PHY 111: MECHANICS AND PROPERTIES
TOPIC : MEASUREMENT,UNITS AND DIMENSIONAL
ANALYSIS
CLASS : A LEVEL AND O LEVEL
PHY 111: MECHANICS AND PROPERTIES
TOPIC : MEASUREMENT,UNITS AND DIMENSIONAL
ANALYSIS
Measurement is a proces of assigning numbers according
to a rule.
Thre are various types of measurements they specically
include :
* Measurements of lenght
* Measurements of mass
* Measurements of time
* Measurements of weight
Measurements of lenght
Lenght can be defined as the extent of an object from end
to end
here below are some materials use fo rmeasuring lenght
1 Metre rule: it is used for measuring the lenght of a desk
2 Tape rule : it is used for measuring the lenght of a field
3 Venier calliper : it is used for measuring the internal and
external
diameter of an object
4 Micrometer Screw guage : it is used for measuring the
external
diameter only of an object
Measurements of mass
Mass can be defined as the quantity of matter in which a
body contains.
Here below are some materials used for measuring mass.
1 Beam balance
2 Triple beam balance
3 Chemical balance
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Measurements of time
Time can be defined as that in which an event is placed or
distingushed
in reference to before or after.
Here below are some materials used for measuring time.
1 Stop clock
2 Stop watch
3 Water clock
4 pendulum clock.
Measurements of weight
Weight is a force that tends to pull a body towards the
centre of the earth. Here are some materials used for
measuring weight .
1 Lever balance
2 Spring balance
3 Dial spring balance
With the aid of some instruments
PHYSICAL QUANTITIES
Physical quantities are quantities that can be measured
physically with the aid of some instruments.
Physical quantities are divided into two parts they are:
1 Fundamental quantities
2 Derived quantities
Fundamental quantities are known as the basic unit of
measurements they are basically seven in number they
include:
QUANTITIES
UNITS
SYMBOLS
* Lenght
Metre
m
* Mass
Kilogram
kg
* Time
Seconds
s
* Current
Ampere
A
* Temperature
Kelvin
k
* Amt of substance
mole
mol
* Light intensity
Candela
c
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Derived quantities involves two or more fundamental
quantities. E.g
Velocity =distance m = ms_1
Time
s
Acceleration = velocity ms_1 = ms_2
Time
s
Force = mass x acceleration = kgms_2 or N
Work = force x distance = Nm
Dimensional analysis
Dimensional analysis is a process of identifying and
proofing a mathematical expression in physics.
It basically has four parts which are.
1 Dimensions of fundamental quantities
2 Dimensions of derived quantities
3 Dimensional proof of mathematical expressions
4 Identifying mathematical expression from dimensional
Quantities.
DIMENSIONS OF FUNDAMENTAL QUANTITIES
QUANTITIES
UNITS
Lenght
metre
Mass
kilogram
Time
seconds
Temperature kelvin
Current
Ampere
Amt of subs
mole
Light intensity candela
SYMBOLS
m
kg
s
k
A
mol
c
DIMENSIONS
L
M
T
0
I
n
J
N. B : In dimensional analysis numbers do not count
they are considered to be 1.
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DIMENSIONS OF DERIVED QUANTITIES
Velocity = Distance = L = LT_1
Time
T
Acceleration = velocity = LT_1 = LT_2
Time
T
Force = mass x acceleration = MLT_2
Work = force x distance = MLT_2 x L = ML2T_2
DIMENSIONAL PROOF OF A MATHEMATICAL
EXPRESSION.
1 v=u+at
LT_1= LT_1 + LT_2 T
LT_1 = LT_1 + LT_1
2 s= ut + 1/2 at2
L= LT_1T + LT_2 T2
L=L + L
3 s = ut + 3/2 kat3
L = LT-1 T + KLT-2 T3
L= L
+ KLT (not correct)
To make it correct find k
K = L-1T-1
L = L + (L-1T-1)LT
L = L (CORRECT)
IDENTIFYING MATHEMATICAL EXPRESSION FROM
THEIR DIMENSIONAL QUANTITIES
1 The period of a pendulum depends on the mass of the
bulb, the lenght of the string and the acceleration due to
gravity acting on the bulb. Deduce an expression of the
period of the pendulum from these quantities
T= K M L g
T = K M x Ly g z
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T = K Mx Ly ( LT-2)z
T= K Mx Ly Lz T-2 z
T = K Mx Ly+Z T-2 Z
X=0 because its not on the other side of the equation
-2z = 1
Z = -1/2
y+z = 0
Y = -z
Y = 1 /2
T = K M0 L1/2 g-1/2
T = K √L
√g
T = K √L/g
EXERCISE
1 Identify the dimensions of the following derived
quantities
(a) Specific heat capacity
(b) Surface tension
(c) Viscosity
(d) Gravitational constant
(e) Young’s modulus
2 Proof the following equations
S= ut + 3/2 ka2t4
V2= u2 + 2ca3s2
3 The wave of an ocean has its density (ρ) and velocity (v)
related by the expression
V = A g x ρy ƛ z .
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