SP015 Pre-Lab Module Answer

SP015 Pre-Lab Module Answer

EXPERIMENT 1: MEASUREMENT AND UNCERTAINTY

Students will able to describe technique of measurement and determine uncertainty of length
of various objects.

INTRODUCTION

1. Complete Table 1.

Basic Quantity Symbol SI Unit Measuring Instrument
(with symbol)
Length l meter rule, vernier caliper,
metre, m micrometer screw gauge
Mass m electronic balance, triple
kilogram, kg beam balance
Time t
second, s stopwatch, sport timer

Electric Current I ampere, A ammeter

Temperature T kelvin, K thermometer

Table 1
2. Vernier caliper is used to measure the diameter of a coin.

3. Micrometer screw gauge is usually used to measure the diameter of a thin wire or the
thickness of a paper.

4. Complete Table 2. Sensitivity Uncertainty
0.1 cm  0.1 cm
Measuring Apparatus 0.002 cm  0.002 cm
Meter rule 0.01 mm  0.01 mm
Vernier caliper 0.001 cm  0.001 cm
Micrometer screw gauge 0.1 C  0.1 C
Travelling microscope 0.1 V  0.1 V
Thermometer 0.01 A  0.01 A
Voltmeter 0.01 g  0.01 g
Ammeter
Electronic Balance Table 2

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SP015 Pre-Lab Module Answer

5. State TWO types of reading.
(i) Single reading
(ii) Repeated reading

6. The repeated readings for a measurement is recorded as a, b, c, d, e, and f. Write the
equation of average value and its uncertainty.

Quantity Equation
Average value, x x  abcd e f
Uncertainty, x
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x  | x  a |  | x  b |  | x  c |  | x  d |  | x  e |  | x  f |

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EXPERIMENT
7. Complete Table 3.

Measurement Measuring Uncertainty Type of reading
Instrument / Smallest (single point /

scale two point /
vernier scale)

Length of a metal rod Meter rule  0.1 cm Two points

Length and width of a Meter rule  0.1 cm Two points
laboratory book

Mass of a ball bearing Electronic balance  0.01 g Single point

Diameter of a coin Vernier caliper  0.002 cm Vernier scale
Vernier scale
Diameter of a ball Micrometer screw  0.01 mm Vernier scale
bearing gauge

External diameter of a Micrometer screw  0.01 mm
glass rod gauge

Table 3

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SP015 Pre-Lab Module Answer

8. Determine the reading for the following measurements.

(a)

0 cm 1 2 Main scale : 1.100 cm
Vernier scale : 0.055 cm

0 1 2 3 4 5 6 7 8 9 10 Actual reading: 1.155 cm

Main Vernier
scale scale

(b) 11 cm 12 cm Main scale : 10.000 cm
Vernier scale : 0.006 cm
10 cm Actual reading: 10.006 cm

01 23 Main scale : 18.30 cm
Vernier scale : 0.00 cm
(c) Actual reading: 18.30 cm

18 cm 19 cm

0 5 10

(d) Main scale : 2.50 mm
Vernier scale : 0.38 mm
45 Actual reading: 2.88 mm
0

40

35

30

(e) Main scale : 6.50 mm
Vernier scale : 0.00 mm
5 Actual reading: 6.50 mm
05

0

45

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SP015 Pre-Lab Module Answer

9. The repeated readings of the diameter of a ball bearing, d are 2.50 mm, 2.52 mm,
2.51 mm and 2.50 mm.
(a) Calculate the average value of the diameter, d and its uncertainty, d . Record
the diameter in terms of its average value and uncertainty, (d  d).
Average value of the diameter,
d  d1  d2  d3  d4  2.50  2.52  2.51  2.50  2.51 mm
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d  | d  d1 |  | d  d2 |  | d  d3 |  | d  d4 |
4

d  | 2.51  2.50 |  | 2.51  2.52 |  | 2.51  2.51 |  | 2.51  2.50 |
4

d  0.01 mm

Diameter of the ball bearing, d = ( 2.51  0.01 ) mm

(b) What is the instrument or apparatus used for this measurement?
Micrometer screw gauge

(c) From (a), calculate the volume of the ball bearing, V and its uncertainty, V.

