eDP 2020

MATRICULATION
DIVISION

PHYSICS

LABORATORY MANUAL
DP014 & DP024

FOURTH EDITION

Photo by Cristian S. on Unsplash

MATRICULATION DIVISION
MINISTRY OF EDUCATION MALAYSIA

PHYSICS

LABORATORY MANUAL
SEMESTER I & II
DP014 & DP024

MINISTRY OF EDUCATION MALAYSIA
MATRICULATION PROGRAMME
FOURTH EDITION

First Printing, 2011 (First Edition)
Second Printing, 2015 (Second Edition)
Third Printing, 2018 (Third Edition)
Fourth Printing, 2020 (Fourth Edition)
Copyright © 2020 Matriculation Division
Ministry of Education Malaysia
All rights reserved. No part of this publication may be reproduced
or transmitted in any form or by any means, electronic or
mechanical, including photocopy, recording or any information
storage and retrieval system, without permission in writing from
the Director of Matriculation Division, Ministry of Education
Malaysia.
Published in Malaysia by
Matriculation Division
Ministry of Education Malaysia,
Aras 6 – 7, Blok E15,
Government Complex Parcel E,
Federal Government Administrative Centre,
62604 Putrajaya,
MALAYSIA.
Tel : 603-88844083
Fax : 603-88844028
Website : http://www.moe.gov.my/v/BM

Malaysia National Library
Physics Laboratory Manual
Semester I & II
DP014 & DP024
Fourth Edition
eISBN 978-983-2604-38-9

NATIONAL EDUCATION PHILOSOPHY

Education in Malaysia is an on-going effort towards
further developing the potential of individuals in a
holistic and integrated manner, so as to produce
individuals who are intellectually, spiritually and
physically balanced and harmonious based on a firm
belief in and devotion to God. Such an effort is
designed to produce Malaysian citizens who are
knowledgeable and competent, who possess high
moral standards and who are responsible and capable
of achieving a high level of personal well-being as
well as being able to contribute to the betterment of
the family, society and the nation at large.

NATIONAL SCIENCE
EDUCATION PHILOSOPHY

In consonance with the National Education
Philosophy, science education in Malaysia nurtures a
science and technology culture by focusing on the
development of individuals who are competitive,
dynamic, robust and resilient and able to master
scientific knowledge and technological competency.



CONTENTS

1.0 Learning Outcomes Page
2.0 Guidance for Students v
3.0 Significant Figures viii
4.0 Uncertainty in Measurement x
xi
Experiment Semester I
1
1 Title 5
2 10
3 Measurement and Uncertainty 13
4 Plotting and Analyzing Linear Graph 18
5 Free Fall 22
6 Linear Momentum
Friction Page
Thermal Conduction 25
28
Semester II 33
36
Experiment Title 40
44
1 Simple Harmonic Motion (SHM) 47
2 Sound Waves 48
3 Ohm’s Law
4 Capacitor
5 Magnetism
6 Geometrical Optics

References

Acknowledgements

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Physics (PDT) Lab Manual

1.0 Learning Outcomes
1.1 Matriculation Science Programme Educational Objectives
Upon a year of graduation from the programme, graduates are:
i. Knowledgeable and technically competent in science
disciplines in-line with higher educational institution
requirement.
ii. Communicate competently and collaborate effectively in group
work to compete in higher education environment.
iii. Solve scientific and mathematical problems innovatively and
creatively.
iv. Engage in life-long learning with strong commitment to continue
the acquisition of new knowledge and skills.

1.2 Matriculation Science Programme Learning Outcomes
At the end of the programme, students should be able to:
1. Acquire knowledge of science and mathematics fundamental in
higher level education.
(PEO 1, MQF LOD 1)
2. Demonstrate manipulative skills in laboratory work.
(PEO 1, MQF LOD 2)
3. Communicate competently and collaborate effectively in group
work with skills needed for admission in higher education
institutions.
(PEO 2, MQF LOD 5)
4. Apply logical, analytical and critical thinking in scientific studies
and problem solving.
(PEO 3, MQF LOD 6)
5. Independently seek and share information related to science and
mathematics.
(PEO 4, MQF LOD 7)

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1.3 Physics 1 (DP015) Course Learning Outcome
At the end of the course, student should be able to:
1. Describe basic concepts of Physics of motion, momentum,
force, energy and heat.
(C2, PLO 1, MQF LOD 1)
2. Demonstrate manipulative skills during experiments of
measurement and uncertainty, plotting and analyzing linear
graph, free fall, linear momentum, friction and thermal
conduction in laboratory.
(P3, PLO 2, MQF LOD 2)
3. Discuss basic concepts of Physics through presentations.
(A2, PLO 3, CS 3, MQF LOD 5)
4. Solve problems related to Physics of motion, momentum,
force, energy and heat.
(C3, PLO 4, CTPS 2, MQF LOD 6)

