EP015 Physics Tutorial

SULIT EP015

LIST OF SELECTED CONSTANT VALUES
SENARAI NILAI PEMALAR TERPILIH

Speed of light in vacuum c = 3.00 × 108 m s-1
Laju cahaya dalam vakum

Permeability of free space ! = 4p × 10-7 H m-1
Ketelapan ruang bebas

Permittivity of free space ! = 8.85 × 10-12 F m-1
Ketelusan ruang bebas

Electron charge magnitude e = 1.60 × 10-19 C
Magnitud cas elektron

Planck constant h = 6.63 × 10-34 J s
Pemalar Planck

Electron mass me = 9.11 × 10-31 kg
Jisim elektron = 5.49 × 10-4 u

Neutron mass mn = 1.674 × 10-27 kg
Jisim neutron = 1.008665 u

Proton mass mp = 1.672 × 10-27 kg
Jisim proton = 1.007277 u

Deuteron mass md = 3.34 × 10-27 kg
Jisim deuteron = 2.014102 u

Molar gas constant R = 8.31 J K-1 mol-1
Pemalar gas molar

Avogadro constant NA = 6.02 × 1023 mol-1
Pemalar Avogadro

Boltzmann constant k = 1.38 × 10-23 J K-1
Pemalar Boltzmann

Free-fall acceleration g = 9.81 m s-2
Pecutan jatuh bebas

2 SULIT

SULIT EP015

LIST OF SELECTED CONSTANT VALUES
SENARAI NILAI PEMALAR TERPILIH

Atomic mass unit 1u = 1.66 × 10-27 kg
Unit jisim atom 1 eV "#$
= 931.5 %!
Electron volt
Elektron volt = 1.6 × 10-19 J

Constant of proportionality k = 1 = 9.0 ´ 109 N m2 C-2
for Coulomb’s law 4pe 0
Pemalar hukum Coulomb

Atmospheric pressure 1 atm = 1.013 ´ 105 Pa
Tekanan atmosfera

Density of water rw = 1000 kg m-3
Ketumpatan air

3 SULIT

SULIT EP015

LIST OF SELECTED FORMULAE
SENARAI RUMUS TERPILIH

1. = + 18. s = rq

2. = + & ' 19. v = rw
'

3. ' = ' + 2 20. at = ra

4. = & ( + ) 21. w = wo + at
'

5. = 1 at2
2
6. = ∆ 22. q = wot +

7. = ∆ = − 23. = % ( & + )
$
8. = .

9. = ⃗ ∙ ⃗ = cos 24. w 2 = wo2 + 2aq

10. = & ' 25. t = rF sin q
'

11. = ℎ å26. I = mr2

12. ( = & ' = & 2
' ' 5
Isolid sphere MR 2
13. = ∆ 27. =

14. Pav = DW 28. I = 12 MRsolid cylinder/disc 2
Dt

15. = %% %⃗ • ⃗ = cos 29. Iring = MR2

16. ! = "! = $ = 30. I rod = 1 ML2
# 12

17. Fc = mv2 = mvw = mrw2 31. ∑ =
r

4 SULIT

SULIT EP015

LIST OF SELECTED FORMULAE
SENARAI RUMUS TERPILIH

32. L = Iw 48. ( = ( <+*
33. = sin $)
34. = cos = ± D ' − '
49. ( = ("
,)

35. = − ' sin = − ' 50. v= T
µ
36. = & '( ' − ')
'

37. = & ' ' 51. = -
' )

38. E = 1 mw2 A2 52. . = >""±∓"""#?
2

39. w = 2p = 2p f F
T 53. s = A

l 54. = ∆)
g )$

40. T = 2p

55. Y =s
e
T = 2p m
41. k 56. = % ∆
$

42. k = 2p 57. 2 = %
l 3 $

43. v = f l 58. P = F
^

A

44. y ( x,t ) = Asin (wt ± kx) 59. Pgauge = Pabs - Patm = r gh

45. ' = cos ( ± ) 60. Pabs = Patm + r gh

46. y = 2Acos kx sin wt

47. ( = (" 61. r = m
$) V

5 SULIT

SULIT EP015

LIST OF SELECTED FORMULAE

SENARAI RUMUS TERPILIH

62. A1v1 = A2v2 75. = % #-6$
7

63. P + 1 rv2 + r gh = constant 76. K tr = 3æ R ö T = 3 kT
2 ç NA ÷ 2
2 è ø

64. FD = 6phrv 77. U = 1 fNkT = 1 fnRT
22
65. 4 = − >∆)*?
5
78. CP - CV = R
66. DL = a LoDT

67. DA = b AoDT 79. CV = Q
nDT

68. DV = gVoDT 80. g = CP
69. b = 2a CV

70. g = 3a 81. ∆ = −

n= m = N 82. pV g = constant
M NA
71. 83. TV g -1 = constant

72. #-6 = F〈 $〉 84. = ln 3% = ln 8&
3& 8%

73. vrms = 3kT 3RT 85. = ∫ = ( 9 − :)
m= M 86. = ∫ = 0

74. = % #-6$
7

6 SULIT

SULIT EP015

7 SULIT

TOPIC 1 : PHYSICAL QUANTITIES AND MEASUREMENTS
1.1 DIMENSIONS OF PHYSICAL QUANTITIES
1.2 SCALARS AND VECTORS
At the end of this topic, students should be able to:
1.1 DIMENSIONS OF PHYSICAL QUANTITIES
1. Define dimension.
2. Determine the dimensions of derived quantities.
3. Verify the homogeneity of equations using dimensional analysis.
1.2 SCALARS AND VECTORS
4. Define scalar and vector quantities.
5. Resolve vector into two perpendicular components (x and y axes).
6. Determine resultant of vectors.

