Chapter 1
Topic 1.1
Measurement in Physics
By
Msc. Eng. Mohamed Zamzam
1
Outline
• Physical Quantities
• Fundamental and derived quantities
• Units
• Significant figures
• Metric multipliers (Prefixes)
• Metric Conversions
• Order of magnitudes
• Estimation
• Scientific notation
• Revision for important rules
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Physical Quantities
• Physics is the study of fundamental laws of nature.
• The laws of physics are described and expressed in terms of Physical quantities.
• Physical quantities are the alphabets of Physics.
• Physical quantities are those things that are measurable such as mass, length, time, velocity, acceleration, force and energy.
• Physical quantities are divided into fundamental and derived quantities.
• Fundamental quantities are measured using fundamental units and derived quantities are measured using derived units.
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Fundamental and Derived Physical Quantities
• Fundamental quantities
They are independent quantities that all other quantities are expressed in terms of them. There are seven (7)
fundamental quantities in nature.
4
Fundamental units
• Units are used in measuring the physical quantities.
• Fundamental units are used in measuring fundamental quantities
• The system of units that is nearly official used everywhere is the international system of units ( SI system )
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Units
•
The system of units that is nearly official used everywhere is the international system of units ( SI system ) but
there are also other systems used in some countries.
(a) In the international system of units (SI system)
the length has unit of meter ……..(m),
the mass has unit of kilogram…..(kg),
the time has unit of second ……..( s ).
(b) In the Gaussian system of units (CGS system),
the length has unit of centimetre ……..(cm),
the mass has unit of gram……………...(g),
the time has unit of second …………….( s ).
(c) In the British system of units (FPS system),
the length has unit of foot ……..(ft),
the mass has unit of pound……(p),
the time has unit of second ……(s).
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Mass
• Measure of amount of matter of an object.
• Has a symbol m.
• Has a SI unit of kilogram (kg).
• Other units are gram (g), pound (lb), ton (t).
scale
balance
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length
• Length is the measurement of something from one end to the other end.
• Has a symbol l.
• Has a SI unit of meter (m)
• Other units include inch (in), feet (ft), centimeters (cm), millimeters (mm) and kilometers (km).
measuring tape
ruler
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Time
• The measured or measurable period during which an action exists.
• Has a symbol of t.
• Has a SI unit of second (s)
• Other units include years, months, days, hours, minutes.
Clock
Digital Stop watch
Analogue Stop watch
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Temperature
• Degree of hotness or coldness of an object.
• Has a symbol of T.
• has a SI unit of Kelvin (k).
• other units include degree Celsius (°C) or degree Fahrenheit (° F).
Different types of thermometers
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Current
• Current is the flow of electrons.
• Has a symbol l.
• Has a SI unit of Ampere (A)
• Other units includes milliampere (mA) or micro-ampere (μA)
Multi meter / Ammeter
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Amount of substance
• A measure of the number of molecules present in a particle.
• Has a symbol of n.
• Has a SI unit of mole (mol).
• 1 mole = 6.02 x 10 23 molecules of a particle
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•
Derived quantities
They are dependent quantities that are a combination of the fundamental quantities.
Derived Quantity
Name
Symbol
Relation
speed
v
v=
total distance
time
=
d
t
velocity
v
v=
displacement
time
=
s
t
acceleration
a
change in velocity
time
=
Force
F
F = mass x acceleration = m x a
Work
W
W = Force x displacement = F x s
Energy
E
E = Force x displacement = F x s
Power
P
Momentum
p
p = mass x velocity = m x v
Area
A
A = Length x Width = L x W
Volume
V
V = Length x Width x Height = L x W x H
Density
ρ
a=
P=
ρ=
Energy
time
mass
Volume
=
=
∆v
t
E
t
m
V
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Derived units
They are the units of the derived quantities.