1.4 Physics 2 (DP015) Course Learning Outcome
At the end of the course, student should be able to:
1. Describe basic concepts of simple harmonic motion,
mechanical wave and sound, direct current, capacitors,
magnetism and optics.
(C2, PLO 1, MQF LOD 1)
2. Demonstrate manipulative skills during experiments of simple
harmonic motion, sound waves, capacitor, ohm’s law,
magnetism and geometrical optics in laboratory.
(P3, PLO 2, MQF LOD 2)
3. Discuss basic concepts of magnetism through group
discussion.
(A2, PLO 3, TS1, MQF LOD 5)
4. Solve problems related to simple harmonic motion, mechanical
wave and sound, direct current, capacitors, magnetism and
optics.
(C3, PLO 4, CTPS 2, MQF LOD 6)

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1.5 Physics Practical Learning Outcomes
Physics experiment is to give the students a better understanding of
the concepts of physics through experiments. The aims of the
experiments in this course are to be able to:
1. introduce students to laboratory work and to equip them with the
practical skills needed to carry out experiment in the laboratory.
2. determine the best range of readings using appropriate measuring
devices.
3. recognise the importance of single and repeated readings in
measurement.
4. analyse and interpret experimental data in order to deduce
conclusions for the experiments.
5. make conclusions in line with the objective(s) of the experiment
which rightfully represents the experimental results.
6. verifying the correct relationships between the physical quantities
in the experiments.
7. identify the limitations and accuracy of observations and
measurements.
8. familiarise student with standard experimental techniques.
9. choose suitable apparatus and to use it correctly and carefully.
10. gain scientific trainings in observing, measuring, recording and
analysing data as well as to determine the uncertainties (errors) of
various physical quantities observed in the experiments.
11. handle apparatus, measuring instruments and materials safely and
efficiently.
12. present a good scientific report for the experiment.
13. follow instructions and procedures given in the laboratory
manual.
14. gain confidence in performing experiments.

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2.0 Guidance for Students
2.1 Ethics in the laboratory
a. Follow the laboratory rules.
b. Students must be punctual for the practical session.
Students are not allowed to leave the laboratory before
the practical session ends without permission.
c. Co-operation between members of the group must be
encouraged so that each member can gain experience in
handling the apparatus and take part in the discussions
about the results of the experiments.

d. Record the data based on the observations and not based
on any assumptions. If the results obtained are different
from the theoretical value, state the possible reasons.

e. Get help from the lecturer or the laboratory assistant
should any problems arise during the practical session.

2.2 Preparation for experiment
2.2.1 Planning for the practical
a. Before entering the laboratory
i) Read and understand the objectives and the
theory of the experiment.
ii) Think and plan the working procedures
properly for the whole experiment. Make sure
you have appropriate table for the data.
iii) Prepare a jotter book for the data and
observations of the experiments during pre-lab
discussion.
b. Inside the laboratory
i) Check the apparatus provided and note down
the important information about the apparatus.

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ii) Arrange the apparatus accordingly.
iii) Conduct the experiment carefully.
iv) Record all measurements and observations

made during the experiment.

2.3 Report writing

The report must be written properly and clearly in English and
explain what has been carried out in the experiment. Each
report must contain name, matriculation number, number of
experiment, title, date and practicum group.

The report must also contain the followings:

i) Objective • state clearly

ii) Theory • write concisely in your own words
• draw and label diagram if necessary

iii) Apparatus • name, range, and sensitivity, e.g
Voltmeter: 0.0 – 10.0 V
Sensitivity: ± 0.1 V

iv) Procedure • write in passive sentences about all the
steps taken during the experiment

v) Observation • data tabulation with units and
uncertainties

• data processing (plotting graph,
calculation to obtain the results of the
experiments and its uncertainties)

vi) Discussion • give comments about the experimental
results by comparing it with the
standard value

• state the source of mistake(s) or error(s)
if any as well as any precaution(s) taken
to overcome them

• answer all the questions given

vii) Conclusion • state briefly the results with reference to
the objectives of the experiment

Reminder: NO PLAGIARISM IS ALLOWED.

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3.0 Significant Figures

The significant figures of a number are those digits carry meaning
contributing to its precision. Therefore, the most basic way to
indicate the precision of a quantity is to write it with the correct
number of significant figures.

The significant figures are all the digits that are known accurately
plus the one estimated digit. For example, we say the distance
between two towns is 200 km, that does not mean we know the
distance to be exactly 200 km. Rather, the distance is 200 km to the
nearest kilometres. If instead we say that the distance is 200.0 km
that would indicate that we know the distance to the nearest tenth of a
kilometre.

More significant figures mean greater precision.

Rules for identifying significant figures:

1. Nonzero digits are always significant.

2. Final or ending zeros written to the right of the decimal point
are significant.

3. Zeros written on either side of the decimal point for the purpose
of spacing the decimal point are not significant.

4. Zeros written between significant figures are significant.

Example:

Value Number of Remarks
0.5 significant figures
0.500 Implies value between 0.45 and
0.050 1 0.55
5.0 3 Implies value between 0.4995 and
1.52 2 0.5005
2 Implies value between 0.0495 and
3 0.0505
Implies value between 4.95 and
5.05
Implies value between 1.515 and
1.525

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Value Number of Remarks
1.52 × 104 significant figures
Implies value between 15150 and
150 3 15250
The zero may or may not be
2 or 3 significant. If the zero is
(ambiguous) significant, the value implied is
between 149.5 and 150.5. If the
zero is not significant, the value
implied is between 145 and 155.