1

KOLEJ MATRIKULASI KEJURUTERAAN JOHOR
KEMENTERIAN PENDIDIKAN MALAYSIA

TUTORIAL 1
(PHYSICAL QUANTITIES AND MEASUREMENT)
SECTION A
1. 891 000 milligrams can be written as ___
A 8.91 ×10-1 kilograms
B 8.91 ×10-2 kilograms
C 8.91 ×102 kilograms
D 8.91 ×101 kilograms
2. Dimension is defined as a ___
A. technique or method which physical quantity can be expressed in
terms of combination of basic quantities
B. technique or method which basic quantity can be expressed in
terms of combination of physical quantities
C. technique or method to determine the homogeneity of equation
D. technique or method to construct an equation
3. Which of the following is the correct dimension of k so that the equation:

momentum = k x density

A. M L2 T-1
B. M L2 T-2
C. L4 T-1
D. L2 T-1

2

SECTION B
1. The pressure of a liquid is given by P = ρgh. Calculate the pressure (in SI
unit) if the density of water, ρ is 1 g cm–3, the acceleration due to gravity, g is
10 ms–2, and the height of water, h is 50 cm ?
(ANS: 5 × 103 Nm-2 or 5 × 103 Pa or 5 × 103 kgm-1 s-2 )
2. a) Show that the expression v = at is dimensionally correct if in this expression v
represents velocity, a is acceleration, and t an instant of time.
b) The equation governing the rate of flow of fluid under streamline



conditions through a horizontal pipe of length l and radius r is = 4 4 where

8

p is the pressure difference across the pipe and η is the viscosity of the fluid.
Deduce the dimension for η.

(ANS: ML-1T-1)
3. Change the following quantities into its SI unit.

a) 50 mm2
b) 4.5 x 10-3 cm3
c) 100 g cm-3
d) 360 km hour-1

(ANS: 5.0 x 10- 5m2 , 4.5 x 10-9 m3 , 105 kg m-3 , 100 m s-1)
4.

FIGURE 1 shows two displacement vector A and B. Determine the
magnitude and direction of the resultant displacement.

(ANS: 1.68 km, 7.5° below negative x-axis)
3

5.

FIGURE 2
FIGURE 2 shows vector P and Q. Calculate the resultant vector of P and Q and
its direction.

(ANS: 53.68 ms-2, 69.96° above positive x-axis)
6. Two vectors A and B respectively can be represented as follow:

A = 20 unit (directed eastwards)
B = 15 unit (directed north-westwards)
Determine A + B by resolving vectors into axes.

(ANS: 14.17 unit, 48.49° above positive x-axis)
7.

FIGURE 3
FIGURE 3 shows how two coplanar force F1 and F2, act on point O

4

a) Resolve the force along the x and y axes as well as determine the
resultant force FR.

b) Determine the direction of the resultant force FR.
(ANS: 5.15 N, 50.28° below positive x-axis)

5

TOPIC 2 : KINEMATICS OF LINEAR MOTION

2.1 LINEAR MOTION
2.2 UNIFORMLY ACCELERATED MOTION
2.3 PROJECTILE MOTION

At the end of this topic, students should be able to:

2.1 LINEAR MOTION

1. Define:
i. instantaneous velocity, average velocity and uniform velocity; and
ii. instantaneous acceleration, average acceleration and uniform acceleration.

2. Interpret the physical meaning of displacement-time, velocity-time and
acceleration-time graphs.

3. Determine the distance travelled, displacement, velocity and acceleration from
appropriate graphs.

2.2 UNIFORMLY ACCELERATED MOTION

4. Apply equations of motion with uniform acceleration:

v = u + at , s = ut + 1 at 2 , v2 = u 2 + 2as , s = 1 (u + v)t
2
2

2.3 PROJECTILE MOTION

5. Describe projectile motion launched at an angle, θ as well as special cases when

 = 0
6. Solve problems related to projectile motion.

6

KOLEJ MATRIKULASI KEJURUTERAAN JOHOR
KEMENTERIAN PENDIDIKAN MALAYSIA

TUTORIAL 2
(KINEMATICS OF LINEAR MOTION)

SECTION A

1. A ball comes back to its starting point after bouncing off the floor. Its average
velocity is ___

A zero
B maximum
C constant
D decreasing

2. Which one below is NOT the example of uniform velocity?

A Rotation of the Earth.
B A car moving on a straight road with constant speed.
C A bouncing ball.
D Movement of hands of a clock.

3. A woman step on the gas pedal of car when the traffic light turns green. Which
one below is TRUE?

Average velocity Average acceleration
A increases constant
B increases increases
C increases zero
D constant constant

4. Which one below is NOT the example of uniform accelerated motion?

A A skydiver jumping out of a plane.
B A stone dropped from the top of a building.
C A ball rolling down a slope.
D A bus driving in a heavy traffic.

7

SECTION B s (m)
1. a)

P
Q

t (s)

T
FIGURE 1

FIGURE 1 shows the displacement-time graph of two cars, P and Q.

Describe the motion of the two cars at time T.

(ANS: DIY)

b) v( )

12 B

6 5 C t (s)
10 15 20
0A
-6 DE

-12

FIGURE 2

FIGURE 2 shows the velocity-time graph of an object moves from rest at
point A and stops at point E after 20 s. Calculate the

i) acceleration during the motion AB, BC, CD and DE.
ii) acceleration at t = 10 s .
iii) total distance travelled by the object.
iv) total displacement of the motion.
v) average velocity for the whole journey A to E.

(ANS: AB : 2.4 ms −2 , BC : −2.4 ms −2 , CD : −2.4 ms −2 , DE : 0 ms −2 ,−2.4 ms −2 ,
150 m,−30 m,−1.5 ms−1 )

8

2. a) Hassan is driving at 108 kmh−1 along a straight road. He suddenly sees a

school girl who runs across the road 100 m ahead of his car. If his reaction
time is 0.7 s and the maximum deceleration of the car is 4.5 ms −2 , determine

the distance travelled by the car before it stops. Is the car will stop before or
after hitting the girl?

b) When the brakes are applied, a car reduces its velocity from 30 ms −1 to

15 ms −1 after moving 75 m. In order to stop the car completely, what is the

extra distance needed?

(ANS: 21m, DIY, 25 m )

3. A car which is initially at rest starts to move along a straight line with constant
acceleration. It reaches a velocity of 60 ms−1 after travelling through a distance of
100 m. Determine the

a) acceleration,
b) time taken to reach the velocity of 60 ms−1 ,
c) velocity at t = 3.0 s .