Volume of ball bearing, Relative uncertainty of volume, V  3d
Vd

V  4 r 3 Uncertainty of volume, V   3d V
3 d

V  4   d 3 V  3 (0.01) (8.28)
3 2 2.51

V  4   2.513 V  0.1 mm3
3 2

V  8.28 mm3

(e) Record the volume, V in terms of its average value and uncertainty, (V  V ).
Volume of the ball bearing, V = ( 8.3  0.1 ) mm3

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SP015 Pre-Lab Module Answer

DATA ANALYSIS Diameter of ball bearing, D  Di (mm)
10. Complete Table 4. D ( 0.01 mm)
15.42 0.04
No. 15.55 0.09
15.30 0.16
1 15.48 0.02
2 15.49 0.03
3 15.45 0.01
4 15.55 0.09
5 D  0.06 mm
6 D  15.46 mm
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Average Table 4

11. Record the diameter, D in terms of its average value (best value) and uncertainty,
(D  D).

Diameter of ball bearing, D = ( 15.46  0.06 ) mm

12. Calculate its percentage of uncertainty.

Percentage of uncertainty of length, %  D   D 100%
D D

%  D   0.06 100%
 D  15.46

%  D   0.39%
D

13. State THREE precautions of this experiment.
(i) Check for zero error before using the apparatus.
(ii) Ensure that eye view is perpendicular to the scale of the instrument.
(iii) Turn the ratchet of the micrometer screw gauge until a click sound is heard.

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SP015 Pre-Lab Module Answer

EXPERIMENT 2: FREE FALL AND PROJECTILE MOTION
Students will able to describe experiment to determine acceleration due to gravity using free
fall and projectile motion.

INTRODUCTION
1. What is meant by free fall motion?

Free fall motion is the motion of an object which is totally under the influence of
gravitational force (acted upon by gravity alone).

2. Under free fall motion, the acceleration of an object is also known as gravitational
acceleration or acceleration due to gravity. What is the symbol and SI unit of this type
of acceleration?
Symbol of gravitational acceleration: g
SI unit of gravitational acceleration: m s-2

3. What is the value of acceleration due to gravity on the surface of Earth?
The value of acceleration due to gravity on the surface of Earth is 9.81 m s-2.

4. Projectile motion of an object is the motion of an object which is projected or thrown.
Under a gravitational field when the air resistance is not present, projectile motion
can be considered as a free fall motion. State TWO differences between free fall motion
and projectile motion.
- Free fall motion is in one dimension. Projectile motion is in two or more dimension.
- Initial horizontal velocity of free fall is always zero but the initial horizontal
velocity of projectile motion is not necessarily zero.
- Free fall motion has no horizontal distance or displacement but projectile motion
has horizontal displacement.

5. State the law applied in these experiments.
Law of conservation of energy.

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SP015 Pre-Lab Module Answer

EXPERIMENT
6. How do we release the steel ball to form a

(a) free fall motion?
The steel ball is attached to the upper contact of free fall electromagnet adaptor
connected to the power supply. When switch is off, the steel ball falls freely.

(b) projectile motion?
The steel ball is released from the curvature railing located on the table and
projected on the drawing paper on the floor.

7. State the measurement apparatus involved. (e.g. type / name of equipment) for both
experiment.

Free fall motion: meter rule and digital timer

Projectile motion: meter rule

8. State the related variables that need to be recorded in this experiment.

Free Fall Motion Projectile Motion

Manipulated variable Height of the steel ball Height of the steel ball on
(change on purpose) from the trap door. the curvature railing.

Responding variable Time taken for the steel Horizontal distance or
(what is measured) ball to fall. range of the steel ball
projected from the table.

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SP015 Pre-Lab Module Answer

9. Construct the table to record the related values for free fall and projectile motion
experiment.

(a) Free Fall Motion

No. height, h (  0.1 cm ) time, t (  0.000001 s ) t 2 ( s2 )
1
2

(b) Projectile Motion Range, R (  0.1 cm ) R 2 ( cm2 )

No. height, h (  0.1 cm )
1
2

10. How do you obtain the value of t for projectile motion from the graph of free fall
motion experiment?

The value of t for projectile motion can be obtained from the graph of free fall motion
experiment using extrapolation method by referring to the value of height from the edge
of the railing to the landing surface, H.

DATA ANALYSIS

11. (a) Write the equations related to both experiments in order to determine the
acceleration due to gravity, g.