4.0 Uncertainty in Measurements

No matter how careful or how accurate are the instruments, the
results of any measurements made at best are only close enough to
their true values (actual values). Obviously, this is because the
instruments have certain smallest scale by which measurement can be
made. Chances are, the true values lie within the smallest scale.
Hence, we have uncertainties in our measurements.

The uncertainty of a measurement depends on its type and how it is

done. For a quantity x with uncertainty x , the measurement should

be recorded as x  x with appropriate unit.

The relative uncertainty of the measurement is defined as x .
x

and therefore its percentage of uncertainty, is given by x 100% .
x

4.1 Single Reading

(a) If the reading is taken from a single point or at the end of
the scale we use:

x = 1  (smallest division of the scale)
2

(b) If the readings are taken from two points on the scale:

x = 2   1   smallest division from the scale  
2

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(c) If the apparatus has a vernier scale:

x = 1  (smallest unit of the vernier scale)

4.2 Repeated Readings

For a set of n repeated measurements, the best value is the
average value, that is

x  n xi

i 1

n

where: n is the number of measurements taken

xi is the ith measurement value

The uncertainty is given by

n
x  xi
x  i1 n

The result should be written in the form of
x  x  x

4.3 Straight Line Graphs

Straight line graphs are very useful in data analysis for many
physics experiments.
From straight line equation, that is, y  mx  c we can easily
determine the gradient m of the graph and its intercept c on the
vertical axis.

When plotting a straight line graph, the line does not necessary
passes through all the points. Therefore, it is important to
determine the uncertainties ∆m and ∆c for the gradient of the
graph and the y-interception respectively.

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Method to determine ∆m and ∆c:
Consider the data obtained is as follows:

x x1 x2 x3………………..xn

y y1 y2 y3………………..yn

(a) Find the centroid x , y , where

x  n xi and y  n yi

i 1 i 1

n n

(b) Draw the best straight line passing through the centroid
and balance.

(c) Determine the gradient of the line by drawing a triangle
using dotted lines. The gradient is given by

m y2  y1
x2  x1

y  
(x2, y2)

 
c (x1, y1) 

0 x

Figure A

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(d) The uncertainty of the slope, ∆ can be calculated using
the following equation

∆ = ∑ (− )
( − 2) ∑ ( − ̅)

where n is the number of readings and ̅ is the average
value of x given by

̅= 1

and the estimated value of y, is given by,
= +̂

(e) The uncertainty of the y-intercept, ∆ can be calculated
using the following equation

∆= 1 (−) 1+∑ ̅
−2 ( − ̅)

4.4 Procedure to draw a straight line graph and to determine
its gradient with its uncertainty
(a) Choose appropriate scales to use at least 80% of the
sectional paper. Draw, label, mark the two axes, and give
the units. Avoid using scales of 3, 7, 9, and the likes or
any multiple of them. Doing so will cause difficulty in
plotting the points later on.
(b) Plot all points clearly with . At this stage you can see
the pattern of the distribution of the graph points. If there
is a point which is clearly too far-off from the rest, it is
necessary to repeat the measurement or omit it.
(c) Calculate the centroid and plot it on the graph.

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Example:
Suppose a set of data is obtained as below. Graph of T2
against  is to be plotted.

 ( 0.1 cm) 10.0 20.0 30.0 40.0 50.0 60.0
T2 ( 0.01 s2) 0.33 0.80 1.31 1.61 2.01 2.26

From the data:

  10.0  20.0  30.0  40.0  50.0  60.0  35.0 cm
6
0.33  0.80 1.311.61 2.01 
T2  6 2.26  1.39 s2

Therefore, the centroid is (35.0 cm, 1.39 s2).

(d) Draw a best straight line through the centroid and
balance. Points above the line are roughly in equal
number and positions to those below the line.

(e) Determine the gradient of the line. Draw a fairly large
right-angle triangle with part of the line as the
hypotenuse.

From the graph in Figure B, the gradient of the line is as
follows:

For the best line:

m  (2.10  0.00) s2
(53.0  0.0) cm

 0.040 s2 cm1

The gradient of the graph and its uncertainty should be
written as follows:

m = (0.040 ± ___) s2 cm-1
Take extra precaution so that the number of significant
figures for the gradient and its uncertainty are in
consistency.