(ANS: 18 ms −2 , 3.3 s, 54 ms −1 )

4. An archer stand on a cliff elevated at 50 m high from the ground and shoots an
arrow at the angle of 30° above the horizontal with the speed of 80 ms-1.

a) How long does it fly in the air?
b) How far from the base of the cliff does the arrow fly until it hits the

ground?
c) Determine the speed of the arrow just before it hits the ground.

(ANS: 9.26 s, 641.53 m,85.93 ms −1 )

5. A leopard can jump to a height of 3.7 m when leaving the ground at an angle of
45 from the horizontal. Determine the initial speed must the leopard takes to
reach that height.

(ANS: 12.05 ms −1 )

6. A mountain climber stands at the top of a 75.0 m cliff that extend over a pool of
water. She throws two stones vertically downward from the same height. Initially,

she throws the first stone with initial speed of 2.0ms−1 . At 1.00 s later she throws
the second stone with initial speed u and both stones hit the water simultaneously.

9

Determine how long after the release of the first stone did the second stone hits
a) the water.
the initial speed u of the second stone.
b)
(ANS: 2.71s, −14.36 ms −1 )

7. u
A

1m

B

x
FIGURE 3

FIGURE 3 shows a rolling ball falls from the edge of a table with initial horizontal
velocity, u of 5 ms −1 . The height of the table is 1 m. Calculate the

a) time taken for the ball to reach point B.
b) horizontal distance, x.
c) magnitude and direction of its velocity at point B.

(ANS: 0.45 s, 2.25 m, 6.67 ms −1,−41.40 )

10

TOPIC 3 : DYNAMICS OF LINEAR MOTION

3.1 MOMENTUM AND IMPULSE
3.2 CONSERVATION OF LINEAR MOMENTUM
3.3 BASIC OF FORCES AND FREE BODY DIAGRAM
3.4 NEWTON’S LAWS OF MOTION

At the end of this topic, students should be able to:

3.1 MOMENTUM AND IMPULSE

1. Define momentum and impulse, = ∆
2. Solve problem related to impulse and impulse-momentum theorem,

J = ∆p = mv– mu (remarks: 1D only).
3. Use F-t graph to determine impulse.

3.2 CONSERVATION OF LINEAR MOMENTUM

4. State the principle of conservation of momentum.
5. Apply the principle of conservation of momentum in elastic and inelastic collisions

in 2D collisions.
6. Differentiate elastics and inelastic collisions. (remarks: similarities & differences).

3.3 BASIC OF FORCES AND FREE BODY DIAGRAM

7. Identify the forces acting on a body in different situations:
i. Weight, W
ii. Tension, T

iii. Normal force, N
iv. Friction, f
v. External force (pull or push), F
8. Sketch free body diagram.
9. Determine static and kinetic friction, ≤ ; ≤

3.4 NEWTON’S LAWS OF MOTION

10. State Newton’s Law of Motion.
11. Apply Newton’s Law of Motion. (remarks: include static and dynamic equilibrium

for Newton’s First Law Motion).

11

KOLEJ MATRIKULASI KEJURUTERAAN JOHOR
KEMENTERIAN PENDIDIKAN MALAYSIA

TUTORIAL 3
(DYNAMICS OF LINEAR MOTION)

SECTION A

1. Which of the following statements is true about the elastic collision between two
objects?
A. The momentum and total energy are conserved but the kinetic energy can
be converted into other forms of energy.
B. Both the momentum and total energy are conserved if and only if the mass
of the two objects is identical.
C. The kinetic energy is conserved whereas the total energy is reduced but can
be increased.
D. Momentum, kinetic energy and total energy must be conserved.

2. The purpose of an airbag or crumple zone in a car is to increase the time taken for
the driver to stop. What is the advantage of this?
A. It reduces the driver’s momentum.
B. It reduces the driver’s energy.
C. It reduces the force on the driver.
D. It reduces the energy of the impact

3. A tennis player returns a serve. How does the force on the ball relate to its
momentum?
A. The force is the rate of change of momentum of the ball
B. The force is the overall change of momentum multiplied by the time taken
to cause the change
C. The force is the momentum of the ball as it is hit
D. The force is the momentum of the ball leaving the racket divided by the
time taken to cause the change

12

4. An object will remain stationary on an inclined plane because ___
A. the static frictional force is acting upward along the inclined plane.
B. The static frictional force is acting downward along the inclined plane.
C. the dynamic frictional force is acting upward along the inclined plane.
D. the dynamic frictional force is acting upward along the inclined plane.

5. If a nonzero net force is acting on an object, which of the following must we assume
regarding the object’s condition?
A. The object is at rest.
B. The object is moving with constant velocity.
C. The object is being accelerated.
D. The object is losing mass.

SECTION B

1. A 0.10 kg ball is thrown straight up into the air with an initial speed of 15 ms-1.
Find the momentum of the ball
a) at its maximum height and
b) halfway to its maximum height.
(ANS: a) 0 kgms-1 b) 1.061 kgms-1)

2. An object has a kinetic energy of 275 J and a momentum of 25.0 kg m s-1. Find
a) the speed
b) mass of the object.
(ANS: a) 22 ms-1 b) 1.14 kg)

3. A force, F acting on an object of mass 2.0 kg varies with time t in the way as shown
in FIGURE 1. The velocity of the object is 4.0 m s-1 before the application of the
force. Determine the velocity of the object after applying the force for 0.2s.

F(N)

100

t(s)

0.2 (ANS: 9 ms-1)
FIGURE 1

13

4. A 75.0kg ice skater moving at 10.0 m s-1 crashes into a stationary skater of equal
mass. After the collision, the two skaters move as a unit at 5.00 m s-1. Suppose the
average force a skater can experience without breaking a bone is 4 500 N. If the
impact time is 0.100 s, does a bone break?
(ANS: 3750 N)

5.

FIGURE 2

A 2 kg ball A moves to the right with velocity of 4 ms-1 collides with another 1 kg
ball B moving in the opposite way with velocity of 0.5 m s-1 as shown in
FIGURE 2. After the collision, both balls move at 300 and 150 from the horizontal.
Calculate the final velocity of each ball after the collision. Assume the collision is
an elastic.