Free fall motion: h  1 gt 2
2

Projectile motion: h  7R2
10gt 2
8

11. (b) Sketch a suitable graph for SP015 Pre-Lab Module Answer
(i) free fall motion.
h (cm) (ii) projectile motion.
h (cm)

0 t 2 (s2) 0 R2 (cm2)

(c) How the acceleration due to gravity, g can be determined from the graphs?

(i) Free Fall Motion

Using the gradient of the h against t 2 graph, m= 1 g
2

Thus, acceleration due to gravity, g = 2m

(ii) Projectile Motion

Using the gradient of the h against R2 graph, k = 7
10gt 2

Thus, acceleration due to gravity, g = 7
10k t 2

12. State THREE precautions of the experiments.
(i) For projectile motion, the steel ball should not be obstructed by the edge of the
table.

(ii) Since the reaction time of the observer varies each time while pressing the button
to release the ball so the experiment should be repeated.

(iii) The curvature railing at the edge of the table should be horizontal so that the
initial vertical velocity is zero as the ball leaves the edge of the table.

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SP015 Pre-Lab Module Answer

EXPERIMENT 3(b): ENERGY
Students will able to explain the experiment to determine the acceleration due to gravity, g
from the experiment.

INTRODUCTION
1. State the law of conservation of energy.

Law of conservation of energy states that in the absence of external force, the total
energy of a system remains constant.

2. What is gravitational potential energy and kinetic energy?

Gravitational potential energy is the energy stored in a body due to its height or
vertical position.

Kinetic energy is the energy of a body which is in motion.

3. What is the symbol and SI unit of gravitational potential energy and kinetic energy?

Energy Gravitational Potential Energy Kinetic Energy
Symbol U K
Unit Joule, J

4. Based on the situations below, answer the questions:

h = 10 m h=5m
ground
ground
SITUATION A SITUATION B

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SP015 Pre-Lab Module Answer

4. (a) Using the law of conservation of energy, determine the velocity of the ball just
before it reaches the ground.

Situation A Situation B

U K U K

mgh  1 mv2 mgh  1 mv2
2 2

gh  1 v2 gh  1 v2
2 2

v  2gh v  2gh

v  2(9.81)(10) v  2(9.81)(5)
v  14.01 m s2 v  9.90 m s2

(b) From the answers calculated in question (a), what can we deduce about the
relation between the released height and the velocity of the ball before hitting the
ground?
Velocity of ball is proportional to the released height.

EXPERIMENT
5. What is the energy owned by the ball bearing when it is attached to the free fall

adaptor?
Gravitational potential energy.

6. What is the usage of the photo gate?
Photo gate is used as a velocity detector.

7. State the change in mechanical energy in this experiment.
The gravitational potential energy is converted to the kinetic energy.

8. State the related variables that need to be recorded in this experiment.
(a) Manipulated variable: Falling distance, h
(b) Responding variable: Time required for the ball to travel through a distance, s

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SP015 Pre-Lab Module Answer

9. How is the final velocity of ball bearing determined?
Final velocity of ball bearing determined using equation v  s
t

DATA ANALYSIS
10. An equation for a straight line graph is y = mx + c, where y is the quantity on the

vertical axis and x is the quantity on the horizontal axis as shown in FIGURE 1.
y

x
0

FIGURE 1

The velocity of ball bearing, v is related to the height of released, h by the following
equation:

v 2 = 2gh …….. (1)

where g is the acceleration due to the gravity.

(a) Based on the equation (1) and the graph, determine the variables for x-axis and y-
axis.

Variables for x-axis: v2

Variables for y-axis: h

(b) From the graph what does the gradient, m represents?
Gradient, m = 2g

(c) From the gradient of the graph, how can we determine the value of g?

Gravitational acceleration, g  1 m
2

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SP015 Pre-Lab Module Answer

11. State TWO types of errors during experiment and give an example for each error.
(i) Random error
(ii) Systematic error

12. Based on the situation below identify either random or systematic error.

Situation Random error /
Systematic error
Measurement of height varies due to incorrect position
of eye view when measuring the height with a ruler. Random error

Some of the numbers on the timer display are broken Systematic error
and missing. Thus, the reading can be taken only to the
nearest decimal point.