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T2 (s2) Graph of T2 against 
2.4 m

2.2

2.0

1.8
Wrong best straight line

1.6

1.4

1.2

1.0 2.10 – 0.00

0.8
0.6

0.4  (cm)

0.2

53.0 – 0.0

0 10 20 30 40 50 60

Figure B

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4.5 Calculation of uncertainties

Rewrite the data in the form of

 −  −  T2 − −

10.0 -25.0 625.0 0.33 0.4 -0.070 0.0049
20.0 -15.0 225.0 0.80 0.8 0.000 0.0000
30.0 -5.0 25.0 1.31 1.2 0.110 0.0121
40.0 5.0 25.0 1.61 1.6 0.010 0.0001
50.0 15.0 225.0 2.01 2.0 0.010 0.0001
60.0 25.0 625.0 2.26 2.4 -0.140 0.0196
Ʃ=0.0368
Ʃ=210.0 Ʃ=1750.0

Where,  is the average of ,
 = = 35.0 cm

Where, is the expected value of T2

= 0.04

Calculate the uncertainty of slope, Δm

∆ = ∑( )

( )∑ ( ̅)

= ( . )
)(

= ±0.002
Then, calculate the uncertainty of y-intercept, Δc

∆= ∑ (−) 1+∑ ̅
∆= −2 ( − ̅)

0.0368 1 + 35
6−2 6 1750

∆ = ±0.09

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The data given in section 4.4 was obtained from an experiment
to verify the relation between T2 and  . Theoretically, the
quantities obey the following relation,

T 2   k  
p

where k is a natural number equals 39.48 and p is a physical
constant. Calculate p and its uncertainty.

Solution:

From the equation, we know that

k  gradient m
p

p  k
m

 39.48
0.040
 987 cm s2

Since k is a natural number which has no uncertainties, that is
k = 0.

∆ = ∆ +∆

= 0+ . 987
.
= 49.35

so we write, or p = (1000  50) cm s–2
p = (987  49.35) cm s–2

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SEMESTER I

DP014 Lab Manual

EXPERIMENT 1 : MEASUREMENT AND UNCERTAINTY

Course Learning Objective: Demonstrate manipulative skills during
experiments in measurement and uncertainty, plotting and analyzing
linear graph, free fall, linear momentum, friction and thermal conduction
in laboratory.
(P3, CLO2, PLO 2, MQF LOD 2)

Learning Outcomes: At the end of this lesson, students should be able to
measure and determine the uncertainty of physical quantities.

Student Learning Time (SLT):
Face-to-face Non face-to-face
2 hours 0

Theory:

Measuring some physical quantities is part and parcel of any physics
experiment. It is important to realise that not all measured values are
exactly the same as the actual values. This could be due to the errors
that we made during the measurement, or perhaps the apparatus that
we used may not be accurate or sensitive enough. Therefore, as a rule,
the uncertainty of a measurement must be taken and it has to be
recorded together with the measured value.

The uncertainty of a measurement depends on the type of measurement
and how it is done. For a quantity x with the uncertainty x, its
measurement is recorded as below:

x  x

The relative uncertainty of the measurement is defined as:

x
x

and therefore its percentage of uncertainty, is given by x 100%
x

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1. Single Reading

1.1 If the reading is taken from a single point or at the end
of the scale,

x = 1 (the smallest division from the scale)
2

1.2 If the readings are taken from two points on the scale,

x = 2  [ 1  (the smallest division from the scale)]
2

1.3 If the apparatus uses a vernier scale,
∆x = 1  (the smallest unit from the vernier scale)

2. Repeated Readings

For a set of n repeated measurements of x, the best value is the average
value

n
xi
x i 1 1.1

n

where n = the number of measurements taken
xi = the ith measurement

The uncertainty is given by  xi
n
x  n x 1.2

i1

The result should be written as

x  x  x 1.3

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3. Combination of uncertainties

We adopt maximum uncertainty.

3.1 Addition or subtraction
x  a bc  x  a  b  c

3.2 Multiplication with constant k
x  ka  x  ka

3.3 Multiplication or division x  a b c 
x a b c
x  ab    
c

3.4 Powers  x n  a 
x a
x  an

Apparatus:

A micrometer screw gauge
A vernier callipers
A metre rule
A ball bearing
A coin
A metal rod
A glass rod
An electronic balance

Procedure:

a) Use appropriate instrument to perform steps (a) to (f). Record all
your measurement in appropriate table. Determine the
uncertainty and the percentage of uncertainty for each set of
readings.

Measurement for single reading

a) The length of the metal rod.
b) The length and width of laboratory manual.
c) The mass of ball bearing.

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DP014 Lab Manual

Measurement for repeated readings
i) The diameter of the ball bearing.
ii) The diameter of the coin.
iii) The external diameter of the glass rod.
b) Calculate the following derived quantities and it uncertainties.
i) Perimeter of laboratory manual.
ii) Circumference of the coin
iii) Surface area of ball bearing.
iv) Volume of ball bearing.
v) Density of ball bearing.

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DP014 Lab Manual

EXPERIMENT 2: PLOTTING AND ANALYZING LINEAR GRAPH
Course Learning Objective: Demonstrate manipulative skills during
experiments in measurement and uncertainty, plotting and analyzing
linear graph, free fall, linear momentum, friction and thermal conduction
in laboratory.
(P3, CLO2, PLO 2, MQF LOD 2)

Learning Outcomes: At the end of this lesson, students should be able to
develop skill in plotting and analyzing linear graphs.

Student Learning Time (SLT):
Face-to-face Non face-to-face
2 hours 0

Theory:

Graphs are often used to represent the dependence or relationship of
two or more experimental quantities. In experimental work, the
independent variable is usually represented by the x-axis while the
dependent variable is represented by the y-axis. The shape of the
graphs can take many forms, but our focus will only be on linear
graphs. Linear graphs obey the following equation

y  mx  c 2.1

where m is the gradient of the graph and c is the intercept on the y-axis.

