SP015 Buku Tutorial Fizik Sesi 2020-2021 (Kolej Matrikulasi Negeri Sembilan)

Kolej Matrikulasi Negeri Sembilan

TOPIC 9
SIMPLE HARMONIC MOTION

9.1 Kinematics of simple harmonic motion

a) Explain SHM.

b) Solve problems related to SHM displacement equation, y  A sin t.

c) Derive equations:

i. Velocity, v  dy   A2  y2
dtt

ii. Acceleration,   dv  d2y  2 y
dt dt2

iii. Kinetic energy, K  1 m2(A2  y2) and potential energy, U  1 m2 y2
22

d) Emphasize the relationship between total SHM energy and amplitude.
e) Apply velocity, acceleration, kinetic energy and potential energy for SHM.

9.2 Graphs of simple harmonic motion.
a) Discuss the following graphs:
i. displacement-time
ii. velocity-time
iii. acceleration-time
iv. energy-displacement

9.3 Period of simple harmonic motion
a) Use expression for period of SHM, T for simple pendulum and single spring.
b) Determine the acceleration, g due to gravity using simple pendulum.
(Experiment 5: SHM)
c) Investigate the effect of large amplitude oscillation to the accuracy of
acceleration due to gravity, g obtained from the experiment.
(Experiment 5: SHM)

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OBJECTIVE QUESTIONS Kolej Matrikulasi Negeri Sembilan
(C2, PLO 1, MQF LOD 1)

1. Define simple harmonic motion
A. Periodic motion without loss of energy in which the acceleration is inversely
proportional to its displacement from the equilibrium position and is directed
towards the equilibrium position but in opposite direction of the displacement
B. Periodic motion without loss of energy in which the acceleration is inversely
proportional to its displacement from the equilibrium position and is directed
towards the equilibrium position but in same direction of the displacement
C. Periodic motion without loss of energy in which the acceleration is directly
proportional to its displacement from the equilibrium position and is directed
towards the equilibrium position but in opposite direction of the displacement
D. Periodic motion without loss of energy in which the acceleration is directly
proportional to its displacement from the equilibrium position and is directed
towards the equilibrium position but in same direction of the displacement

2. Which of the following statements is true about the magnitude of the acceleration
for an object undergoing simple harmonic motion?
A. Directly proportional to velocity
B. Inversely proportional to velocity
C. Directly proportional to displacement
D. Inversely proportional to displacement

3. A 5 kg ball is compressed at the highest end of a spring and undergoing simple
harmonic motion. At which position the speed is maximum?

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4. For a particle undergoing simple harmonic motion, which of the following graphs

represents the variation of velocity, v, against time t graph when a body initially at

maximum – A amplitude.

A. v B. v

t t

C. v D. v

t
t

5. Which of the following represent graph of energy against displacement for an
object that undergoes simple harmonic motion?

A. B.

C. D.

ANSWER:
1. C 2. C 3. B 4. A 5. A

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STRUCTURED QUESTIONS Kolej Matrikulasi Negeri Sembilan
(C4, PLO 4, CTPS 3, MQF LOD 6)

1. The displacement of a particle undergoing a simple harmonic motion is given as: y
= 8 sin 4πt where y is measured in meter and t in second. Determine
(a) the amplitude
(b) the angular velocity
(c) the period of oscillation
(d) the displacement when t = 0.2 s

2. The displacement of a particle oscillating in simple harmonic motion is given as: y
= 4 sin 10πt where y is measured in cm and t in second. Find
(a) the maximum velocity of the particle
(b) the velocity of the particle when y = 3 cm
(c) Sketch a graph of velocity, v against time, t for this particle

3. One end of a tuning fork oscillates in simple harmonic motion of amplitude 0.50

mm and period of oscillation of 0.001 s. Determine

(a) the maximum acceleration
(b) the acceleration when the displacement is 0.10 mm
(c) Deduce an expression for the displacement, y in terms of the time, t.

Assume that when t = 0 s, the end is at the equilibrium position.

4. The displacement of a particle in simple harmonic motion is described by the
equation: y = 5.0 cos (2πt + π/3) where y in meter and t in seconds. When t =
4.0 s, determine:
(a) the displacement
(b) the velocity
(c) the acceleration
(d) the phase

5. (a) y (m) v (m s-1)
6
2

t (s) T t(s)

-6

2 FIGURE 9.1

The following graphs above in FIGURE 9.1 show the variation of displacement,
y and velocity, v with time, t for an object in simple harmonic motion. Determine
the frequency of the object.

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(b) Kolej Matrikulasi Negeri Sembilan
y (m) a (m s-2)

4 10

t (s) t (s)

10
4

FIGURE 9.2
For the graphs shown in FIGURE 9.2 above, determine the frequency of the
motion.

(c)
F (N)

4

x (m)
-0.1 0.1

-4

FIGURE 9.3
The graph in FIGURE 9.3 shows the relationship between the force, F and its
displacement, x for an object of mass 2 kg which is in simple harmonic motion.
Determine;
(i) the period of oscillation
(ii) the maximum speed of the object.

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6. U (J)

18

8

x (m)

-0.15 -0.1 0.1 0.15

FIGURE 9.4

A particle of mass 1 kg undergoes simple harmonic motion and its potential energy
U changes with displacement x from a fixed point as shown in FIGURE 9.4 above.
Determine
(a) amplitude
(b) period
(c) velocity of the particle when x = 0.1 m
(d) force on the particle when x = 0.1 m

7. U (J)

1.0

0.1 x (m)

FIGURE 9.5

An object of mass 1 kg undergoing simple harmonic motion and its potential
energy, U varies according to displacement, x as FIGURE 9.5 above. Determine
the frequency of the object.

8. On the same axes, sketch graphs to show the variation of
(a) potential energy
(b) kinetic energy
(c) total energy
with displacement for a particle in simple harmonic motion.