(ANS: 1.37 ms-1, 5.3 ms-1)
6. A 600 g body, P is initially at rest. A 400 g body, Q which is initially moving with

a velocity of 125 cm s-1 toward the right along the x-axis, strikes P. After the
collision, Q has a velocity of 100 cm s-1 at an angle of 370 above the x-axis in the
first quadrant. Both bodies move on a horizontal plane. Calculate:

a) The magnitude and direction of the velocity of P after the collision.
b) The loss kinetic energy during the collision.

(ANS: a) 0.502 ms-1 , 53.21° below + x-axis, b) 0.0369 J)

14

7.

300

FIGURE 3

2.0 kg object is placed on a rough plane inclined at 30° with the horizontal as
shown in FIGURE 3. It is released from rest and accelerates at 4.0 m s-2. Calculate
the frictional force acting on the object.

(ANS: 1.81 N)

8. A 3.0 kg cube is placed on a rough plane. The plane is then slowly tilted until the
cube starts to move from rest. This occurred when the angle of inclination is 25°.
Calculate the coefficient of static friction between the cube and the rough plane.
(ANS: 0.466)

9. A wooden block of mass 2.0 kg slides down with constant velocity on an inclined
rough plane of 30° from the horizontal axis.
a) Sketch a free body diagram to show forces acting on the wooden block.
b) Calculate the kinetic frictional force between the wooden block and the
rough inclined plane.
(ANS: b) 9.81 N)

10.
4 kg A

300

FIGURE 4

B
1 kg

FIGURE 4 shows a 4.0 kg block A on a rough 30° inclined plane is connected to
a freely hanging 1.0 kg block B by a mass-less cable passing over the frictionless

15

pulley. When the objects are released from rest, object A slides down the inclined
plane with a friction force of 6.0 N. Calculate

a) the acceleration of the objects
b) the tension in the cable.

(ANS: a) 4.69ms -2 b) 5.12 N)

11.

FIGURE 5
A window washer pushes his scrub brush up a vertical window at constant
speed by applying a force F as shown in FIGURE 5. The brush weighs 10.0 N
and the coefficient of kinetic friction is k= 0.125. Calculate

a) the magnitude of the force F
b) the normal force exerted by the window on the brush.

(ANS: a) 14.6 N b) 9.38 N)

12.

FIGURE 6

FIGURE 6 shows three wooden blocks connected by a rope of negligible mass are
being dragged by a horizontal force, F. Suppose that F = 1000 N, m1 = 3 kg, m2 =
15 kg and m3 = 30 kg. Determine

a) the acceleration of blocks system.
b) the tension of the rope, T1 and T2.
(Neglect the friction between the floor and the wooden blocks.)

(ANS: a) 20.8 ms -2 b) 936 N, 624 N)
16

TOPIC 4: WORK, ENERGY AND POWER
4.1 WORK
4.2 ENERGY AND CONSERVATION OF ENERGY
4.3 POWER

At the end of this topic, students should be able to:
4.1 WORK
1. State the physical meaning of dot (scalar) product for work.
2. Define and apply work done by a constant force.
3. Determine work done from a force-displacement graph.
4.2 ENERGY AND CONSERVATION OF ENERGY
4. Define and use:

a. Gravitational potential energy
b. Elastic potential energy for spring
c. Kinetic energy
5. State the principle of conservation of energy.
6. Apply the principle of conservation of mechanical energy.
7. State and apply work-energy theorem.
4.3 POWER
8. Define and use average power and instantaneous power.

17

KOLEJ MATRIKULASI KEJURUTERAAN JOHOR
KEMENTERIAN PENDIDIKAN MALAYSIA

TUTORIAL 4
(WORK, ENERGY AND POWER)

SECTION A

1. The work done is 0 J if ___
A The body shows displacement in the opposite direction of the force applied.
B The body shows displacement in the same direction as that of the force
applied.
C The body shows a displacement in perpendicular direction to the force
applied.
D The body masses obliquely to the direction of the force applied.

2. A ball is dropped from a height of 10 m.
A Its potential energy increases and kinetic energy decreases during the falls
B Its potential energy is equal to the kinetic energy during the fall.
C The potential energy decreases and the kinetic energy increases during the
fall.
D The potential energy is zero and kinetic energy is maximum while it is
falling.

3. According to the work-energy theorem, total change in energy is equal to the
_____
A total work done.
B half of the total work done.
C total work done added with frictional losses.
D square of the total work done.

4. The spring will have maximum potential energy when ___
A it is pulled out
B it is compressed
C it is pulled out and compressed
D neither (A) nor (B)

18

5. A trolley is pulled along a smooth horizontal track by a constant force. Which

of the following graphs best describe the variation of the trolley’s kinetic

energy, K with time, t if air resistance is negligible?

AK B

K

t t

CK DK

t t

SECTION B
1.

FIGURE 1

FIGURE 1 shows four situations in which a force is applied to an object. In all four
cases, the force has the same magnitude, and the displacement of the object is to
the right and of the same magnitude. Rank the situations in order of the work done
by the force on the object, from most positive to most negative.

2. A 500 kg helicopter ascends vertically from the ground with an acceleration of
2 m s-2 over a 5.0 s interval. Calculate the :
a) work done by the lifting force.
b) work done by the gravitational force.
c) net work done on the helicopter.
(ANS: 1.48  105 J, -1.23  105 J, 2.50  104 J)

19

3. A block of mass 25.0 kg is pulled 1.2 m along a frictionless horizontal table by a
constant force of 36 N directed at 35° above the horizontal. Determine the total
work done on the block.
(ANS: 35.4 J)

4. A horizontal constant force of 480 N is applied to an object of mass 30 kg on a
rough inclined plane 50° to the horizontal. If the force of friction is 50 N, how much
work is done to push object through at distance of 2 m up the plane.
(ANS: 66.2 J)

5.

F (N)

10

8 10 12 s (cm)

4
-5

FIGURE 2

FIGURE 2 shows an object of mass 5.0 kg moving along a straight line is acted
upon by a force as shown in the force-displacement graph. Determine the total
work done on the object.