Derived Quantity
SI units
Name
Symbol
Relation
speed
v
v=
velocity
v
v =𝑡
acceleration
a
Force
F
F=mxa
Work
W
W=Fxs
Energy
E
E=Fxs
Power
P
Momentum
p
p=mxv
Area
A
A=LxW
m2
meters squared
Volume
V
V=LxWxH
m3
meters cubed
Density
ρ
a=
Name
d
t
m
s
= m.s-1
meters per second
𝑠
m
𝑠
= m.s-1
meters per second
∆v
t
m
𝑠2
= m.s-2
meters per seconds squared
P =
ρ=
Symbol
E
t
m
V
N=
kg.m
𝑠2
= kg.m.s-2
Newton = kilogram meters per seconds
squared
J = N. m =
kg.𝑚2
𝑠2
= kg.m2.s-2
Joule = Newton meters = kilogram meters
squared per seconds squared
J = N. m =
kg.𝑚2
𝑠2
= kg.m2.s-2
Joule = Newton meters = kilogram meters
squared per seconds squared
W = kg.m2.s-3
kg.m
𝑠
kg
𝑚3
= kg.m.s-1
= kg.m-3
Watt = kilogram meters squared per seconds
cubed
kilogram meters per second
kilogram per meters cubed
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Using SI units in the correct format
• In IB units writing derived units are in a way that does not involve fractions.
• Denominator units are written in the numerator with negative exponents.
Rewrite the units in the accepted IB format.
•
m
𝐬
•
km
h
•
kg∙m
s2
•
kg
𝑚.𝑠 2
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May 2012 (HL & SL)
Which of the following is a fundamental SI unit?
A. Ampere
B. Joule
C. Newton
D. Volt
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November 2011 (HL & SL)
What is the correct SI unit for momentum?
A. kg m–1 s–1
B. kg m2 s–1
C. kg m s–1
D. kg m s–2
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May 2015 (HL & SL)
Which unit is equivalent to J kg−1?
A. m s−1
B. m s−2
C. m2 s−1
D. m2 s−2
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May 2015 (SL)
Which of the following expresses the watt in terms of fundamental units?
A. kg m2 s
B. kg m2 s–1
C. kg m2 s–2
D. kg m2 s–3
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May 2014 (HL & SL)
Which of the following is a unit of energy?
A. kg m–1 s–1
B. kg m2 s–2
C. kg m s–2
D. kg m2 s–1
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May 2014 (HL)
The force of air resistance F that acts on a car moving at speed v is given by F = kv2 where k is a
constant. What is the unit of k?
A. kg m–1
B. kg m–2 s2
C. kg m–2
D. kg m–2 s–2
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Metric multipliers (Prefixes)
An SI prefix is a name or associated symbol that is written before a unit to indicate the appropriate power of 10. Thus, a
nanometre (nm) is 10−9 m. The most common prefixes are given in the following table :
Power
Prefix
Symbol
Power
Prefix
Symbol
10-15
femto-
F
101
deka-
da
10-12
pico-
p
102
hecto-
h
10-9
nano-
n
103
kilo-
k
10-6
micro-
µ
106
mega-
M
10-3
milli-
m
109
giga-
G
10-2
centi-
c
1012
tera-
T
10-1
deci-
d
1015
peta-
P
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November 2017 (HL)
What is a correct value for the charge on an electron? ( e = 1.6 x 10 -19c)
A. 1.60 x 10–12 µC
B. 1.60 x 10–15 mC
C. 1.60 x 10–22 kC
D. 1.60 x 10–24 MC
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Metric Conversions (You will NOT need to memorize these)
• There are other list of units that are not defined as a part of SI units, and they are commonly used in some countries.
• To convert them to SI units. (i.e., pound → kilogram , or mile → meters), we use Conversion Factors.
Some Alternative Units
SI units
1 ton (t)
103 kg
1 pound (lb)
0.454 kg
1 mile (mi)
1609 m
1 inch (in)
0.0254 m
1 feet (ft)
0.3048 m
1 litre (L)
10-3 m3
1 hour ( h )
3600 s
1 kilo-Watt hour (kWh)
3.6 x 106 J
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Examples
• The Space Needle is 605.0 ft tall. How many meters is this?
• A cheetah can run at speeds up to 70.0 miles per hour. How fast is this in meters per second?
• The density of aluminum is 2.7 g.L-1. What is its density in kg.m-3?
• The area of square is 25 cm2. Find the area in m2.
• The volume of cube is 30 mm3 . Find area in m3.
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Significant Figures
• It is important when calculating numerical values that the final answer is quoted to an appropriate number of
significant figures.
• Therefore, significant figures are used to carry information about how precisely the number is known. A
stopwatch reading of 3.2 s (two significant figures(s.fig.) is less precise than a reading of 3.23 s (three s.fig.)
Integer count (no decimal)
Rule
Non-zero always
count as significant
figure (s.fig.)
Captive zeros (zeros
in between) count
as s.fig.
Leading zeros (zeros
at beginning) don’t
count as s.fig.
