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

Kolej Matrikulasi Negeri Sembilan

CONTENTS

THE GREEK ALPHABET i
ii
LIST OF SELECTED CONSTANT VALUES iii
LIST OF SELECTED FORMULAE
TOPIC 1: PHYSICAL QUANTITES AND MEASUREMENTS 1
TOPIC 2: KINEMATICS OF LINEAR MOTION 6
TOPIC 3: MOMENTUM AND IMPULSE 12
TOPIC 4: FORCES 16
TOPIC 5: WORK, ENERGY AND POWER 22
TOPIC 6: CIRCULAR MOTION 28
TOPIC 7: GRAVITATION 34
TOPIC 8: ROTATIONAL OF RIGID BODY 38
TOPIC 9: SIMPLE HARMONIC MOTION 44
TOPIC 10: MECHANICAL WAVES AND SOUND 51
TOPIC 11: DEFORMATION OF SOLIDS 58
TOPIC 12: HEAT CONDUCTION AND THERMAL EXPANSION 63
TOPIC 13: GAS LAW AND KINETIC THEORY 68
TOPIC 14: THERMODYNAMICS 73

i

The Greek Alphabet Kolej Matrikulasi Negeri Sembilan

A  Alpha
B  Beta
  Gamma
  Delta
  Epsilon
  Zeta
  Eta
  Theta
  Iota
  Kappa
  Lambda
  Mu
  Nu.
  Xi
  Omicron
  Pi
  Rho
  Sigma
  Tau
  Upsilon
  ,  Phi
  Chi
  Psi
  Omega

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Kolej Matrikulasi Negeri Sembilan

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Kolej Matrikulasi Negeri Sembilan
LIST OF SELECTED CONSTANT VALUES

Speed of light in a vacuum c = 3.00 x 108 m s-1
Permeability constant 0 = 4 x 107 H m-1
Permittivity constant 0 = 8.85 x 10-12 F m-1
Elementary charge e = 1.60 x 10-19 C
Planck's constant h = 6.63 x 1034 J s
Electron mass me = 9.11 x 10-31 kg
= 5.49 x 104 u
Neutron mass mn = 1.674 x 10-27 kg
= 1.008665 u
Proton mass mp = 1.672 x 1027 kg
= 1.007277 u
Deuteron mass md = 3.34 x 10-27 kg
= 2.014102 u
Universal gas constant R = 8.31 J K1 mol1
Rydberg's constant RH = 1.097 x 107 m-1
Avogadro constant NA = 6.02 x 1023 mol1
Boltzmann's constant k = 1.38 x 10-23 J K-1
Gravitational constant G = 6.67 x 10-11 N m2 kg-2
Free-fall acceleration g = 9.81 m s2
Atomic mass constant 1u = 1.66 x 10-27 kg
= 931.5 MeV
Electron Volt 1 ev
c2
Constant of proportionality for Coulomb's law, k  1 = 1.6 x 1019 J
4π
0 = 9.0 x 109 m2 C-2

Atmospheric Pressure 1 atm = 1.013 x 105 Pa
= 1000 kg m3
Density of water W

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Kolej Matrikulasi Negeri Sembilan

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Kolej Matrikulasi Negeri Sembilan

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Kolej Matrikulasi Negeri Sembilan
TOPIC 1
PHYSICAL QUANTITIES AND MEASUREMENTS
1.1 Dimensions of physical quantities
a) Define dimension.
b) Determine the dimensions of derived quantities.
c) Verify the homogeneity of equations using dimensional analysis.
1.2 Scalars and vectors
a) Define scalar and vector quantities.
b) Resolve vector into two perpendicular components (x and y axes)

c) Illustrate unit vectors (iˆ, ˆj, kˆ) in Cartesian coordinate. 
d) State the physical meaning of dot (scalar) product: A B  AB cos
e) State the physical meaning of cross (vector)product: A B  AB sin