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9. A block of mass 100 g is suspended from a vertical helix spring of spring constant
20 N/m. The block is pulled to a distance of y = 2 cm from its equilibrium position
of y = 0 cm. Determine
(a) the period of oscillation
(b) the maximum velocity of the block
(c) the total energy of the system

10. An object of mass 200 g is suspended from a vertical helix spring. The spring is
then extended by 2.0 cm. If the object is oscillating in a vertical plane, determine
(a) the angular frequency of the oscillation
(b) the period of oscillation
(c) the maximum velocity of the oscillating object
(d) the maximum kinetic energy of the oscillating object.

11. (a) Determine the length of a simple pendulum whose period is 0.50 s.
(b) Determine the frequency of the simple pendulum if it is in a lift which is
accelerating upwards at 3.00 m s-2.
(c) Determine the frequency of the simple pendulum when the lift is in free fall.

12. The displacement, y, for a particle at time, t, in simple harmonic motion is given by
the equation, y = 10 sin 20 t. Determine the length for a pendulum so that it has the
same period as the particle. Assume g = 10 m s-2.

13. An object of mass 0.1 kg is connected to a helical spring which undergoes simple
harmonic motion of period 1.0 s. Determine the new mass if the period of oscillation
is to be reduced to 0.5 s.

ANSWER: (b) 4π rad s-1 (c) 0.5 s (d) 4.70 m

1. (a) 8 m (b) ±83.12 cm s-1 (c) DIY
2. (a) ±125.66 cm s-1
3. (a) 1.974×104 m s-2 (b) -3.95×103 m s-2 (c) DIY
4. (a) 2.5 m
5. (a) 0.48 Hz (b) -27.21 m s-1 (c) −98.70 m s-2 (d) 26.18 rad
6. (a) 0.15 m
7. 2.25 Hz (b) 0.25 Hz (c) (i) 1.41 s (ii) 0.45 m s-1
8. DIY
9. (a) 0.44 s (b) 0.16 s (c) 4.47 m s-1 (d) 160 N
10. (a) 22.15 rad s-1
11. (a) 0.06 m (b) 0.28 m s-1 (c) 4.0×10-3 J (d) 1.94×10-2 J
12. 0.025 m (b) 0.28 s (c) 0.44 m s-1
13. 0.025 kg (b) 2.33 Hz
(c) 0 Hz

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TOPIC 10
MECHANICAL AND SOUND WAVES

10.1 Properties of waves
a) Define wavelength and wave number.
b) Solve problems related to equation of progressive wave,
y(x, t)  Asin(wt  kx)

c) Discuss and use particle vibrational velocity and wave propagation velocity.
d) Discuss the graphs of

i. displacement-time, y-t.
ii. displacement-distance, y-x.

10.2 Superposition of waves
a) State the principle of superposition of waves for the constructive and
destructive interferences.

b) Use the standing wave equation, y  A cos kx sin wt

c) Discuss progressive and standing wave.

10.3 Sound intensity
a) Define and use sound intensity.
b) Discuss the dependence of intensity on amplitude and distance from a point

source by using graphical illustrations.

10.4 Application of standing waves
a) Solve problems related to the fundamental and overtone frequencies for:

i. stretched string
ii. air columns (open and close end)

b) Use wave speed in a stretched spring string, v  T


c) Investigate standing wave formed in a stretched string.
(Experiment 6: Standing Waves)

d) Determine the mass per unit length of the string.
(Experiment 6: Standing Waves)

10.5 Doppler Effect
a) State Doppler Effect for sound waves.

b) Apply Doppler Effect equation f0   v  vo  f for relative motion between
v  vs

source and observer. Limit to stationary observer and moving source, and

vice versa.

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OBJECTIVE QUESTIONS Kolej Matrikulasi Negeri Sembilan
(C2, PLO 1, MQF LOD 1)

1. A wave is transporting energy from left to right. The particles of the medium are

moving back and forth in a leftward and rightward direction. This type of wave is

known as a

A. mechanical C. transverse

B. electromagnetic D. longitudinal

2. If y = 0.02 sin (400t - 30x) the amplitude, angular frequency and wave number of
the wave are

Amplitude (m) Angular Frequency (rad s-1) Wave Number (m-1)

A. 0.02 400t 30x

B. 0.02 30 400

C. 0.02 400 30

D. 30 0.02 400

3. A certain harmonic wave is passing through a medium. What is the effect on the
wave when the frequency of the wave is reduced by half?
A. The period of wave is halved.
B. The speed of wave is doubled.
C. The amplitude of wave is halved.
D. The wavelength of the wave is doubled.

4.

FIGURE 10.1
Two pulses are traveling towards each other at 10 cm s-1 on a long string at t = 0 s,
as shown in FIGURE 10.1. Which of the following correctly shows the shape of the
string at t = 0.5 s.

A.
B.

C.

D.

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5.

FIGURE 10.2

The graph above shows in FIGURE 10.2 the displacement of the particles in a
transverse progressive wave against the distance from the source at a particular
instant. The points where the speed of the particles is zero and the acceleration
of the particles is maximum.
A. P and R
B. Q and S
C. Q and T
D. P, R and T

6. The principle of superposition states that
A. Two stationary waves superimpose to produce a progressive wave.
B. The total energy of the resultant wave is the sum of the energy carried by
the individual wave.
C. The frequency of the resultant wave is the difference between the
frequencies of the individual waves.
D. The displacement at a point of the resultant wave is the sum of the
displacement of the individual waves acting at that point.

7. In a resonating pipe which is open at one end and closed at the other, there
A. are displacement nodes at each end.
B. are displacement antinodes at each end.
C. is a displacement node at the open end and a displacement antinode at the
closed end.
D. is a displacement node at the closed end and a displacement antinode at
the open end.