(ANS: 0.65 J)

6. A spring is extended by 20 cm when a force of 150 N is applied to it. This spring is
suspended vertically with a load of 8 kg attached at its lower end. Calculate the
a) spring constant, k
b) elongation of the spring, x
c) energy stored in the spring.
(ANS: 750 N m-1, 0.1 m, 3.75 J)

7. A 25 kg boy slides down a 1.2 m inclined plane making an angle of 30° with the
horizontal. If he starts from rest at the top of plane and reaches the end of the plane
with a speed of 2.0 m s-1, find the work done by the friction.
(ANS: 97.15 J)

20

8.

FIGURE 3
FIGURE 3 shows a ball of mass m=1.80 kg is released from rest at a height h =65.0
cm above a light vertical spring of force constant k. The ball strikes the top of the
spring and compresses it a distance d = 9.0 cm. Neglecting any energy losses
during the collision, find

a) the speed of the ball just as it touches the spring
b) the force constant of the spring.

(ANS: 3.57 m s-1, 3.22 kN m-1)
9.

FIGURE 4
FIGURE 4 shows two objects (m1 = 5 kg and m2 = 3kg) are connected by a light
string passing over a light, frictionless pulley. The 5 kg object is released from rest
at a point h = 4 m above the table.

a) Determine the speed of each object when the two pass each other.
b) Determine the speed of each object at the moment the 5kg object hits the

table.
21

c) How much higher does the 3kg object travel after the 5kg object hits the
table?
(ANS: 3.13 m s-1, 4.43 m s-1, 1.0m)

10. A mechanic pushes a 2.50 × 103 kg car from rest to a speed of v, doing 5000 J of
work in the process. During this time, the car moves 25.0 m. Neglecting friction
between car and road, determine

a) the final speed, v.
b) the net force on the block.

(ANS: 2 ms-1, 200 N)

11. A 2000 kg car moves down a level highway under the actions of two forces. One
is a 1000 N forward force exerted on the drive wheels by the road and the other is
950 N resistive force. Use the work-kinetic energy theorem to find the speed of the
car after it has moved a distance of 20 m, assuming it starts from rest.
(ANS: 1.0 ms-1)

12. A car accelerates from 0 to 100 km per hour in 3 minutes. If the mass of the car is
1500 kg, determine the power delivered by its engine.
(ANS: 3.22 × 103 W)

13. A construction worker used a motor-driven cable to pull a 70 kg crate of bricks up
a 30° inclined slope of length 60 m. Assuming the slope is smooth and the man is
pulling at constant speed of 2 m s-1, determine the

a) work done by the man.
b) power of the motor.

(ANS: 20.6 kJ, 686.7 W)

14. A 1.5 × 103 kg car starts from rest and accelerates uniformly to 18.0 m s-1 in 12.0 s.
Assume that air resistance remains constant at 400 N during this time. Find

a) the average power developed by the engine in hp.
b) the instantaneous power output of the engine at t =12.0 s, just before the

car stops accelerating.
(Given that, 1hp = 746 W)

(ANS: 32 hp, 64 hp)

22

15. A 1000 kg elevator carries a maximum load of 800 kg. A constant frictional force
of 4000 N retards its motion upward. What is the minimum power (in kW and in
hp) must the motor deliver to lift the fully loaded elevator at a constant speed of
3 ms-1?
(Given that, 1hp = 746 W)
(ANS: 64.9 kW @ 87.1 hp)

23

TOPIC 5 : CIRCULAR MOTION
5.1 PARAMETERS IN CIRCULAR MOTION
5.2 UNIFORM CIRCULAR MOTION
5.3 CENTRIPETAL FORCE

At the end of this topic, students should be able to:
5.1 PARAMETERS IN CIRCULAR MOTION
1. Define and use angular displacement, period, frequency, and angular velocity.
5.2 UNIFORM CIRCULAR MOTION
2. Describe uniform circular motion
3. Convert units between degrees, radian, and revolution or rotation.
5.3 CENTRIPETAL FORCE
4. Define centripetal acceleration and centripetal force
5. Solve problems related to centripetal force for uniform circular motion cases:

horizontal, vertical and conical pendulum.

24

KOLEJ MATRIKULASI KEJURUTERAAN JOHOR
KEMENTERIAN PENDIDIKAN MALAYSIA

TUTORIAL 5
(CIRCULAR MOTION)

SECTION A

1. Which of these statements is incorrect about uniform circular motion?

A. The speed is always constant
B. The velocity is changing with time
C. The object is speeding up or slowing down
D. The direction of the velocity is changing with time

2. The blades of a table fan make 25 revolutions in one minute. What is the angular
velocity of the blades?

A. 1.31 rad s-1
B. 2.62 rad s-1
C. 78.5 rad s-1
D. 157 rad s-1

3. The three hands on a clock are called the hour hand, the minute hand and the
second hand. What is the angular velocity of the second hand?

A. 0.105 rad s-1
B. 1.05 rad s-1
C. 5.1 rad s-1
D. 1.5 rad s-1

SECTION B

1. A gramophone rotates at 331 rev min-1 and has a radius of 0.15 m. What is

a) its angular velocity
b) the speed of a point on its circumference
c) the centripetal acceleration of a point on its circumference

(ANS: 34.66 rad s-1 , 5.2 ms-1 , 180.27 ms-2 )

25

2. Calculate the centripetal acceleration of an object at the Equator due to rotation of the

Earth. The radius of Earth is 6.37 x 106 m.
(ANS: 0.034 ms-2)

3. A mass moves in a horizontal circle with a constant speed of 1. When the same mass
moves in the same circular path with a speed of 2 , the new centripetal force is half that

of the first. What is the value of 2 ? (ANS: 0.034 ms-2)

1

4. A 2 kg ball attached to a 2.5 m string is whirled in a vertical circle with a constant speedof
6 ms-1.

a) Determine the centripetal force of the ball

b) Calculate the tension of the string at the highest and lowest point of the circle.
(ANS: 28.8 N , 9.18 N , 48.42 N)

5. A 4 kg object is attached to a vertical rod by two strings as shown in FIGURE 1.

FIGURE 1

The object rotates in a horizontal circle at constant speed 6.00 m/s. Find the tension
in
a) the upper string
b) the lower string

(ANS: 108.63 N , 56.3 N)