Note: Direction of cross product is determined by corkscrew method or right
hand rule.
1.3 Significant figures and uncertainties analysis
a) State the significant figures of a given number.
b) Use the rules for stating the significant figures at the end of a calculation
(addition, subtraction, multiplication or division).
c) Determine the uncertainty for average value and derived quantities.
d) Calculate basic combination (propagation) of uncertainties.
e) State the sources of uncertainty in the results of an experiment.
f) Draw a linear graph and determine its gradient, y-intercept and its respective
uncertainties.
g) Measure and determine the uncertainty of physical quantities.
(Experiment 1: Measurement and uncertainty)
h) Write a laboratory report.
(Experiment 1: Measurement and uncertainty)

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

1. Dimension can be defined as
A. a physical quantity
B. a technique or method which the physical quantity can be expressed in
terms of combination of basic quantities
C. algebraic quantities through the procedure of dimensional analysis
D. a combination of basic quantities

2. M L T–2 is the dimension of
A. force
B. pressure
C. acceleration
D. coefficient of friction

3. Which of the following pairings is incorrect?

Derived Quantities Derived Unit Base Unit
kg m−2 s−2
A. Work Nm kg m s−2
kg m2 s−3
B. Force N kg m−1 s−2
C. Power J s−1
D. Pressure N m−2

4. Identify the row that contains two scalar quantities and one vector quantity.

A. distance acceleration velocity

B. speed mass acceleration

C. distance weight force

D. velocity force mass

5. Vector quantity is defined as
A. a physical quantity characterized by presence of magnitude only.
B. a quantity with direction only
C. a physical quantity with both magnitude and direction
D. a combination of basic quantities

6. Identify which of the following quantities can be described by their magnitude and
direction.
A. time
B. mass
C. energy
D. acceleration

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7. P and Q are two vectors. Which of the following figures will result in a scalar

product of zero?

A. P C. P

QQ

B. P D.

Q Q

8. When two vectors are perpendicular,
A. Dot product is zero
B. Dot product is equal to 1.
C. Cross product is zero
D. Both dot product and vector product are equal to 1.

ANSWERS:
1. B 2. A 3. A 4. B 5. C 6. D 7. C 8. A

STRUCTURED QUESTIONS

(C4, PLO 4, CTPS 3, MQF LOD 6)

1. Determine the dimensions of following derived quantities:
(a) speed
(b) momentum
(c) density
(d) work
(e) power

2. Show that s  ut  1 at2 is homogeneous.
2

3. Verify the homogeneity of equation v2  u  at by using dimensional analysis.

4. The viscous force, F when a metal sphere is going its way downward is given by
the equation :
F  A a rb vc

where A is a dimensionless constant
ŋ is the dimension of viscosity of the fluid and has the unit of kg m –1 s–1
r is the radius of the metal sphere
v is the velocity of the metal sphere

Determine the value of a, b, and c and write down the formula again.

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5.

y
8N

12 N 30°

50° x
20 N

FIGURE 1.1

FIGURE 1.1 shows three forces 12 N, 8 N and 20 N. Calculate the magnitude and
direction of the resultant force.

6.

y
B = 3.7 km

40°
x

30°

A = 5.2 km

FIGURE 1.2

Two displacement vector A and B are shown in FIGURE 1.2. Find the magnitude
and direction of the resultant displacement.

7. A girl pushes a box across the floor and causes it to undergo two displacements A
and B. Displacement A is 1.5 m along the positive x-axis, while displacement B is
1.4 m along the positive-y axis. Determine the magnitude and direction of the
resultant displacement.

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8.

F1

30° F2

FIGURE 1.3

Two forces F1 = 8 N and F2 = 12 N are acting on a wooden block shown in FIGURE
1.3. Calculate the magnitude and direction of the resultant force acting on the
wooden block.

9. Fighter jet starting from airbase A flies 300 km east, then 350 km at 30° west of
north and then 150 km north to arrive finally at airbase B.
(a) The next day, another fighter jet flies directly from A to B in a straight line.
In what direction should the pilot travel in this direct flight?
(b) How far will the pilot travel in this direct flight?