Instead of using the hand to release the ball bearing, it Random error
is suggested that the ball can be released using the
automatic control or trigger.

Sometimes the time measured is hardly detected by the Systematic error
photo gates. This is due to the position of the gates
where the ball bearing failed to hit the motion sensor.
Therefore, the free fall adaptor and photo gates must
be realigned properly.

13. List the POSSIBLE precautions of this experiment:

(i) The photo gate is placed exactly parallel to the free fall adaptor and the table.

(ii) All connecting wires are connected properly to the right terminal of the timer,
photo gate and free fall adaptor.

(iii) The trigger of free fall adaptor must be pressed gently to avoid undesired
impulsive force on the ball bearing.

(iv) The contact between the observer and table is avoided as less as possible. This is
to prevent the vibration on the apparatus.

(v) The ball bearing is ensured to move in a straight line passing through the photo
gates.

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SP015 Pre-Lab Module Answer

EXPERIMENT 4: ROTATIONAL MOTION OF A RIGID BODY
Students will able to explain the experiment to determine the moment of inertia of a fly-wheel
from experiment.
INTRODUCTION
1. What is a rigid body?

Rigid body is a body which does not change its size and shape when the force is
exerted on it.

2. What is meant by moment of inertia?

Moment of inertia is the tendency of a body to resist rotational motion, expressed as
the sum of the product of the mass of each particle in the body and the square of its
perpendicular distance from the axis of rotation.

3. What is the symbol and SI unit for moment of inertia?
Symbol of moment of inertia: I
SI unit of moment of inertia: kg m2

4. Moment of inertia depends on mass and radius from axis of rotation.

5. Complete TABLE 4 with correct analogues between linear motion and rotational
motion.

Linear Motion Rotational Motion
Mass, m Moment of inertia, I
Acceleration, a Angular acceleration, 
Net force, F Net torque, 

6. A motor capable of producing a constant torque of 100 N m is connected to a fly-wheel
which rotates with an angular acceleration of 1000 rad s-2. Calculate moment of inertia
of the fly-wheel.

Using equation,   I

Moment of inertia, I    100  0.1 kg m2
 1000

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SP015 Pre-Lab Module Answer

EXPERIMENT

7. Identify the forces exerted on the fly-wheel and falling slotted mass which causes
acceleration.

(a) Fly-wheel (b) Falling slotted mass

 T
R a

TW

8. By referring to the diagram in 7.(a) and 7.(b), deduce equation by using Newton’s 2nd
law of motion.

(a) Fly-wheel:    net
TR   I

(b) Falling slotted mass: 
F  Fnet
mg  T  ma

T  mg  ma

9. For this experiment, identify the
(a) manipulated variable: mass of the hanging slotted mass
(b) responding variable: time taken to reach the ground

10. Complete the observation table with the suitable equation.

Acceleration Angular acceleration Tension in the string
  a  2a T  m (g  a)
a  2h Rd
t2

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SP015 Pre-Lab Module Answer

DATA ANALYSIS
11. Write the equation of the graph of  against T.

   R  T   
I  I

12. Base on the linear graph equation y = mx + c, fill in the suitable quantity by referring
the equation in question 11.

(a) y-axis :

(b) x-axis :T

(c) gradient, k : R
I

(d) y–interception : 
I

13. How do we determine the value of moment of inertia of the fly-wheel from this graph?

Using the gradient of  against T graph, k = R

I
Thus, moment of inertia of the fly-wheel, I  R  d

k 2k

14. List the POSSIBLE precautions of this experiment.
(i) Make sure the slotted mass released from a fixed height.
(ii) Avoid any external force when releasing the slotted mass.
(iii) Wound the string around the axle neatly.
(iv) Apply lubricants around the axis of rotation of the fly-wheel to reduce frictional
torque.
(v) Take repeated reading of time, t for each slotted mass.

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SP015 Pre-Lab Module Answer

EXPERIMENT 5: SIMPLE HARMONIC MOTION (SHM)
Students will able to:
(a) explain the experiment to determine the acceleration due to gravity, g using a simple

pendulum.
(b) describe the effect of large amplitude oscillation to the accuracy of g obtained from the

experiment

INTRODUCTION
1. What is a simple pendulum?

A simple pendulum is an object which can be considered as a point mass suspended
from a pivot using a string or a rod of negligible mass.