8. A sound source is emitting waves uniformly in all directions. If an observer move
to a point twice as far away from the source, the frequency of the sound will be
A. unchanged
B. half as great
C. one-fourth as great
D. twice as great

9. When you hear the horn of a car that is approaching you, the frequency that you
hear is larger than that heard by a person in the car because

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A. wave crests are farther apart by the distance the car travels in one period.
B. wave crests are closer together by the distance the car travels in one

period.
C. the speed of sound in air is increased by the speed of the car.
D. a speeding car emits more wave crests in each period.
10. While you are sounding a tone on a toy whistle, you notice a friend running toward
you. If you want her to hear the same frequency that you hear even though she
is approaching, you must
A. stay put.
B. run towards her at the same speed.
C. run away from her at the same speed.
D. stay put and play a note of higher frequency.
11. A person standing in the street is unaware of a bird dropping that is falling from
a point directly above him with increasing velocity. If the dropping were producing
sound of a fixed frequency, as it approaches the person would hear the sound
A. drop in frequency.
B. stay at the same frequency.
C. increase in frequency.
D. decrease in loudness
ANSWERS:
1. D 2. C 3. D 4. B 5. A 6. D 7. D 8. A 9. B 10. C 11. C

54

STRUCTURED QUESTIONS Kolej Matrikulasi Negeri Sembilan
(C4, PLO 4, CTPS 3, MQF LOD 6)

1 A progressive wave is described as

y  2 sin 2  t  x 
 0.40 80

where x and y are in cm and t is in seconds. Determine the following from this

wave

(a) amplitude

(b) wavelength

(c) frequency

(d) speed

2

FIGURE 10.3 (a)

FIGURE 10.3 (b)

FIGURE 10.3 (a) shows a graph of displacement, y against time, t and FIGURE
10.3 (b) shows a graph of displacement, y against distance, x of a progressive
wave. From the graphs, deduce
(a) the angular frequency.
(b) the wave number.
(c) the wave propagation velocity.
(d) the particle vibrational velocity when displaced vertically 1.2 cm from

the equilibrium position.
(e) the displacement equation of the progressive wave.

3 The progressive wave equation is given as y(x,t) = 5 sin (3πt – 1/2πx) where x
and y in meter and time in second.
Calculate period, wavelength and speed of the wave.

4 Two sinusoidal waves traveling in opposite directions interfere to produce a
standing wave as given by the equation y  (1.50m)cos(0.400x)sin(200t) where y
and x in meters and t in seconds. For the sinusoidal waves, calculate the
(a) wavelength
(b) frequency
(c) speed

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5 Two waves in a long string are given by

y1 = (0.02m) sin (40t – x ) y2 = (0.02m) sin (40t + x )
2 2

where y1, y2, and x are in meters and t in seconds. Calculate

(a) positions of the nodes of the resulting standing wave.

(b) maximum displacement of an element in the string at x = 0.400 m.

6 The velocity of two opposite direction transverse wave that form a stationary
wave on a string is 300 m s1. If the maximum verticals displacement and
frequency of the wave is 2.0 cm and 100 Hz,
(a) Calculate
(i) the angular frequency.
(ii) the wave number.
(iii) the wave propagation velocity.
(iv) the particle vibrational velocity when particle displaced vertically
1.2 cm from the equilibrium position.
(v) the distance between two successive nodes.
(b) Write the displacement equation of the progressive wave.
(c) Write the displacement equation of the stationary wave.

7.

FIGURE 10.4

In FIGURE 10.4, 120 µW of sound power passes perpendicularly through the
surface labelled 1 and 2. These surfaces have areas of A1 = 400 dm2 and A2 =
1200 dm2. Determine the sound intensity at each surface.

8. (a) The overall length of a piccolo is 32.0 cm. The resonating air column
vibrates as in a pipe open at both ends. Calculate the frequency of the
lowest note a piccolo can play. (Speed of sound is 331 m s-1)

(b) A steel wire in a piano has a length of 0.70 m and a mass of 4.30 ×10–3
kg.To what tension must this wire be stretched in order that the fundamental
vibration correspond to middle C (fC = 261.6 Hz on the chromatic musical
scale)?

9. An organ pipe of length 33 cm is open at one end and closed at the other. By
assuming that end correction is negligible, calculate the
(Speed of sound is 331 m s-1)

(a) frequency of the fundamental note and the first overtone.

(b) length of a pipe open at both ends and having fundamental frequency that
is equal to the different between the two frequencies calculated in (a).

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10. A variable length air column is placed just below a vibrating wire that is fixed at
both ends. The length of the air column open at open end is gradually increased
until the first position of resonance is observed at 34.0 cm. The wire is 120 cm
long and is vibrating in its third harmonic. Calculate the speed of transverse
waves in the wire. (Speed of sound is 331 m s-1)

11. A boy standing at a bus stops when the fire engine with velocity 40 ms-1 emitting
siren with frequency 550 Hz pass through him. Calculate the frequency heard
by the boy when it
(Speed of sound is 343 m s-1)
(a) is approaching him.
(b) is moving away from him.

12. A sound source which can produce sound of frequency of 300 Hz move away
from a stationary observer. The observer notice that the frequency of sound
heard changes by 10 Hz when the source is moving away. Determine the speed
of the sound source. (Speed of sound is 330 m s-1)

13. A bat flying at 5.0 m s-1 emits a chirp at 40 kHz. If this sound pulse is reflected

by a wall, what is the frequency of the echo received by the bat? (Speed of
sound is 331 m s-1)

14. A sound source and an observer are located on the same horizontal straight
line. The observer hears sound of frequency 510 Hz when the sound source
moves towards him. When the sound source passes him and moves away, he
hears a sound of frequency 450 Hz. Determine the speed of the sound source.
(Speed of sound is 343 m s-1)

ANSWERS:

1. (a) 2 cm (b) 80 cm (c) 2.5 Hz (d) 200 cm s-1

2. (a) 0.5π rad s-1 (b) 0.4π cm-1 (c) 1.25 x 10-2 m s-1 (d) ±2.51×10-2 m s-1 (e) DIY