10.

y
A

B 25° x
19°
O

FIGURE 1.4

Vectors A and B are placed at point O as shown in FIGURE 1.4. The magnitude
of both vectors are A = 5.6 N and B = 2 m.
(a) Calculate the dot (scalar) product of the two vectors.
(b) At what angle between the two vectors will the dot product be at maximum?
(c) Calculate the magnitude and direction for cross (vector) product of these

two vectors.

ANSWERS:

4. Value a =1, b = 1, c = –1, the equation F  A r v1

5. 26.357 N, 47.14° above –ve x-axis
6. 1.68 km at 7.50° below –ve x-axis

7. 2.05 m, 43.02° above positive x-axis

8. 19.35 N at 11.93° above +ve x-axis

9. (a) 74.6° N of E (b) 470 km
10. (a) –8.06 N m (b) 0° (c) 7.78 N m

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TOPIC 2
KINEMATICS OF LINEAR MOTION

2.1 Linear motion
a) Define
i. instantaneous velocity, average velocity and uniform velocity.
ii. instantaneous acceleration, average acceleration and uniform acceleration
b) Discuss the physical meaning of displacement-time, velocity time and
acceleration-time graphs.
c) Determine the distance travelled, displacement, velocity and acceleration from
appropriate graphs.

2.2 Uniformly accelerated motion

a) Apply equations of motion with uniform acceleration:
v  u  at

s  ut  1 at2
2
 
v2  u2  2a  s

2.3 Projectile Motions
a) Describe projectile motion launched at an angle, θ as well as special cases
when θ=0° and θ=90° (free fall).

b) Solve problems related to projectile motion

c) Determine the acceleration due to gravity, g using free fall and projectile motion

(Experiment 2: Free fall and projectile motion)

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

1. A ball which has been dropped vertically downward on to the floor rebounds
upward. Which of the following graph shows the variation of velocity with time?
vv

A. B.

0 t 0 t
C. v D. v

0t 0t

2. Without air resistance, an object dropped from a plane flying at constant speed in
a straight line will
A. quickly lag behind the plane
B. remain vertically under the plane
C. move ahead of the plane
D. float around the area

3. The slope of displacement–time graph of a car will gives
A. the car’s velocity.
B. the car’s acceleration.
C. the car’s distance travel at a time
D. the average time traveled

4. You are throwing a ball straight up in the air. At the highest point, the ball’s
A. velocity and acceleration are zero
B. velocity is nonzero but acceleration is zero
C. velocity is zero but acceleration is not zero
D. velocity and acceleration are both nonzero

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5. A ball is thrown from the point P and follows the path shown in FIGURE 2.1.

FIGURE 2.1
The vertical component of the acceleration of the ball is
A. zero at Q
B. the same at P and at R
C. greater at R than at P
D. greater at R than at Q
ANSWERS:
1. B 2. B 3. A 4. C 5. B

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STRUCTURED QUESTIONS Object B Kolej Matrikulasi Negeri Sembilan
(C4, PLO 4, CTPS 3, MQF LOD 6)
1. Displacement
Object A Object C

Displacement Displacement

time time time

FIGURE 2.2

The displacement-time graphs of object A, B and C are as shown in FIGURE 2.2
below.
(a) What is represented by the gradient of above graphs?
(b) Explain how the velocity of each object changes (if any).

2.

FIGURE 2.3

Based on the graph shown in FIGURE 2.3 above,
(a) Describe the motion of the particle from A to E.
(b) Sketch a - t graph
(c) Sketch s - t graph.

FIGURE 2.4

3. From the graph v - t shown in FIGURE 2.4 below,
(a) Describe the motion of the object from B to C.
(b) Calculate
(i) acceleration.
(ii) deceleration.
(iii) total distance travelled.

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4. The speed of a car traveling along a straight road decreases uniformly from

12 m s–1 to 8.0 m s –1 over 88.0 m. Calculate
(a) the acceleration of the car.
(b) the time of the car traveling over 88.0 m.
(c) the time taken for the car to stop.
(d) the total distance traveled by the car until it rests.

5.