1. Procedure to draw a graph
1.1 Axes scale, label and title
a) Choose the scale on each axis such that all data
points should be shown and should fill not less
than half the size of the plotted area. The scales
should be in multiples of 10, 5, 2 or 1 and DO
NOT USE odd multiples. In some cases it may
be necessary to adjust the graph with an axis that
does not start at zero.

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b) Label the scales of each axis with simple
numbers. In cases where the numbers are very
large or very small, use scientific notation.

c) Axes title should represent the relevant
quantities with appropriate units.

1.2 Plotting the data points and the straight line

a) Determine the centroid which is defined as
follows:

n xi n yi
x  i 1 y  i 1 2.2

n n

b) The data points should be plotted using the
symbol . Use the symbol  to plot the centroid.

c) Draw a best fit solid straight line. The line must
pass through the centroid and as many data
points as possible as shown in Figure 2.1. It may
not necessarily passes through every data point
and the origin.

1.3 Determination of gradient

a) The gradient of the graph is determined by
choosing two points (x1, y1) and (x2, y2) which
lie on the line (NOT THE DATA POINTS) and
could be read accurately. Draw a right angle
triangle using these two points.

b) The value of the gradient is calculated as:

m y2  y1 2.3
x2  x1

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DP014 Lab Manual

y

 
(x2, y2)

 y2  y1





c (x1, y1) x2  x1

0 x

Figure 2.1
Note: The size of the triangle is such that (x2 – x1) is greater

than 50% of the x-axis data range (refer Figure 2.1).

2. Transformation to linear graph

The relationship between physical quantities may not be linear.
However, the relationship often can be transformed into a linear form
and hence a linear graph may be plotted. For example, the relationship

between the period, T of oscillation of a simple pendulum of length  is

given as

T  2  2.4
g

which can be expressed in linear form as

T 2  4 2  2.5
g

Thus a plot of T2 against  is a straight line passing through the origin

with gradient given by 4
g
 2

m 2.6

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DP014 Lab Manual

Exercise

1. Table 2.1 shows data taken in a free fall experiment.
Measurement were made of the distance of fall (y) at each
precisely measured times. Complete the table. Use proper
number of significant figures in the table entries.

Table 2.1

Distance, y Time, t ( 0.001 s) t (s) t2 (s2)
( 0.1 cm)
t1 t2 t3
10.0
20.0 0.143 0.139 0.140
30.0
40.0 0.202 0.199 0.200
50.0
60.0 0.247 0.245 0.249
70.0
0.286 0.286 0.280

0.319 0.320 0.317

0.350 0.346 0.352

0.378 0.380 0.376

a) The equation of motion for an object in free fall starting

from rest is y 1 gt 2 , where g is the acceleration due to
2

gravity. This is a parabolic equation, which has the general
form y  ax 2 .

b) Convert the curve to a straight line by plotting a graph of y
against t2.

c) Determine the slope of the line and calculate the
experimental value of g.

2. A physical pendulum which is made of a rod has its axis of
oscillation at a distance, h from its centre of mass as shown in
Figure 2.2. The period of oscillation, T is tabulated in Table 2.2.

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DP014 Lab Manual

h Pin (axis of
H oscillation)
Centre of mass



Figure 2.2

Table 2.2

h 0.200 0.400 0.600 0.800 1.000 1.200 1.400 1.600
( 0.001 m) 2.65 2.54 2.39 2.20 2.00 1.83 1.55 1.26
T ( 0.01 s)

T2 (s2)

The period of oscillation is given as

T  2 H h 2.7
g

where H is a constant and g is the acceleration due to gravity.
a) Complete Table 2.2
b) Express equation 2.7 in linear form as equation 2.1.
c) Plot a linear graph to determine H and g.

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DP014 Lab Manual

EXPERIMENT 3 : FREE FALL

Course Learning Objective: Demonstrate manipulative skills during
experiments in measurement and uncertainty, plotting and analyzing linear
graph, free fall, linear momentum, friction and thermal conduction in
laboratory.
(P3, CLO2, PLO 2, MQF LOD 2)

Learning Outcomes: At the end of this lesson, students should be able to
determine the acceleration due to gravity, g using free fall motion

Student Learning Time (SLT):
Face-to-face Non face-to-face
2 hours 0

Theory:

When a body of mass, m falls freely from a certain height, h above the
ground, it experiences a linear motion. The body will obey the equation
of motion,

s  ut  1 at 2 3.1
2
By substituting,

s = –h = downward displacement of the body from the falling
point to the ground

u = 0 = the initial velocity of the body
a = –g = the downward acceleration due to gravity
t = time taken for the body to reach the ground

we obtain the displacement of the body, h as

h  1 gt 2 3.2
2

Apparatus:
A retort stand with a clamp
A timer
A metre rule
A free fall adaptor
A horizontal table
A steel ball (diameter of 1.0 cm)

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Procedure: DP014 Lab Manual
electromagnet
clamp
steel ball h timer
retort
stand

trap door

Figure 3.1

electromagnet N1 P : +ve
P2 N : ve
N
steel ball
retort H 12 V N1
stand hinged P1
trap door
clamp timer
container P3 P1 N P2 N3 P3

N
3

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DP014 Lab Manual

a) Set up the apparatus as in Figure 3.1 or Figure 3.2 (Set up for free
fall apparatus with separate power supply to electromagnet).

b) Switch on the circuit and attach the steel ball onto the upper
contact.

c) Adjust the height of the electromagnet above the point of impact.
d) Begin with a small value of h.
e) Switch off the circuit and let the ball fall. Record the value of h

and t.
f) Take 6 sets of reading at different values of h and t.
g) Plot a graph of h against t2.
h) Determine the value of g from the gradient of the graph.
Note: The value range of h-axis should be extended slightly more
than the height of the table H.