6. A 5000 kg truck is making a turn at a corner of radius 55 m. The road is flat and
the coefficient of kinetic friction between the tyres and the road is 0.58.

a) Sketch and label a free body diagram for the truck

26

b) Calculate the maximum velocity of the truck without skidding
c) Calculate the maximum angular velocity of the truck
d) Calculate the maximum centripetal acceleration of the truck

(ANS: 17.69 ms-1 , 0.321 rad s-1 , 28449 N)

7. A 0.2 kg, 50 cm pendulum is swirled horizontally at an angle of 37 with the
vertical asshown in the FIGURE 2.

FIGURE 2

a) Sketch and label a free body diagram for the pendulum bob

b) Calculate the tension of the string

c) Calculate the speed of the pendulum

(ANS: 2.46 N , 1.49 ms-1)

8. A ball of mass 0.35 kg is attached to the end of a horizontal cord and is rotated in
a circle ofradius 1.0 m on a frictionless horizontal surface. If the cord will break
when the tension in itexceeds 80 N, determine.

a) The maximum speed of the ball
b) The minimum period of the ball.

(ANS: 15.12 ms-1 , 0.42 s)

27

9. FIGURE 3 shows a child riding on a Ferris Wheel “Eye on Malacca” of 4.5 m in
diameter, rotating at constant speed.

FIGURE 3
a) Draw the free body diagram and write equations for forces acting on the

passenger at position A and B.
b) What is the maximum angular speed so that the passenger is not thrown

out form the chair?
(ANS: 2.09 rad s-1)

28

TOPIC 6: ROTATION OF RIGID BODY

6.1 ROTATIONAL KINEMATICS
6.2 EQUILIBRIUM OF A UNIFORM RIGID BODY
6.3 ROTATIONAL DYNAMICS
6.4 CONSERVATION OF ANGULAR MOMENTUM

At the end of this topic, students should be able to:

6.1 ROTATIONAL KINEMATICS
1. Define and use:

i. angular displacement, 
ii. average angular velocity,av
iii. instantaneous angular velocity, 
iv. average angular acceleration,  av
v. instantaneous angular acceleration, 
2. Analyse parameters in rotational motion with their corresponding quantities in
linear motion:

s = r ,v = r, at = ra, ac = r 2 = v2
r

3. Solve problem related to rotational motion with constant angular acceleration:

 = o + t, = o + 1 t2,2 = o2 + 2 , = 1 (0 + )t
2 2

6.2 EQUILIBRIUM OF A UNIFORM RIGID BODY

4. State the physical meaning of cross (vector) product for torque,  = rF sin 

5. Apply torque.

6. State conditions for equilibrium of rigid body,  F = 0 and  = 0

7. Solve problems related to equilibrium of a uniform rigid body. (remarks: limit to
5 forces)

6.3 ROTATIONAL DYNAMICS

8. Define and use moment of inertia, I = mr2

9. Use the moment of inertia of a uniform rigid body (sphere, cylinder, ring, disc,
and rod)

29

10. Determine the moment of inertia of a flywheel

11. State and use net torque,  = I

6.4 CONSERVATION OF ANGULAR MOMENTUM
12. Explain and use angular momentum, L = I
13. State and use principle of conservation of angular momentum.

30

KOLEJ MATRIKULASI KEJURUTERAAN JOHOR
KEMENTERIAN PENDIDIKAN MALAYSIA

TUTORIAL 6
(ROTATION OF RIGID BODY)

SECTION A

1. A heavy uniform plank of length L is supported by two forces F1 and F2 at a point
at a distance L/4 and L/8 from its ends as shown in FIGURE 1. Determine the
ratio of F2 : F1.
A. 1 : 3
B. 2 : 3
C. 3 : 2
D. 2 : 6

2. An ice skater is spinning with his arms folded inwards. Later the ice skater
stretches his arms outwards. Which of the following pairs of quantities will
increase?
A. period of rotation and moment of inertia.
B. kinetic energy and moment of inertia.
C. angular momentum and period of revolution.
D. angular momentum and kinetic energy.

SECTION B
1. A rotating wheel decelerates uniformly and makes N revolutions before stopping.

The time taken is T. What is the initial angular velocity of the wheel?
(ANS: 2 N/ T)

2. A motorcycle wheel with a radius 0.3 m rotates freely about a fixed axis. A steady
force of 10 N is applied tangentially for the wheel’s rim for 2 s. If the wheel moves
from rest and its moments of inertia about the axis is 0.5 kg m2, what is the final
angular velocity?
(ANS: 12 rad s-1)

31

3. A rigid body rotates about a fixed axis through a point in the body, with uniform
angular velocity of 600 rpm. The velocity then decreases at a constant retardation
to 300 rpm. in 6.0 s. Determine:
a) the angular acceleration
b) the number of revolutions the body has turned through in the 6.0 s
c) the extra time needed by the body to come to a stop if it continues
to slow down at the same rate.
(ANS: -5.2 rad s-2, 45 revolutions, 6.0 s)

4.
a) State the conditions for a particle that is acted upon by a system of forces
for it to be in equilibrium.

b) FIGURE 2 shows a 1 m rod of mass 2 kg is pivoted at point P. A load of
mass 6 kg is suspended at one end and another load of mass M is suspended
at Q. If the system is in equilibrium, determine the value of M.

c) FIGURE 3 shows a 10 kg uniform beam with 2.0 m long is pivoted at the
centre. A 20 N force is exerted 0.5 from centre of the beam. If the beam is in
equilibrium, determine F.
(ANS: 1.2 kg, 13 N)

32

5. FIGURE 4 shows a uniform ladder 3 m long and has a mass of 30 kg. The ladder
is at rest with its upper end against a smooth vertical wall and its lower end on
rough ground. The ladder is placed at the angle of 50° with the horizontal, to
maintain its position.

FIGURE 4
a) Draw a free-body diagram of this system and show the forces acting on it.
b) Calculate the reaction forces at A and B.
c) Calculate the least coefficient of friction between the ground and the ladder.

(ANS: 294.3 N, 123.4 N, 0.4)
6.