3. (a) 2/3 s, 4 m, 6 m s-1 (b) DIY (c) DIY

4. (a) 15.7 m (b) 31.8 Hz (c) 499 m s-1

5. (a) π, 3π, 5π (b) 0.039 m

6. (a) (i) 200π rad s-1 (ii) 0.667π m-1 (iii) 300 m s-1 (iv) ±1005 cm s-1 (v) 1.5 m

(b) DIY (c) DIY

7. I1 = 3.0×10-5 W m-2, I2 = 1.0×10-5 W m-2

8. (a) 517 Hz (b) 823.95 N

9. (a) 251 Hz, 753 Hz (b) 0.33 m
10. 194.7 m s-1 (b) 492.6 Hz

11. (a) 622.6 Hz
12. 11.4 m s-1

13. 41.2 kHz
14. 21.4 m s-1

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TOPIC 11
DEFORMATION OF SOLIDS

11.1 Stress and Strain
11.2
a) Distinguish between stress and strain for tensile and compression force.

b) Discuss the graph of stress-strain for a metal under tension.

c) Discuss elastic and plastic deformation

d) Discuss graph of force-elongation, f-e for brittle and ductile materials.

Young’s Modulus
a) Define Young’s Modulus.

b) Discuss strain energy from force-elongation graph.
c) Discuss strain energy per unit volume from stress –strain graph.
d) Solve problems related to the Young’s Modulus.

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OBJECTIVE QUESTIONS Kolej Matrikulasi Negeri Sembilan
(C2, PLO 1, MQF LOD 1)

1. Shape of true stressstrain curve for a material depends on

A. Strain C. Temperature

B. Strain rate D. All

2. It is possible, while tightening the nuts on the wheel of your car, to use too much
torque and break off one of the bolts. This happens when the
A. shear stress exceeds the breaking strength
B. compressive stress becomes too large
C. the screw has too low an elastic constant
D. volumetric stress on the bolt is too great

3. When a wire extended by a force F, the extension produced is x. If F=kx, the
value of the force constant k is affected by
A. the force F and extension x only
B. original length and the type of material only
C. force F, original length, and the extension x

D. original length, cross-sectional area, and the type of material

4. A metal part fails via fatigue…
A. when it gets tired
B. as a result of the repeated application of a cyclic stress
C. when the stress exceeds the breaking strength
D. when the metal is very old and loaded very large

5. force

force

Copper Aluminum

FIGURE 11.1

FIGURE 11.1 shows that the same force is applied to copper and aluminum
wire which have the same length. If the Young’s modulus of aluminum is larger
that of copper, which statement is true?

A. The stress of aluminum wire is larger that of copper wire.
B. The strain of the aluminum wire is larger that of copper wire.
C. The extension of copper wire is larger that of aluminum wire.
D. The final length of the copper wire is smaller that of the aluminum wire.

6. The strain energy stored in a wire elongated x m by a force, F is equal to Fx

if,
A. the weight of the wire is negligible
B. the wire is stretched below its elastic limit
C. the cross-sectional area of the wire remains constant
D. the applied force is proportional to elongation of the wire

ANSWERS:

1. D 2. A 3. D 4. B 5. C 6. D

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STRUCTURED QUESTIONS Kolej Matrikulasi Negeri Sembilan
(C4, PLO 4, CTPS 3, MQF LOD 6)

1. (a) A wire originally 2.0 m long suffers a 0.1% strain. What is its final
stretched length?

(b) A length of copper of square cross section measuring 1.0 mm by 1.0 mm
is stretched by a tension of 40 N. What is the tensile stress in Pa?

2.

FIGURE 11.2

A piece of bone under tension and compression as in FIGURE 11.2.
(a) Which portion of the graph shows that the bone is brittle?
(b) Use the graph, calculate the Young’s modulus for bone under conditions

of compression and tension respectively.

3. F(N)

F(N)

Wire X Wire Y
300 750

200 500
100 250

0.5 1.0 1.5 e (mm) 2.0 4.0 6.0 e (mm)

FIGURE 11.3

The force F against elongation e graphs for wire X and wire Y as shown in

FIGURE 11.3. The wires have the same original length and same cross
sectional area of 5.0 mm2.

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(a) Calculate the work done to extend wire X and wire Y by 1.5 mm. State

which wire is more rigid.

(b) From the graphs above, calculate the ratio of the Young’ modulus of wire
X to the Young’ modulus of wire Y.

4. A brass wire 2.5 m long of cross section area 1.0×10–3 cm2 is stretched 1.0 mm
by a load of 0.4 kg.
(a) Calculate the Young Modulus for brass.
(b) What percentage strain does the wire suffer?
(c) Use the value of Y to calculate the force required to produce a 4.0 %
strain in the same wire. Is your answer for the force reliable? If it isn’t,
would it be greater or smaller than your answer?

5. A wire X has length 100 cm and diameter 2.0 mm. A wire Y has length 200 cm
and diameter 4.0 mm. Forces of same magnitude pull both wires and the
extensions of X and Y are produced are 0.10 mm and 0.04 mm respectively.
Determine the ratio of the Young’s modulus for wire X to that for wire Y.

6. An object of mass 6.0×103 kg is suspended from a steel cable of length 50 m
and cross-sectional area 2.0×10–4 m2. Determine the extension of the cable
when the mass-cable system
(a) at rest.
(b) moves upwards at constant speed.
(c) moves upwards at constant acceleration 2.0 m s–2
Assume the cross-sectional area to be constant.
[Young’s modulus for steel = 2.0×1011 Pa; g = 9.81 m s–2]

7.

