic
no. of another but different nucleon
no.
Half-Life (t1/2)
The time it takes for half of a
substance to radioactively decay.
Energy gained in a
nuclear reaction
ΔE = Δmc2(Einstein’s formula)
(m = mass, c = speed of light)
Refractive index (n)
s
Np / Ns= Vp / Vs
...where, N = No. of Turns
Period (T)
No
unit.
VpIp = VsIs or Pp = Ps
…where, p = primary, s = secondary
NUCLEAR PHYSICS
Өi when r = 90o
Critical angle
n = 1/sin c
Total internal
reflection
When angle of incidence exceeds the
critical angle. (Өi>Өcrit)
Magnification
M = h i / ho
M = d i / do
Lens formula
1 = 1 + 1
f
d o di
1 = 1 + 1
f
u
v
MR. K EVIN HOSEIN
PHYSICS O’ L EVEL STUDY AID
(use sparingly)
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