FIGURE 5
FIGURE 5 shows a string wound around a wheel with the free end of the string
tied to the ceiling. The mass of the wheel is 0.5 kg and its radius are 40 cm. When
the wheel is released, it will fall downwards and, at the same time, rotate. If the
moment of inertia of the wheel about its axis of rotation is 0.2 kg m2. Calculate the
linear acceleration of the wheel and also the tension of the string.

(ANS: 2.80 m s-2, 3.50 N)

33

7.

a) FIGURE 6

b) FIGURE 6 shows a solid cylinder of radius 18.0 cm is free to rotate about a
8. smooth horizontal axle. A mass of 0.38 kg hangs from a string wound
around the cylinder as shown in. When the system released from rest, the
a) mass takes 2.0 s to fall through a height of 5.0 m. What is the moment of
inertia of the cylinder?
b)
(ANS: 3.60 x 10-2 kg m2)

The cylinder is then replaced by a hollow cylinder of the same mass and
dimensions. Discuss qualitatively the effect on the speed of the mass after
the mass has fallen through a height of 5.0 m.

A figure skater increases her spin rotation rate from an initial rate of 1.0 rev
every 2.0 s to a final rate of 3.0 rev s-1. Her initial moment of inertia was
4.6 kg m2.

i. Calculate her final moment of inertia.
ii. How does she physically accomplish this change?

A bicycle wheel of radius 0.32 m has a moment of inertia of 0.035 kg m2
about its axle. When the wheel is lifted from the ground and set spinning at
a frequency of 10 Hz it comes to rest after 30 min. Calculate

i. the angular deceleration of the wheel.
ii. the average frictional torque acting on it.

(ANS: 0.77 kg m2, -0.35 rad s-2, -0.012 N m)

34

TOPIC 7 : SIMPLE HARMONIC MOTION AND WAVES

7.1 KINEMATICS OF SIMPLE HARMONIC MOTION
7.2 GRAPH OF SIMPLE HARMONIC MOTION
7.3 PERIOD OF SIMPLE HARMONIC MOTION

At the end of this chapter, students should be able to:

7.1 KINEMATICS OF SIMPLE HARMONIC MOTION
1. Explain SHM

2. Apply SHM displacement equation y = Asin t
3. Use equations:

i. velocity, = = ± √ 2 − 2
ii. acceleration, = − 2 = − 2
iii. kinetic energy, K = 1 2( 2 − 2)

2

iv. potential energy, U = 1 2 2

2

4. Emphasise the relationship between total SHM energy and amplitude.
5. Apply equation of velocity, acceleration, kinetic energy and potential energy for

SHM

7.2 GRAPH OF SIMPLE HARMONIC MOTION
6. Analyse the following graphs:

i. displacement - time
ii. velocity - time
iii. acceleration - time
iv. energy - displacement

7.3 PERIOD OF SIMPLE HARMONIC MOTION
7. Use expression for period of SHM, T for simple pendulum and mass-spring

system

T = 2 l
• Simple pendulum oscillation: g

• Mass spring oscillation: T = 2 m
k

35

KOLEJ MATRIKULASI KEJURUTERAAN JOHOR
KEMENTERIAN PENDIDIKAN MALAYSIA

TUTORIAL 7
(SIMPLE HARMONIC MOTION AND WAVES)

SECTION A

1. In simple harmonic motion, velocity at equilibrium position is __________.
A. minimum
B. constant
C. maximum
D. zero

2. Which one of the following statements is TRUE when an object performs simple
harmonic motion about a central point O?
A. The acceleration is always away from O
B. The acceleration and velocity are always in opposite directions
C. The acceleration and the displacement from O are always in the same
direction
D. The acceleration is always directed towards O

3. Which one of the following statements concerning the acceleration of an object
moving with simple harmonic motion is CORRECT?
A. It is constant
B. It is at a maximum when the object moves through the centre of the
oscillation
C. It is zero when the object moves through the centre of the oscillation
D. It is zero when the object is at the extremity of the oscillation

4. The frequency of a body moving with simple harmonic motion is doubled. If the
amplitude remains the same, which one of the following is also doubled?
A. The period
B. The total energy
C. The maximum velocity
D. The maximum acceleration

36

5. Which one of the following gives the phase difference between the particle velocity
and the particle displacement in simple harmonic motion?
A. π/4 rad
B. π/2 rad
C. 3π/4 rad
D. 2π rad

6. A simple pendulum and a mass-spring system are taken to the Moon, where the
gravitational field strength is less than on Earth. Which line, A to D, CORRECTLY
describes the change, if any, in the period when compared with its value on Earth?

Period of Pendulum Period of Mass-Spring System
A decrease decrease
B increase increase
C no change decrease
D increase no change

7. A body executes simple harmonic motion. Which one of the graphs, A to D, best
shows the relationship between the kinetic energy, Ek, of the body and its distance
from the centre of oscillation?

37

8. When a mass suspended on a spring is displaced, the system oscillates with simple
harmonic motion. Which one of the following statements regarding the energy of
the system is INCORRECT?

A . The potential energy has a minimum value when the spring is fully
compressed or fully extended.

B. The kinetic energy has a maximum value at the equilibrium position.
C. The sum of the kinetic and potential energies at any time is constant.
D. The potential energy has zero value when the mass is at rest.

9. A particle oscillating in simple harmonic motion is
A. never in equilibrium because it is in motion
B. never in equilibrium because there is always a force
C. in equilibrium at the end of its path because its velocity is zero there
D. in equilibrium at the centre of its path because the acceleration is zero
there

SECTION B

1. The equation of motion for a particle oscillating in SHM is given as,
x = 3 sin 2t

where x is the displacement in meter and t is the time in second. Determine
a) amplitude
b) frequency of oscillation
c) the position of particle at t = 0.2s
(ANS: 3 m, 0.32 Hz. 1.168 m)

2. The displacement, x of a particle varies with time, t is given by
x = 4 sin 2πt

where x is in cm and t in s . Calculate the
a) frequency of the motion.
b) velocity of the particle at t = 0.2s .
c) acceleration of the particle at t= 0. 2s
(ANS: 1 Hz, 7.77 cms-1, 150.2 cms-2)