200

0.05

FIGURE 11.4

A metal rod of 10.0 mm diameter and 30 cm length is stretched by forces of
various magnitudes. Stress against strain graph of the wire is as shown in
FIGURE 11.4. Calculate the Young’s modulus for the metal of the rod and the
extension if the strain in the rod is 0.05.

8. A metal bar that has a cross-sectional area of 4.0 cm2 and length of 50.0 cm is
stretched by a force of 1.0×104 N.

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(a) Find the stress on the wire.
(b) If the bar elongates by 0.5 cm, what is the strain in the wire?
(c) Determine the Young’s Modulus of the wire.
(d) Calculate the strain energy per unit volume stored in the wire.

9. A wire has a mass 5.3 g and length 2.50 m. A force of 50 N can extend it by 2.3
mm. Determine
(a) the Young’s Modulus for the metal of the wire
(b) the strain energy stored in the stretched wire

3 -3

[Density of the metal of the wire = 2.7×10 kg m ]

10.

160

0.08

FIGURE 11.5

Stress against strain graph of the wire is as shown in FIGURE 11.5. What are
the parameters represented by
(a) the Young’s Modulus?
(b) the strain energy per unit volume?
Calculate their values.

ANSWERS:

1. (a) 2.002 m (b) 4.0×107 Pa

2. (a) For compression: when stress is equal to 2×107 Pa

For tension: when stress is equal to 3.5×107 Pa

(b) 1×109 Pa, 1.75×109 Pa

3. (a) 0.225 J, 0.141 J (b) 1.6

4. (a) 9.8×1010 Pa (b) 0.04 % (c) 392.4 N

5. 0.8 (b) 7.36×10–2 m (c) 8.86×10–2 m
6. (a) 7.36×10–2 m

7. 4×109 N m-2, 1.5 cm
8. (a) 2.5×107 N m–2 (b) 0.01 (c) 2.5×109 N m−2 (d) 125×103 J m–3

9. (a) 6.9×1010 Pa (b) 5.8×10-2 J

10. (a) Gradient, 2×109 Pa (b) Area under the graph, 6.4×106 J m–3

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TOPIC 12
HEAT CONDUCTION AND THERMAL EXPANSION
12.1 Heat conduction
a) Define heat conduction.

b) Solve problems related to rate of heat transfer, dQ  kA dT  through a
dt  dx 

cross-sectional area (maximum two objects in series).
c) Discuss graphs of temperature-distance, T-x for heat conduction through

insulated and non- insulated rods. (Maximum two rods in series).
12.2 Thermal expansion

a) Define coefficient of linear, area and volume thermal expansion.
b) Solve problems related to thermal expansion of linear, area and volume

(include expansion of liquid in a container):
L  L  T ,   2 ,   3

63

OBJECTIVE QUESTIONS Kolej Matrikulasi Negeri Sembilan
(C2, PLO 1, MQF LOD 1)

1. Which of the following statements best represents the characteristic of heat as

a form of energy?
A. Heat needs a medium ……….
B. The magnitude of heat depends on its density

C.Heat is transferred from a point or region to another

D.Heat is transferred from a high pressure region to low pressure region

2. Thermal conductivity, k depends on the ……….

A. type of material C. triple point of the material

B. shape of the material D. boiling point of the material

3. Temperature is a ………
A. form of heat transfers where energy is radiated in the form of rays.
B. form of heat transfer.
C.form of energy contained in an object associated with the motion of
molecules.
D. measure of the hotness or coldness of an object

4. Why do ceramic tiles in a kitchen or bathroom feel cooler than a floor mat that
is kept at the same temperature?
A. Ceramic has a lower thermal conductivity value.
B. Ceramic is a metal and is therefore a better conductor of heat.
C. Ceramic could not be the same temperature as the floor mat
D. Ceramic has a higher thermal conductivity value.

5. The coefficient of area expansion is
A. half the coefficient of linear expansion.
B. double the coefficient of linear expansion.
C triple the coefficient of volume expansion.
D. double the coefficient of volume expansion.

ANSWER:

1. C 2. A 3. D 4. D 5. B

64

STRUCTURED QUESTIONS Kolej Matrikulasi Negeri Sembilan
(C4, PLO 4, CTPS 3, MQF LOD 6)

1. Two metallic rods X and Y with similar length and cross-sectional area are
joined together and insulated. At a steady state, the temperatures of rod X and
rod Y are 100 ºC and 40 ºC respectively at each end as shown in FIGURE 12.1.
The thermal conductivity of X is twice the value of Y. Calculate the temperature
at the junction between X and Y.

100 oC X Y 40 oC

FIGURE 12.1

2. (a) An aluminum rod has a diameter of 3 cm and thickness of 0.6 m.
One end of the rod is placed in boiling water and the other end in ice.
Calculate the quantity of heat transferred through the rod within 1 minute.
(Given, k = 205 W m-1 K-1)

(b) Two insulated metals plumbum and copper with a thickness of 40 mm
and 60 mm respectively are joining together. The temperature of
plumbum is fixed at 70 oC and copper is at 30 oC. If the thermal
conductivity of the copper is 4 times of the thermal conductivity of
plumbum, calculate the boundary temperature in steady state. Assume
that the cross sectional area is the same.

3. (a) Two metal bars X and Y have the lengths of 70 cm and 30 cm as shown

in FIGURE 12.2. Both have the same cross sectional area. At one end

of the metal X, heat supplied from boiling water at 100 ºC and one end
of the metal Y is placed in melting ice at 0 0C. Both metals are well-
insulated. The temperature at the junction is 15 0C. Calculate the ratio of
thermal conductivity between metal X and Y. (Assume the heat flow is

steady and no energy is lost to the surroundings).

1000C 70cm 30cm 00C

X Y

FIGURE 12.2

(b) The rate of heat conduction is 80 kJ per hour at a thin wall with an area
of 14 cm2. If the temperature gradient across the wall is 15 0C m-1,

calculate the thermal conductivity of the wall.