2. Periodic motion is a repeated motion of an object in equal interval of time through its
initial position.

3. In SHM, state TWO quantities that is proportional to the displacement of the object.
(i) acceleration
(ii) restoring force

4. The condition for the simple pendulum to perform SHM are
(a) the mass of the spherical bob is considered as a point mass.
(b) the mass of the string is negligible.
(c) amplitude of oscillation is small where  < 10

5. Does the period of oscillation of simple pendulum depend on mass? (Yes / No)

EXPERIMENT
6. How to determine the period of a simple pendulum, T using the time recorded, t for N

number of oscillations,?
Period T can be determined by dividing the time taken to the number of oscillations
counted, N or using equation,

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SP015 Pre-Lab Module Answer

7. If we vary the length of a pendulum, the period will change. Construct an appropriate
table to record the data of length,  ; time taken, t and corresponding T and T 2.

No.  (  0.1 cm ) t (  0.01 s ) T (s) T 2 (s2)
1
2

8. What is the title of the graph that needs to be plotted in this experiment?
Graph of T 2 against 

9. Which procedure that investigates the effect of large amplitude of oscillation? State the
related angle used.
Procedure step (6) and the related angle,  = 70

DATA ANALYSIS
10. How to determine the value of g from the gradient of the graph?

Using the gradient of T 2 against  graph, m  42
g

Thus, gravitational acceleration, g  42
m

11. How to calculate the percentage of error between the value gexperiment and gstandard? Take
gstandard = 9.81 m s-2.

Percentage of error of gravitational acceleration,

%  g   g experiment  gstandard 100%
g g sta nda rd

Note: If the value is smaller than 10%, is considered as accurate.

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SP015 Pre-Lab Module Answer
12. Predict what would happen to the displacement of the simple pendulum if large

amplitude is used.
Non-linear path or not in a straight line or does not obey SHM.
13. List the POSSIBLE precautions of this experiment.
(i) The bob of the pendulum was displaced with a small angle.
(ii) The amplitude of the oscillation of a simple pendulum should be as small as

possible.
(iii) The simple pendulum oscillates in a vertical plane only.
(iv) Switch off the fan to reduce the air resistance.

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SP015 Pre-Lab Module Answer
EXPERIMENT 6: STANDING WAVES
Students will able to explain the experiment to investigate standing waves formed in stretched string.

INTRODUCTION
1. What is the meaning of standing waves?

Standing wave is a form of wave in which the profile of the wave does not move
through the medium.

2. Sketch standing wave formed in a stretched string and label the node (N) and antinode
(A).
A AA AA
N NN N

3. How standing wave is formed?
Standing wave is formed from the superposition two or more progressive waves
travelling at opposite direction.

4. What is the symbol and SI unit for mass per unit length?
Symbol of moment of inertia: 
SI unit of moment of inertia: kg m2

EXPERIMENT
5. State the manipulative and responding variables in this experiment.

(a) Manipulated variable: Mass of the slotted mass.
(b) Responding variable: Length between two consecutive nodes.

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SP015 Pre-Lab Module Answer

6. Construct the observation table.

No. Mass, m (g) Length,  (  0.1 cm ) T (N)  2 (m2)
1
2
3

7. Sketch a free body diagram to show that T = W.
T

W

8. Suggest a way to determine the actual value for mass per unit length of the string or
wire used in this experiment.
Weigh the mass and measure the length of the string or wire.
Then, use the recorded values to calculate the actual value for mass per unit length of
the string or wire using equation:
m


9. Suggest how to identify the position of two consecutive nodes formed in the string or
wire.
The position of two consecutive nodes formed in the string or wire can be observed by
positioning the wooden wedges at two consecutive nodes.

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SP015 Pre-Lab Module Answer

DATA ANALYSIS
10. Write the equation that relates period, T and frequency, f.

Equation: T  4f 22

11. Sketch a graph to show the relationship between T and 2 .
T (N)

0  2 (m2)

12. How do you determine the mass per unit length from this graph?
Using the gradient of T against 2 graph, k  4f 2
Thus, mass per unit length,   m
4f 2

13. Throughout the experiment the terminals are connected to AC power supply. In your
opinion why is this essential?
Terminals are connected to AC power supply to produce the vibration in the string or wire.

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