38

3. The equation of motion for a particle oscillating in SHM is given as,
x = 5 sin (3t -π/2)

where x is the displacement in cm, determine,
a) the amplitude
b) period of oscillation
c) the displacement at time t = 2s
d) maximum velocity
e) maximum acceleration
f) velocity when its displacement is 4 cm
g) Sketch the graph of displacement against time
(ANS: 5 cm, 2.09 s, -4.8 cm, 0.15 ms-1, 0.45 ms-2, 9 cms-1)

4. An object of mass 3.0 kg executes linear SHM on a smooth horizontal surface at
frequency 10 Hz & with amplitude 5.0 cm. Neglect all resistance forces. Determine
a) the energy of the system
b) the potential & kinetic energy when the displacement of the object is 3.0cm.
(ANS: 14.8 J, 5.33 J, 9.47 J)

5. A 0.5 kg block connected to a light spring for which the force constant is
20.0 Nm-1 oscillates on a horizontal, frictionless track.
a) calculate the total energy of the system and the maximum speed of the block
if the amplitude of the motion is 3.0 cm.
b) compute the kinetic & potential energies of the system when displacement
is 2.0 cm
(ANS: 9x10-3J, 0.19ms-1, 5x10-3J, 4x10-3J)

6. A block of a mass 4 kg is attached to a spring and undergoes SHM with period of
T=0.25s, The total energy of the system is 3.5 J.
a) Calculate the force constant of the spring
b) Determine the amplitude of the motion
(ANS: 2.53x103 Nm-1, 0.053 m)

7. A student uses a simple pendulum of length 80.0 cm to determine the
gravitational acceleration. If there are 20 oscillations in 35.9s, find :
a) the value of g .
b) the period of oscillation if the experiment is done in the moon, where its
gravitational field strength is only 1/6 of that of the earth
(ANS: 9.80 ms-2, 4.4 s)

39

8. If a particle undergoes simple harmonic motion with amplitude of 0.2 m, what is
the total distance travelled in one period.
(ANS: 0.8 m)

9. A 0.2 kg block is attached to a light spring of force constant of 11 N/m on a
horizontal frictionless surface. If the block is displaced a distance of 8cm from its
equilibrium position, find
a) the amplitude, the angular frequency, the period and the frequency of
motion when the block is released.
b) the maximum force exerted on the block
c) the total mechanical energy of the system
d) the maximum speed and maximum acceleration of the block
e) the velocity of the block when its displacement is 2cm
f) the acceleration of the block when its displacement is 3cm.

(ANS: 8 cm, 7.42 rad/s, 0.85 s,1.17 Hz, 0.88 N, 0.035 J, 0.593 ms-1, -4.40 ms-2,
0.575 ms-1, -1.65ms-2)

10. A 175 g mass is suspended from a vertical spring. When the mass is pulled down
a distance of 76mm and released, the time taken for 25 oscillations is 23 s.
calculate
a) the period of oscillation
b) the maximum speed of the mass
c) total energy of the system and sketch its graph on a energy-time axes.
(ANS: 0.92 s, 0.52 ms-1,0.024 J)

40

TOPIC 8 : PHYSICS OF MATTERS

8.1 STRESS AND STRAIN
8.2 YOUNG’S MODULUS
8.3 HYDROSTATIC PRESSURE
8.4 FLUID DYNAMICS
8.5 VISCOSITY
8.6 HEAT CONDUCTION
8.7 THERMAL EXPANSION

At the end of this topic, students should be able to:

8.1 STRESS AND STRAIN

1. Distinguish between stress and strain for tensile and compression force.
2. Analyse the graph of stress-strain for a metal under tension.
3. Explain elastic and plastic deformations.
4. Analyse graph of force-elongation for brittle and ductile materials.

8.2 YOUNG’S MODULUS

5. Define and use Young’s Modulus.
6. Apply strain energy from force-elongation graph.
7. Apply strain energy per unit volume from stress-strain graph.

8.3 HYDROSTATIC PRESSURE

8. Express and use atmospheric pressure, gauge pressure and absolute pressure.

8.4 FLUID DYNAMICS

9. Illustrate fluid flow (remarks: laminar flow only).
10. Explain continuity principle and Bernoulli principle.
11. Use continuity and Bernoulli’s equations.

8.5 VISCOSITY

12. Explain viscosity.
13. State and use Stoke’s law.
14. Explain the terminal velocity in fluid using graph of velocity-time.

41

8.6 HEAT CONDUCTION
15. Define heat conduction.
16. Solve problems related to rate of heat transfer through a cross-sectional area

(*maximum two insulated objects in series).
17. Analyse graphs of temperature-distance for heat conduction through insulated

and non-insulated rods (*maximum two rods in series).
8.7 THERMAL EXPANSION
18. Define coefficient of linear expansion, area expansion and volume expansion.
19. Solve problems related to thermal expansion of linear, area and volume (*include

expansion of liquid in a container).

42

KOLEJ MATRIKULASI KEJURUTERAAN JOHOR
KEMENTERIAN PENDIDIKAN MALAYSIA

TUTORIAL 8
(PHYSICS OF MATTERS)

SECTION A

1. A wire is stretched until it undergoes plastic deformation. Which of the following
statements is TRUE of plastic deformation?

A The bonds between atoms are all broken.
B The extension is directly proportional to force.
C The atomic planes in the wire slide over each other.
D The wire returns to its original length when the force is removed.

2. Two copper wires have different length. Which of the following statements is
TRUE about the Young’s Modulus of these wires?

A The longer copper wire has greater Young’s Modulus.
B The shorter copper wire has greater Young’s Modulus.
C Both wires have the same Young’s Modulus.
D Both wires have no Young’s Modulus at all.

3. Several cans of different sizes and shapes are all filled with the same liquid to the
same depth. Which of the following statements is CORRECT?

A The weight of the liquid in each can is the same.
B The pressure on the bottom of each can is the same.
C The least pressure is at the bottom of the can with the largest bottom area.
D The least pressure is at the bottom of the can with the smallest bottom area.

4. A strip is made of two metals P and Q of the same length and cross-sectional area
as shown in FIGURE 8.1. The linear expansion of metal P is greater than Q. What
will happen to the strip when it is heated?

PQ

FIGURE 8.1

43