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Kolej Matrikulasi Negeri Sembilan

4. (a) A glass window of cross-sectional area 1.50 m2 and thickness 0.20 cm
is closed in winter. The temperatures of the inner and outer surfaces of
the window are 15 °C and 0 °C.
i) Calculate the rate of heat flow through the window.
ii) Suggest how you would reduce the amount of heat loss to the
surroundings through this window.
(Thermal conductivity of glass = 0.84 W m-1 K-1)

(b) A copper plate of thickness 1.0 cm is sealed to a steel plate of thickness
10 cm as shown in FIGURE 12.3. The temperatures of the exposed
surfaces of the copper and steel plates are 30 C and 15 C respectively.
When both rods are in the steady condition the temperature is 29.8 oC.
Determine the thermal conductivity of copper if the amount of heat
flowing through the plates is 2310 J. (A = 50×10-4 m2, t = 1 minute).

FIGURE 12.3

1.0 cm 10.0 cm

5. An electric bulb rated at 80 W, 240 V has inside it a heating filament. Each end

of the filament is connected to a supporting straight wire of diameter 1.0 mm

and length 4.0 cm. When the bulb is switched on and functioning at the given
rating, the filament temperature is 1000 oC. The temperature at the other end
of each supporting wire is 60 oC. Estimate the ratio of power loss due to thermal

conduction of heat away from the filament along the supporting wire to the

power supplied to the filament.
(Thermal conductivity of the material of supporting wire = 59 W m-1 K-1)

6. X Y

1.0 cm 10.0 cm

FIGURE 12.4

A material X of thickness 1.0 cm and cross-sectional area of 1.0 m2 is in thermal
contact with another material Y of thickness 10 cm, as shown in FIGURE 12.4
above. The temperature of the exposed surface of X and Y are 30oC and 15oC
respectively. Determine

a) the temperature of the interface between the two materials.
b) the amount of heat flowing through unit area of X and Y per second.

(Thermal conductivity of X and Y are 0.13 W m-1 K-1 and 0.29 W m-1 K-1)

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Kolej Matrikulasi Negeri Sembilan

7. A 100 cm rod A expands by 8.0 mm when heated from 0 oC to 100 oC.
Calculate the coefficient of linear expansion for rod A.

8. A technician cuts a hole of area 2.0 cm2 through a copper sheet. The
temperature of the sheet rises to 150 oC. Find the area of the hole when the
sheet is cooled down to room temperature 30 oC.
(The coefficient of linear expansion of copper is 1.7×10-5 K-1)

9. A 60.0 liter steel tank is full of petrol at a temperature of 30 oC. If the tank’s lid
is not tight how much petrol will spill out at 40 oC?
(Coefficient of linear expansion of steel is 1.2×10−5 K-1)
(Coefficient of volume expansion of petrol is 9.5×10−4 K-1)

10. A copper radiator of capacity 15.0 L is filled with coolant at 30 oC. When the
engine is running, the temperature of the radiator rises to 96 oC and the coolant

overflows.

(a) Explain why the coolant overflows.
(b) Calculate the amount of coolant spilt out in cm3.
(Coefficient of linear expansion of copper = 1.7×105 K1)
(Coefficient of volume expansion of coolant = 4.0×104 K1)

ANSWER:

1. 80 oC (b) 40.9 °C
2. (a) 1449.06 J (b) 1056 W m-1 K-1
3. (a) 0.41 (b) 385 W m-1 K-1
4. (a) (i) 9450 W
5. 0.0272 (b) 35.6 J
6. (a) 27.26 oC
7. 8×10-5 oC-1
8. 1.992 cm2
9. 0.5484 liter
10. 0.0345 cm3

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Kolej Matrikulasi Negeri Sembilan

TOPIC 13
GAS LAWS AND KINETIC THEORY

13.1 Ideal gas equations

a) Solve problems related to ideal gas equation, pV  nRT

b) Discuss the following graphs of an ideal gas:
i. p-V graph at constant temperature.
ii. V-T graph at constant pressure.
iii. p-T graph at constant volume.

13.2 Kinetic Theory of Gases

a) State the assumptions of kinetic theory of gases.

b) Discuss root mean square (rms) speed of gas molecules

c) Solve problems related to root mean square (rms) speed of gas

molecules.

d) Solve problems related to the equations, pV  1 Nmvrms 2 and pressure
3

p  1  vrms 2 .
3

13.3 Molecular kinetic energy and internal energy

a) Discuss translational kinetic energy of a molecule, Ktr  3 R   3 kT
 NA T 2
2  

b) Discuss degrees of freedom, f for monoatomic, diatomic and polyatomic

gas molecules.

c) State the principle of equipartition of energy.

d) Discuss internal energy of gas.

e) Solve problems related to internal energy, U  1 fNkT
2

68

OBJECTIVE QUESTIONS Kolej Matrikulasi Negeri Sembilan
(C2, PLO 1, MQF LOD 1)

1. Which one of the following graphs represents Gay-Lussac’s Law?

A. V (m3) C. P (Pa)

T (K) V (m3)

B. P (Pa) D. V (m3)

T (K) T (K)

2. State Boyle’s Law and Charles’s Law. Charles’s Law
Boyle’s law

A. The volume of a fixed mass of gas The pressure of a fixed mass of gas at

at constant pressure is directly constant temperature is inversely

proportional to its absolute proportional to its volume.

temperature

B. The pressure of a fixed mass of gas The pressure of a fixed mass of gas at

at constant temperature is inversely constant volume is directly proportional

proportional to its volume. to its absolute temperature

C. The pressure of a fixed mass of gas The volume of a fixed mass of gas at

at constant temperature is inversely constant pressure is directly

proportional to its volume. proportional to its absolute temperature

D. The pressure of a fixed mass of gas The volume of a fixed mass of gas at

at constant volume is directly constant pressure is directly

proportional to its absolute proportional to its absolute temperature

temperature

3. Which of the following statements is not true of the kinetic theory of gases?
A. Each degree of freedom is associated with an amount of energy given
by 1 kT .
2
B. The temperature of a gas is proportional to the average kinetic energy
of the molecules.
C. For a gas of diatomic molecules, the average translational kinetic energy
per molecule is 5 kT .
2
D. The pressure of a gas depends on the average value of the square of
the speeds of the molecules.