Trailing zeros (zeros
at the end) don’t
count as s.fig.
Example
Number of s.fig
3456
4
504
3
00234
3
200
1
Decimal count
Rule
Leading zeros
(zeros at
beginning) don’t
count as s.fig.
Captive zeros
(zeros in
between) count
as s.fig.
Trailing zeros (
zeros at the end)
count as s.fig.
Example
Number of s.fig
0.00234
3
0.504
3
0.2300
4
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Example
Round Each Number to 3 significant figures
•
4.06
• 2.006
• 0.003456
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November 2017 (SL)
How many significant figures are there in the number 0.0450?
A. 2
B. 3
C. 4
D. 5
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Order of Magnitude
• Expressing a quantity to the nearest power of 10 gives what is called the order of magnitude of that quantity.
• It is used in comparing the size of physical quantities.
• For example, an average adult human mass is closer to 100 kg making the order of magnitude 102. The mass of a
sheet of A4 paper may be 3.8 g making the order of magnitude to be 10-3 kg. This suggests that the ratio of adult
mass to the mass of a piece of paper = 105 = 100 000. In other words, There are five order of magnitudes
difference between them.
Example
The average life time of a human (70 years)
Order of magnitude is 102
the age of universe ( 1.7 x 1010)
Order of magnitude is 1010
We can use approximate ratio 1010/ 102 = 108. Age of universe is 108 times the age of
human, or we can say that there are 8 orders of magnitude difference between them.
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Estimation
• Estimation is a skill that is used by scientists and others in order to
produce a value that is a useable approximation to a true value.
• When making estimates different people will produce different
answers.
Example
Estimate the volume of a class room ?
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Scientific notation
Scientific notation is used when writing very large or very small numbers. When a number is written Scientific
notation means writing a number in the form a × 10b, where a is decimal such that 1 ≤ a < 10 and b is a positive
or negative integer. The number of digits in a is the number of significant figures in the number. The speed of
light is often written as 3 x 108 m/s instead of 3000 000 00 m/s.
Number
Scientific notation
50400
5.04 x 104
608000
6.08 x 105
0.000 305
3.05 x 10-4
0.005900
5.900 x 10-3
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Reading only ( order of magnitude + Estimation) questions
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May 2012 (SL)
What is the order of magnitude of the mass, in kg, of an apple?
A. 10–3
B. 10–1
C. 10+1
D. 10+3
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May 2013 (HL)
The mass of an elephant is 104 kg. The mass of a mouse is 10–2 kg. What is the ratio of the mass of the
mass of the elephant
mass of the mouse
A. 10–8
B. 10–6
C. 106
D. 108
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?
May 2015 (HL)
Which of the following expresses the ratio of
mass of proton
mass of electron
as a difference in orders of
magnitude? me = 9.1 x 10-31 kg, mp = 1.67 x 10-27 kg
A. – 3
B. 0
C. 3
D. 6
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November 2015 (SL)
One kilogram of ice of density 1000 kg m–3 is frozen in the shape of a cube. The diameter of a water molecule is
10–10 m. What is the difference in the orders of magnitude of the length of one side of the ice cube and the
diameter of a water molecule?
A. 7
B. 9
C. 11
D. 13
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Revision for Important Rules
Square
Cube
Area = L2
Circumference = 4 L
Area = 6 L2
Volume = L3
Rectangle
Cuboid
Area = L x w
Circumference = 2 L + 2 w
Volume = L x w x h
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Circle
Sphere
Area = π r 2
Area = 4 π r 2
Circumference = 2 π r
Volume = 3 π r 3
4
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Triangle
1
Area = 2 b h
Circumference = 𝑎 + 𝑏 + 𝑐
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Proportionality
Directly proportional
Inversely proportional
x α
xα 𝑦
1
𝑦
1
x = constant. 𝑦
x = constant. 𝑦
𝒙𝟏
𝒙𝟐
𝒙𝟏
𝒙𝟐
𝒚
= 𝒚𝟏
𝟐
=
𝒚𝟐
𝒚𝟏
x
y
x
y
1
2
40
1
2
4
20
2
3
6
10
4
4
8
5
8
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Example
• If x is directly proportional to y and given y = 9 when x = 5, find:
a) the value of y when x = 15
b) the value of x when y = 6
• Suppose that x is inversely proportional to y and that y = 8 when x = 3. Calculate the value of
y when x = 10.
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