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DP014 Lab Manual

EXPERIMENT 4 : LINEAR MOMENTUM

Course Learning Objective: Demonstrate manipulative skills during
experiments in measurement and uncertainty, plotting and analyzing linear
graph, free fall, linear momentum, friction and thermal conduction in
laboratory.
(P3, CLO2, PLO 2, MQF LOD 2)

Learning Outcomes: At the end of this lesson, students should be able to
verify the principle of conservation of linear momentum.

Student Learning Time (SLT):
Face-to-face Non face-to-face
2 hours 0

Theory:

Linear momentum, p is a vector quantity defined as the product of
mass and velocity. aFsorp a mbvo.dyIn of mass, m and velocity, v; its
momentum is given  the absence of external force, the

total momentum of the system is conserved. This is known as the
Principle of Conservation of Linear Momentum.

Applying the principle of conservation of linear momentum in
collision, the total momentum of the colliding bodies remains the same
bcvo1e,flloiardneindagnvbd2oadafirteeesrt(htihe.ee:vbceoolodllcyiisti1ioesna.nbdLeefbotordmey1a2na)dnadasfmitne2rFbtihegeuthrceeol4mli.s1aisoasnnedsoofu1fb, towud2oy,
1 and body 2 respectively and written as

m1u1  m2u2  m1v1  m2v2 4.1

Since momentum is a vector quantity, the principle of conservation of
linear momentum is equally true in both x-axis and y-axis direction.

In the case of an oblique impact, we resolve the momentum into x-axis
and y-axis and respectively and written as

x-axis m1u1  m1v1 cos  m2v2 cos  4.2

and y-axis 0  m1v1 sin  m2v2 sin  4.3

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DP014 Lab Manual

m1 m2 m1 m2
u1
u2 v1 v2
m1
u1 a) head-on collision

m1 v1
α
m2 β
u2

b) oblique collision m2 v2
Figure 4.1

In this experiment, we shall study the collision between two ball
bearings on a curved track. Tgahiensfirmstobmaellntbuemarinmg1ui1s released from the
top of the track so that it before it hits the

second ball bearing which is stationary at the horizontal end of the
track.

A ball bearing 1 A ball bearing 1
curved track
horizontal end ball bearing 2
string
table h pendulum bob
drawing paper carbon paper
R= xo Figure 4.2b
Figure 4.2a

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DP014 Lab Manual

Let h be the height of the ball bearing 1 from the falling point to the
ground when it starts to fall freely and R is its horizontal displacement.
If t is the time of flight, then from the kinematics equation,
 
h  0  1 g t2
2

t 2h
g

The horizontal displacement of the ball bearing,

R  uxt

where

Ru 2h
g

Thus, uR g 4.4
2h

Evidently, the velocity of the ball bearing is directly proportional to its
horizontal displacement, R.

Since the balls fall from the same height, by substituting equations 4.2
and 4.3 respectively into equation 4.4,

x-axis m1x0  m1x1  m2 x2 4.5

and y-axis 0  m1 y1  m2 y2 4.6

Evidently, if equations 4.5 and 4.6 are practically satisfied, the
principle of conservation of linear momentum is thus verified.

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DP014 Lab Manual

curved track carbon paper
table
pendulum bob landing point of
R1 ball bearing 1

 m1 y2 x
y1 m2

R2

x1 x–axis
x2 direction

(top view) xo
Figure 4.3

Apparatus:
A level table
A curved track.
(Important: The lower end of the track must be horizontal)
2 ball bearings (diameter of 1.0 cm)
A piece of string
A pendulum bob
A metre rule
A piece of drawing paper (A3)
A piece of carbon paper (A4)
A retort stand

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DP014 Lab Manual

Procedure:
a) Weigh the mass of the two ball bearings, m1 and m2.
b) Set up the apparatus as in Figure 4.2a.
c) Mark point A on the curved track as in Figure 4.2a.
d) Release ball bearing 1 from point A.
e) Observe the landing point of ball bearing 1 on the floor in order

to place the carbon paper on top of a drawing paper so as to mark
accurately the point where the ball bearing will land on the floor.
f) Release ball bearing 1 from point A and measure the distance
from the bottom end of the pendulum bob to the landing point of
ball bearing 1, xo. Repeat this step to obtain at least five readings
and calculate the average value of xo.
g) Place ball bearing 2 on the end of the horizontal track slightly off
the path of ball bearing 1 so that an oblique collision occurs.
h) Release ball bearing 1 from point A (Refer to Figure 4.2b).
These two ball bearings will subsequently collide and fall freely
in a projectile motion.
i) Measure the position of landing points for each ball bearing i.e.,
(x1,y1) for ball bearing 1, and (x2,y2) for ball bearing 2.
(Refer to Figure 4.3)
j) Repeat step (g) to (i) for at least another four sets.
k) Does your result satisfy equations 4.5 and 4.6? Give comments.