100 m

FIGURE 2.5

En. Hassan is driving at 108 km h–1 along a straight road suddenly sees a school
girl runs across the road 100 m ahead of his car as shown FIGURE 2.5. If his
reaction time is 0.7 s and the maximum deceleration of the car is 4.5 m s–2. Does
the car will hit the girl? Explain.

6. In a 100 m race, a runner P accelerating uniformly takes 2.00 s and another runner
Q 2.50 s to reach their maximum speeds which they each maintain for rest of the
race. They cross the finish line simultaneously, both setting a time of 12.0 s.
(a) What are the respective maximum speeds of P and Q?
(b) What is the acceleration of each runner?
(c) Which runner is ahead at the 6.00 s, and how much?
(d) Sketch the speed–time graphs for the runners in same axis.

7. A student drops a stone from a second floor window, 15 m above the ground.
(a) How long does it take for the stone to reach the ground?
(b) Calculate the velocity before it hits the ground.
(c) If another stone with twice its weight of the first stone dropped from the same
height, how long does it take to reach the ground in comparison with the first
stone. Explain. (air resistance is negligible).

8.

FIGURE 2.6

A rocket is launched upwards from the ground with the initial velocity of 35 m s–1
as shown in FIGURE 2.6. The magnitude of its acceleration is 5.0 m s–2. Suddenly
the engine breaks down at height h = 20 km from the ground. Neglect air
resistance. Calculate
(a) the speed of the rocket at height 20 km.

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(b) the maximum height achieved by the rocket.
(c) the time of flight of the rocket.

9. 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 m s–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) Calculate the speed of the arrow just before it hits the ground.

10.

A u  5 m s1

1m

C xB

FIGURE 2.7

In the FIGURE 2.7, a rolling ball falls from the edge of a table with initial horizontal
velocity of 5 m s–1. The height of the table is 1 m. Calculate
(a) the time taken for the ball to reach point B
(b) the horizontal distance x.
(c) the magnitude and the direction of its velocity at point B.

ANSWERS:

3. (a) 0 (b) (i) 5 m s–2 (ii) −10 m s–2 (iii) 180 m

4. (a) –0.455 m s–2 (b) 8.79 s (c) 26.4 s (d) 158 m

5. Yes . The car stops 21 m after hitting the girl

6. (a) 9.09 m s–1 , 9.30 m s–1 (b) 4.55 m s–2 ,3.72 m s–2 (c) P ahead by 1.3 m

7. (a) 1.75 s (b) −17.2 m s–1

8. (a) 448.6 m s–1 (b) 30.26 km (c) 207 s

9. (a) 9.23 s (b) 639 m (c) 85.76 m s–1
(b) 2.25 m (c) 6.67 m s–1, 41.4o below the +ve x-axis
10. (a) 0.45 s

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TOPIC 3
MOMENTUM AND IMPULSE

3.1 Momentum and impulse 

a) Define momentum and impulse, J  Ft

b) SJolvepprobmlevmf related to impulse and impulse-momentum theorem,

 mvi

c) Use F-t graph to determine impulse.

3.2 Conservation of linear momentum
a) State the principle of conservation of linear momentum.
b) Apply the principle of conservation of momentum in elastic and inelastic
collisions in 1D and 2D collisions.
c) Differentiate elastic and inelastic collisions.

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OBJECTIVE QUESTIONS Kolej Matrikulasi Negeri Sembilan
(C2, PLO 1, MQF LOD 1)
1. What is definition for linear momentum?
A. The product of a force, F and the time, t.
B. The change of momentum.
C. The ratio between mass and velocity.
D. The product between mass and velocity

2. What is definition for impulse?
A The product of a mass and acceleration of gravity.
B the product of a force, F and the time, t
C the ratio between mass and velocity.
D the ratio between change of momentum over time taken.

3. Which graph show the relationship between impulse and force?
A. B.

CD

4. Choose the correct statement of the principle of conservation of linear momentum.
A “The momentum of that system is constant.”
B “The total momentum of that system is constant.”
C “The product between mass and velocity in a closed system.”
D “When the net external force on a system is zero, the total momentum of
that system is constant.”