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Kolej Matrikulasi Negeri Sembilan

4. State the assumptions made in the kinetic theory of gases.
i. All gases are made up of identical atoms or molecules
ii. All atoms or molecules move randomly and haphazardly
iii. Inter-atomic or molecular collisions are inelastic
iv. Atoms and molecules move with constant speed between collisions

A. i, ii, iii C. i, iii, iv
B. i, ii, iv D. i, ii, iii, iv

5. State the principle of equipartition of energy.
A. Degrees of freedom depend on the absolute temperature of the gases
B. The mean (average) kinetic energy of every degrees of freedom of a
molecule is 3 kT .
2
C. Degrees of freedom depend on the pressure of the gases
D. The mean (average) kinetic energy of every degrees of freedom of a
molecule is 1 kT .
2

6. Define the degrees of freedom of a molecule.
A. the sum of total kinetic energy and total potential energy of the gas
molecules
B. number of independent ways in which an atom or molecule can absorb
or release or store the energy
C. types of independent ways in which an atom or molecule can release
the energy
D. none of the above

ANSWER:

1. B 2. C 3. C 4. B 5. D 6. B

70

STRUCTURED QUESTIONS Kolej Matrikulasi Negeri Sembilan
(C4, PLO 4, CTPS 3, MQF LOD 6)

1. A gas of mass 0.3 kg is contained in a 0.5 m3 container at a pressure of
1.4105Pa . Determine the rms speed of the gas molecules.

2. (a) A vessel of volume 45 liters contains 3.0 moles of gas at 35 ºC.
Calculate the gas pressure.

(b) When the pressure of an ideal gas is increased from 5.5 x 104 Pa to
1.5 x 105 Pa, its volume decrease from 2.5 x10-3 m3 to 0.5 x 10-3 m3. If
the initial root mean square (rms) velocity of the gas is v , determine the

final rms velocity of the gas in terms of v .

3. A fixed mass of an ideal gas is at pressure of P. What will be the new pressure
of the gas if its temperature is halved and its volume doubled?

4. The rms speed of hydrogen molecules at a particular temperature is 1330 m s–
1. What is the rms speed of nitrogen molecules at the same temperature?
(The molar mass of hydrogen is 2.0 g mol–1 and for nitrogen is 28 g mol–1)

5. Determine the temperature at which rms speed of a helium molecule is 1.3
times greater than the rms speed at the temperature of 310 K.

6. (a) The rms speed of the atoms of a monatomic gas at a temperature
of 20 ºC is 603 m s–1. Find the mass of an atom of the gas.

(b) What is the root mean square speed of oxygen molecules at 300 K?
(Given that molar mass of oxygen is 32.0 g mol–1)

7. (a) Use the kinetic theory of gases to explain quantitatively how a gas
pressure on the wall of the container.

(b) A tank has a volume of 0.700 m3 and contains 2.50 mol of helium gas at
10 ºC. If helium behaves like ideal gas, calculate
(i) the total translational kinetic energy of the molecule of the gas
(ii) the average molecular kinetic energy

8. A balloon of diameter 20.0 cm is filled with helium gas at 30 ºC at 1.00 atm.
(a) How many atoms of helium gas fill a balloon having a diameter of 20.0
cm at 30 ºC at 1.00 atm?
(b) Calculate the average kinetic energy of the helium atoms.

9. The pressure of a gas in a container of volume 300 cm3 is 1.6 x 106 Pa. If the
temperature of the gas is 100 0C, calculate the number of molecules in the gas.

10. A vessel contains N molecules of an ideal monoatomic gas at a pressure, p and
temperature, T. Write an expression for the total kinetic energy of the molecule
in terms of N, T and k (Boltzmann constant).

11. Determine the total internal energy for 4 mol of an ideal monoatomic gas at the
following temperatures.

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Kolej Matrikulasi Negeri Sembilan

(a) 200 K
(b) 303 K

12. (a) Find the average molecular kinetic energy of an ideal monoatomic gas
at the following temperature.
(i) 100 K
(ii) 475 K

(b) Three moles of an ideal monatomic gas contained in a 9.0 x 10-3 m3
vessels is at a pressure of 9.0 x 105 Pa. Find the average kinetic energy

of the gas molecule.

13. Find the internal energy of 30 g of Argon gas at 90 0C.
(Molar mass of Argon = 40 g, Avogadro constant; NA = 6.02 × 1023 mol–1,
Boltzmann constant, 1.38 x 10-23 J K-1)

ANSWER:

1. 837.5 m s–1 (b) 0.739 v m s-1
2. (a) 1.71 x 105 Pa
(b) 483 m s-1
3. Pnew  1P (b) (i) 8.82×103 J
4 (b) 6.27×10-21 J

4. 355 m s–1 (b) 15.11×103 J
(ii) 9.83×10-21 J
5. 524 K
6. (a) 3.3×10-26 kg

7. (a) DIY (ii) 5.86×10-21 J
8. (a) 1.02×1023 atoms (b) 6.73×10-21 J
9. 9.27 x 1022 molecules

10. DIY
11. (a) 9.97×103 J
12. (a) (i) 2.07×10-21 J
13. 3.39 x 103 J

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Kolej Matrikulasi Negeri Sembilan

TOPIC 14
THERMODYNAMICS

14.1 First Law of Thermodynamics
a) State the first law of thermodynamics.
b) Solve problem related to first law of thermodynamics.