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DP014 Lab Manual

EXPERIMENT 5: FRICTION

Course Learning Objective: Demonstrate manipulative skills during
experiments in measurement and uncertainty, plotting and analyzing linear
graph, free fall, linear momentum, friction and thermal conduction in
laboratory.
(P3, CLO2, PLO 2, MQF LOD 2)

Learning Outcomes: At the end of this lesson, students should be able to
determine the coefficients of static friction and kinetic friction.

Student Learning Time (SLT):
Face-to-face Non face-to-face
2 hours 0

Theory:

Static friction (at the onset of motion):
R

fF

mg

Figure 5.1

By referring to Figure 5.1, if force F is increased, frictional force f
also increases accordingly and the object still remain at rest. However,
for a certain value of F, the object starts to move. At this stage, the
frictional force is known as the limiting static frictional force fs which
is the maximum value of f. Hence,

fs = sR 5.1
fs = s mg 5.2
s = coefficient of static friction
where, fs = static frictional force
R = normal reaction force

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DP014 Lab Manual

Kinetic friction (in motion):

Now, if the object is in motion, the frictional force is known as kinetic
friction fk. The kinetic frictional force is less than the static frictional
force. That explains why it is difficult to move an object which is
initially at rest, but once it is in motion, less force is needed to
maintain the motion.
fk = kR
5.3

where k = coefficient of kinetic friction
fk = kinetic frictional force
R = normal reaction force

Since fk < fs, therefore s > k.

Apparatus:
A piece of plywood
A wooden block
Two sets of slotted mass (2 g, 5 g, 10 g, 20 g)
Sand granules or small metal pallets (each about 2 g)
Weighing pan or a tin can
A set of pulley with clamp
A piece of string
Plasticine
A balance

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Procedure: DP014 Lab Manual

resting slotted mass mr pulley
wooden block mb string
plywood
sand granules
plasticine weighing pan or
table tin can
e slotted
mass

Figure 5.2

a) Weigh the mass of the wooden block, mb.
b) Set up the apparatus as in Figure 5.2. Make sure that the string

from the block is tied up horizontally to the pulley. Mark the
initial position of the wooden block.
c) Add the slotted mass into the weighing pan or tin can gradually
until the wooden block begins to slip. If the wooden block still
remains static, begin adding the sand granules or the metal
pallets gradually until the block starts to move.
Note: Add the mass gently to avoid impulsive force.
d) Weigh and record the total mass, mh required to move the
wooden block. Repeat this step three times to get the average
value of mh.
e) Add different masses of mr onto the wooden block and repeat
step (c) and (e).

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DP014 Lab Manual

f) Repeat step (e) for at least five different values of mr.

g) Plot a graph of fs against R where fs  mh g and R  mr  mb  g.

h) Determine s, the coefficient of static friction from the graph.
i) Repeat step (c) but exert a little push (using tic-tac pen) to the

wooden block every time each mass is added. Weigh and record
the total mass, mh when the block moves slowly and steadily
along the plywood.
j) Add different masses of mr onto the wooden block and repeat
step (i).
k) Repeat step (j) for at least five different values of mr.

l) Plot a graph of fk against R where fk = mh g and R  mr  mb  g.

m) Determine k, the coefficient of kinetic friction from the graph.
n) Compare the value of s and k. Does this confirm to the theory?

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DP014 Lab Manual

EXPERIMENT 6: THERMAL CONDUCTION

Course Learning Objective: Demonstrate manipulative skills during
experiments in measurement and uncertainty, plotting and analyzing linear
graph, free fall, linear momentum, friction and thermal conduction in
laboratory.
(P3, CLO2, PLO 2, MQF LOD 2)

Learning Outcomes: At the end of this lesson, students should be able to
determine the thermal conductivity of glass.

Student Learning Time (SLT):
Face-to-face Non face-to-face
2 hours 0

Theory:

Thermal conductivity k could be expressed in terms of the rate of flow
of heat,

dQ  kA dT 6.1
dt dx

where dQ = rate of heat flow
dt
A = tangential surface area for heat flow

dT = temperature gradient
dx

Relationship between temperature T and time t for this experiment is
given by

logT0  logT  kt 6.2
Brx 6.3
or,

where T = temperature (in Kelvin)
T0 = 293 K

 t = time

B = constant 4.84106 J m 3 K 1
r = average radius of the boiling tube
x = thickness of the wall of the boiling tube

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Apparatus: DP014 Lab Manual
A boiling tube
A digital thermometer digital
A mercury thermometer thermometer
A 1000 cm3 beaker
Two stirrers stirrer
A cork boiling tube
A stopwatch ice-water mixture
A vernier callipers warm water
A retort stand and clamp beaker
Ice cubes
Hot water