5. If the car is moving to the right in a constant velocity change their direction without
changing their speed. What do you think about their movement of the system?
A The change of momentum is zero.
B Total momentum is constant.
C Impulse is zero.
D All the answer above is wrong.

ANSWERS:

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

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STRUCTURED QUESTIONS
(C4, PLO 4, CTPS 3, MQF LOD 6)

1. A system is made up of two objects moving along a straight line. One object of
mass 1.5 kg moves to the right at a speed of 10.0 m s−1. The other object of mass
2.0 kg moves to the left at a speed of 12.0 m s−1. Determine the total momentum
of the system.

2. An object A of mass 2.0 kg moves to the right at a speed of 5.0 m s−1. It collides
with another object B and rebounds to the left at a speed of 3.0 m s−1. Determine
the change in momentum of object A.

3. A ball with mass 400 g is moving horizontally with a speed 13.0 m s−1, hits a wall
and rebound at 18.0 m s−1 within 0.1 s. Calculate the magnitude of force by wall act
to the ball.

4. (a) F (N)

t (s)

FIGURE 3.1

FIGURE 3.1 shows graph F versus t. Based on the graph, what
represents impulse?

(b) Net force of 8.0 N acts on an 18.0 kg body for one minute.
(i) Determine the impulse due to the force.
(ii) Calculate the initial velocity of the body if the final velocity is
60.0 m s−1.

5. An object of mass 0.25 kg moves at a speed of 24.0 m s−1 along a straight line.
After it has collided with another object, it moves at a speed of 40.0 m s−1 in the
opposite direction. Determine
(a) the impulse acting on the object.
(b) the average force applied on the object if the impulsive force has acted for
t = 4.0 ms.

6. 18.0 m s−1

A BC

FIGURE 3.2

Three blocks A, B, and C of masses m, 2m, and 3m respectively are placed
on horizontal smooth plane as shown in FIGURE 3.2. Block A with speed

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18.0 m s−1 collides and stick with block B. Both objects collide and stick with block
C together its move with common velocity v. Calculate the velocity v.

7. 1.5 kg ball was kicked with initial velocity of 40.0 m s−1 at the angle of 30o
with the horizontal line. Calculate the initial momentum of the ball and also
the horizontal and vertical components of the initial momentum.

8. Object A of mass 1 kg travels in a straight line and has speed of 14.14 m s−1. It
collides with a stationary object B of mass 3.0 kg. After the collision, object A has
speed of 2.83 m s−1 and keeps its direction. Determine the speed of object B after
the collision.

9. An object A of mass 1.0 kg moving at a speed of 5.0 m s−1 to the right collides with
an object B of mass 2.0 kg initially moving at a speed of 4.0 m s−1 to the left. The
collision is a completely inelastic collision. After the collision, calculate the velocity
of each object.

10.

vA = 2.0 m s−1 A

uA = 4.0 m s−1 uB = 0 m s−1 α =37°
A B

Before collision β = 27° B
vB

After collision

FIGURE 3.3

FIGURE 3.3 shows a collision of two balls. Ball A has mass of 0.5 kg and ball B
has mass of 0.3 kg. Ball A has an initial velocity of 4.0 m s−1 in the positive x-
direction and final velocity of 2.0 m s−1. Ball B is initially at rest. Calculate the final
speed of ball B. Given α = 37o and β = 27o.