14.2 Thermodynamic processes
a) Define the following thermodynamics processes:

i. Isothermal
ii. Isochoric
iii. Isobaric
iv. Adiabatic
b) Discuss p-V graph for all the thermodynamic processes.

14.3 Thermodynamics work
a) Discuss work done in isothermal, isochoric and isobaric processes.
b) Solve problem related to work done in:
i. Isothermal process,
W  nRT ln V2  nRT p1
V1 p2
ii. Isobaric process,

W  pdV  p(V2 V1)

iii. Isochoric process,

W   pdV  0

73

OBJECTIVE QUESTIONS Kolej Matrikulasi Negeri Sembilan
(C2, PLO 1, MQF LOD 1)

1. Based on the first law of thermodynamic, in which the equation is Q = ΔU +W,
which of the following statement is correct?
A. When a piston is being compressed, the work is done by the gas.
B. When the heat is out of the system, the value of Q is positive in sign.
C. The change in internal energy, ΔU is mainly dependent on temperature.
D. When an ideal gas expands and undergoes changing in volume, there
is no work done on the gas.

2. Which of the following graphs indicates an adiabatic expansion of an ideal gas?

P P
A. C.

V V
P
P
B. D.

VV

3. During an isothermal expansion, the volume of a gas changes from V1 to V2.

Which of the statements below is true about this gas?

A. Heat is lost from the gas.

B. Internal energy of the gas increases.

C. The amount of work done is WP(V2V1).

D. The work done on the gas is WnRlTnV2
V1

4. When the gas is heated at constant pressure, the heat supplied is to

A. increase the volume of the gas

B. increase the pressure of the gas

C. decrease the volume of the gas

D. convert it to do work on the gas

5. An ideal gas undergoes an isothermal process. Which of the following law can

be applied to the gas?
A. Boyle’s law
B. Charles’ law
C. Pascal’s law

D. Pressure law

ANSWER:
1. C 2. A 3. D 4. A 5. A

74

STRUCTURED QUESTIONS Kolej Matrikulasi Negeri Sembilan
(C4, PLO 4, CTPS 3, MQF LOD 6)

1. In each of the following situations, find the change in internal energy of the
system.
(a) A system absorbs 2090 J of heat and at the same time does 400 J of
work.
(b) A system absorbs 1255 J of heat and at the same time 420 J of work is
done on it.
(c) 5020 J is removed from a gas held at constant volume. Give your answer
in kilojoules.

2. Sketch and label p-V graph for all the thermodynamic processes in the same
axes (either expansion or compression).
(a) isothermal
(b) isovolumetric
(c) isobaric
(d) adiabatic

3. As an ideal gas is compressed isothermally, the compressing agent does 36 J
of work. How much heat flows from the gas during the compression process?

4. (a) A gas undergoes the following thermodynamic processes:
isobaric expansion, heated at constant volume, compressed
isothermally and finally expands adiabatically back to its initial pressure
and volume. Sketch all processed given on the same P-V graph.

(b) A gas of volume 0.02m3 at a pressure of 2.0 × 105 Pa undergoes an
isothermal compression. If the final pressure is 4.0×105 Pa, what is its

volume?

5. A fixed mass of ideal monatomic gas is contained in a cylinder. The cylinder
volume can be varied by moving a piston in or out. The gas has an initial volume
0.010 m3 at 100 kPa pressure and its temperature is initially 300 K. The gas is
cooled at constant pressure until its volume is 0.006 m3.
(a) Sketch a graph of pressure against volume for the above process.
(b) Calculate the
(i) Final temperature of the gas
(ii) Work done on the gas
(iii) Number of the moles of gas

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Kolej Matrikulasi Negeri Sembilan

P
B

C
A

V

FIGURE 14.1

6. A sample containing 1.00 mol of the ideal gas helium undergoes the cycle of
operations as shown in FIGURE 14.1 below. BC is an isothermal process.
Pressure at stp is at point A and pressure at B is 2.0 atm, calculate
(a) Temperature at A.
(b) Temperature at B.
(c) Volume at C
(stp: 1 atm = 1.013×105 Pa, T = 273.15 K, V = 0.0224 m3)

7. (a) Sketch the pressure-volume graph for an isothermal compression.
(b) Two moles of an ideal gas are compressed isothermally from 800 cm3 to
200 cm3 at 800C.Calculate the work done on the gas.

P (×105) Pa)

A B
3 C

V (m3)

0.02 0.04

FIGURE 14.2

8. An ideal gas has undergoes two processes AB and BC as shown in FIGURE
14.2 below. 8 kJ of heat is supplied to the process AB and 4 kJ of heat is
dissipated from the gas in the process BC. Calculate
(a) the work done for AB and BC.
(b) the changes in internal energy for AB and BC.

9. An ideal gas at a pressure of 1.0 x 105 Pa and a volume of 0.4 m3 is heated at
constant pressure until its volume achieves 1.0 m3. Then, the gas is heated at
constant volume until its final pressure is 3.0 x 105 Pa. Determine the total work

done by the gas.

76

10. Kolej Matrikulasi Negeri Sembilan
P(105 ) Pa c

b
10

5a d

V (103 ) m3

2 6

FIGURE 14.3

Referring to the FIGURE 14.3 below, an amount of 160 J of heat is added to
the system in process of ab. While in the process of bd, 600 J of heat is added.
Determine the change in internal energy in the process of abd.

ANSWER

1. (a) 1.69 kJ (b) 1.68 kJ (c) –5.02 kJ
2. DIY
3. –36 J (b) 0.01 m3
4. (a) DIY
5. (a) DIY (b) (i) 180 K (ii) –400 J (iii) 0.4 moles
6. (a) 273.06 K
7. (a) DIY (b) 546.12 K (c) 44.8×10-3 m3
8. (a) 0 J, 6000 J
9. 60 kJ (b) –8136.65 J
10. 3240 J
(b) 2000 J, –4000 J (temperature decrease)

77