Procedure:

retort stand

stirrer

1 cm

mercury
thermometer

Figure 6.1

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DP014 Lab Manual

a) Measure the internal and external diameters of a boiling tube and
calculate the average radius r and the thickness x of the wall of
the boiling tube.

b) Fill up a beaker with water and ice.
c) By referring to Figure 6.1, clamp the boiling tube on a retort

stand and lower the boiling tube into the beaker until the whole
of the boiling tube almost submerge in the ice and water mixture.
The temperature of the ice-water mixture inside the beaker
should be 0 C.
d) Pour hot water into the boiling tube until the water level inside
the tube reaches about 1 cm below the ice-water level in the
beaker.
e) Insert the stirrer and thermometer through the cork.
f) Record at regular time t and the corresponding temperature T
starting from 30 ⁰C until it drops to 3 ⁰C. The ice-water mixture
in the beaker and the warm water in the boiling tube should be
constantly stirred throughout the experiment.
g) Tabulate t, T and log T.
h) Plot a graph of log T against t.
i) Calculate the gradient of the graph and determine the thermal
conductivity of glass.
j) Compare the result with the standard value k = 0.8 W m-1 K-1 for
glass. Give comments.

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SEMESTER II

DP024 Lab Manual

EXPERIMENT 1 : SIMPLE HARMONIC MOTION (SHM)

Course Learning Objective: Demonstrate manipulative skills during
experiments in simple harmonic motion, sound waves, capacitor, Ohm’s
law, magnetism and geometrical optics in laboratory.
(P3, CLO2, PLO 2, MQF LOD 2)

Learning Outcomes: At the end of this lesson, students should be able
to:

i) determine the acceleration g due to gravity using a
simple pendulum.

ii) investigate the effect of large amplitude oscillation to
the accuracy of g obtained from the experiment.

Student Learning Time (SLT):
Face-to-face Non face-to-face
2 hours 0

Theory:

An oscillation of a simple pendulum is a simple harmonic motion if:

i) the mass of the spherical bob is a point mass
ii) the mass of the string is negligible
iii) amplitude of the oscillation is small (< 10)

According to the theory of SHM, the period of oscillation of a simple
pendulum, T is given as:

T  2 l 1.1
g

Where l = length of pendulum
g = acceleration due to gravity

Rearrange equation 2.1, we obtained

T 2  4 2l 1.2
g

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DP024 Lab Manual

Evidently, a graph of T2 against l is a straight line of gradient equals
4 2
g . Hence from the gradient of the graph, the value of g can be

calculated.

Apparatus:

A piece of string (105 cm)
A small pendulum bob
A pair of small flat pieces of wood or cork
A retort stand with a clamp
A stop watch
A metre rule
A protractor with a hole at the centre of the semicircle
An optical pin
A pair of scissors or a cutter
A stabilizing weight or a G-clamp

Procedure:

a) Set up a simple pendulum as in Figure 1.1.

b) Measure the length, l of the pendulum.

c) Release the pendulum at less than 10 from the vertical in one
plane and measure the time for 20 oscillations. Repeat the
operation and calculate the average value. Then calculate the
period of oscillation, T of the pendulum.

Note : Start the stopwatch after several complete oscillations.

d) Repeat step (c) at least 5 times with different values of length, l
of the pendulum. Record the values for l and T.

e) Plot a graph of T2 against l and determine the value of g from the
graph.

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retort stand DP024 Lab Manual

a pair of wood or cork
optical pin (axis of
oscillation)

 protractor

l
string

weight pendulum
table bob

Figure 2.1

f) Fix the length of pendulum at 100 cm. Release the pendulum
through a large arc of about 70 from the vertical. Record the
time for 5 complete oscillations. Repeat the operation and
calculate the average value. Then calculate the period, T of the
oscillation of the simple pendulum.

g) Calculate the acceleration due to gravity, g using equation 2.1
and the value of l and T from step (f).

h) Compare the values of g obtained from step (e) and step (g).
Does your result differ from the standard value? Give comments.

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DP024 Lab Manual

EXPERIMENT 2: SOUND WAVES

Course Learning Objective: Demonstrate manipulative skills during
experiments in simple harmonic motion, sound waves, capacitor, Ohm’s
law, magnetism and geometrical optics in laboratory.
(P3, CLO2, PLO 2, MQF LOD 2)

Learning Outcomes: At the end of this lesson, students should be able
to determine the speed of sound using a resonance tube.

Student Learning Time (SLT):
Face-to-face Non face-to-face
2 hours 0

Theory:

AA A l3

l1 N

NN l2

A A

N N
A

N

(a) (b) (c)
Figure 2.1

Sound waves propagating down the tube are reflected at the closed end
and stationary waves are produced by the interference of the incident
and reflected wave trains. Since the air is at rest at the closed end, it is
therefore a node. The open end must be an antinode. The antinode is
situated at a short distance c (known as the end correction) beyond the
open end of the tube. Figure 2.1 shows the positions of nodes and
antinodes of the vibration for the first three conditions of resonance.
Note: Sound waves are longitudinal and are shown as transverse in
order to create a clear picture of what is happening.

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