ANSWERS:

1. −9.0 kg m s−1
2. −16.0 kg m s−1
3. 124 N
4. (b) (i) 480 N s (ii) 33.33 m s−1
5. (a) −16 kg m s-1 (b) −4000 N
6. 3 m s−1
7. 60 kg m s−1, 51.96 kg m s−1, 30 kg m s−1
8. 3.77 m s−1
9. −1.0 m s−1
10. 4.494 m s−1

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TOPIC 4
FORCES

4.1 Basic of forces and free body diagram
a) Identify the forces acting on a body in different situations:
i. Weight
ii. Tension
iii. Normal force
iv. Friction
v. External force (pull or push)
b) Sketch free body diagram.
c) Determine static and kinetic friction.
fs  sN, fk  k N

4.2 Newton's Laws of Motion
a) State Newton's laws of motion.
b) Apply Newton's laws of motion.

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

1. Newton’s First Law of Motion is consistent with the concept of;

A. force B. inertia C. momentum D. impulse

2. Two cars collide head-on. At every moment during the collision, the magnitude of
the force the first car exerts on the second is exactly equal to the magnitude of the
force the second car exerts on the first. This is an example of

A. Newton's first law.
B. Newton's third law.
C. Newton's second law.
D. Newton's law of gravitation.

3. If there is no net force acting on an object, its means that

A. the object is at rest.
B. the acceleration is zero.
C. the object is moving with constant velocity.
D. all of above.

4. Which force always pulls downward on objects?

A. Support force
B. Friction force
C. Gravity
D. Air resistance

5. When you slide a box across the floor, you must apply a force which is stronger
than ……….

A. support force
B. friction force
C. gravity
D. air resistance

ANSWERS:

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

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STRUCTURED QUESTIONS Kolej Matrikulasi Negeri Sembilan
(C4, PLO 4, CTPS 3, MQF LOD 6)
1.
FIGURE 4.3
v

Rough Surface

200
FIGURE 4.1

FIGURE 4.2

Based on FIGURE 4.1, FIGURE 4.2 and FIGURE 4.3, sketch free body diagram
to identify the forces acting on a body in different situations.

2. v

v F
F
Smooth table
Rough table FIGURE 4.5
FIGURE 4.4

Based on FIGURE 4.4 and FIGURE 4.5, sketch their free body diagram.
3.

250

FIGURE 4.6

A 3.0 kg cube is placed on a rough plane as shown in FIGURE 4.6. 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 static frictional force between the cube and
the rough plane.

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4.

F =12 N
1

F =20 N
2

o 55.0°

30.0 A

o

45.0

F3=30 N

FIGURE 4.7

Calculate the magnitude and direction of a force that balance the three forces acted
at particle A as shown in FIGURE 4.7

5.

Fm

θ

FIGURE 4.8

A body of mass m is on an inclined plane at an angle of θ with the horizontal. The
body moves up the plane at a constant velocity when a horizontal force, F acts on
it as shown in FIGURE 4.8. What is the friction between the body and the inclined
plane in terms of F, mg and θ?

6.

30°

FIGURE 4.9

A 2.0 kg object is placed on a rough plane inclined at 30° with the horizontal as
shown in FIGURE 4.9. It is released from rest and accelerates at 4.0 m s–2.
Calculate the frictional force acting on the object.

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7.

FIGURE 4.10

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 pulley as shown in
FIGURE 4.10. 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 and
(b) the tension in the cable.
8.

FIGURE 4.11
Blocks A and B of masses 3.5 kg and 2.0 kg respectively are connected with a light
string across a smooth pulley as shown in FIGURE 4.11. At t = 0 s, block A is pulled
by a 30 N force F. The coefficient of kinetic friction between block A and the table
is 0.20. Calculate
(a) the acceleration of both blocks.
(b) the time taken by block B to move upwards by 1.0 m.

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9.

 AB
F

FIGURE 4.12

Two blocks, A of mass 10 kg and B of mass 30 kg, are side by side and in contact
with each another. They are pushed along a smooth floor under the action of a
constant force F of magnitude 200 N applied to A as shown in FIGURE 4.12.
Determine

(a) the acceleration of the blocks,
(b) the force exerted by A on B.

10.

FIGURE 4.13

Two wooden blocks Q and R of masses 2.0 kg and 1.5 kg respectively are on
smooth table as shown in FIGURE 4.13. A force of 7.0 N acts on the block Q so
that both the blocks accelerate together. What is the horizontal force that Q exerted
on R?

ANSWERS:

3. 12.44 N
4. (b) 31.68 N, 2.50o
5. F cos  mg sin

6. (b) 1.81 N (b) 5.12 N
7. (a) 4.69 m s–2 (b) 2.11 s
8. (a) 0.45 m s–2 (b) 150 N
9. (a) 5.0 m s–2

10. 3.0 N

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Kolej Matrikulasi Negeri Sembilan

TOPIC 5
WORK, ENERGY AND POWER

5.1 Work  
a) Define F s
work done by a constant force, W  

b) Apply work done by a constant force and from a force displacement graph.

5.2 Energy and Conservation of Energy
a) State the principle of conservation of energy
b) Apply the principle of conservation of energy (mechanical energy and heat
energy due to friction)

c) State and apply the work energy theorem, W  K

5.3 Power

a) Define and use average power, Pav  W and instantaneous power,
t
 
P  F  v

b) Verify the law of conservation of energy.

(Experiment 3: Energy)

22

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

1. Below is the definition of work done, EXCEPT

A. Product of the component of the force parallel to the displacement times the
displacement of a body.

B. Product of the component of the force perpendicular to the displacement
times the displacement of a body.

C. Scalar (dot) product between force and displacement of a body.
D. Work done by a force of 1 N which results in a displacement of 1 m in the

direction of the force is equals to 1 Joule (J).

2. Principle of conservation of energy states that

A. In an isolated (closed) system, the total energy of that system is constant.
B. In an isolated (closed) system, the total mechanical energy of that system is

constant.
C. In an isolated (closed) system, the total kinetic energy of that system is

constant.
D. In an isolated (closed) system, the total energy of that system is zero.

3. Which statement is TRUE about work-energy theorem?

A. Work done by the nett force on a body equals to the change in the body’s

mechanical energy
B. Work done by the nett force on a body equals to the change in the body’s

kinetic energy
C. Work done by the nett force on a body equals to the total in the body’s

mechanical energy
D. Work done on the nett force on a body equals to the total in the body’s kinetic

energy

4. Definition of average power is given by

A. Elastic potential energy per unit time
B. Rate at which energy is conserved
C. The change of kinetic energy per unit time
D. Rate at which work is done

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Kolej Matrikulasi Negeri Sembilan

5. Instantaneous power is defined as

A. Scalar (dot) product between magnitude of force and acceleration
B. Scalar (dot) product between magnitude of force and velocity
C. Vector (cross) product between magnitude of force and acceleration
D. Vector (cross) product between magnitude of force and velocity

ANSWERS:

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

24

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

1. (a) A boy pushes a box with a constant force of 180 N at an angle of 30° with
the horizontal. How much work is done if the box is pushed through a
distance of 15 m?

(b) A 3.0 kg box is lifted vertically from rest to a distance of 2.0 m with a constant
upward applied force of 60.0 N. Calculate
(i) the work done by the applied force
(ii) the work done by gravity

2.

α
O
FIGURE 5.1

Write down the equation of work done by force, F at point O as shown in FIGURE
5.1, in terms of F , S and  .
3.

F

37˚

FIGURE 5.2

A tourist drags his luggage of mass 20 kg with a force F at a constant velocity
across the floor as shown in FIGURE 5.2. The kinetics frictional force between the
rollers of the luggage and the floor is 60 N. The luggage is dragged 0.80 m along
the floor. Calculate
(a) the work done on the luggage by the normal force.
(b) the work done on the luggage by force F.

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Kolej Matrikulasi Negeri Sembilan

4.

(N)

350 (cm)
300
250
200
150
100

50

1 2 345 6 7

FIGURE 5.3

The graph in FIGURE 5.3 shows the magnitude of force F exerted by a given spring
as a function of the distance the spring is stretched, x. Calculate the work done
when the spring is stretched;
(a) from x  0 cm to x  5 cm.
(b) from x  2 cm to x  7 cm.

5. A force of magnitude 800 N caused an extension of 20 cm on a spring. Determine
the elastic potential energy of the spring when the extension of the spring is 30 cm.

6.
D

B

C 20.0 m

15.0 m

10.0 m

A

FIGURE 5.4

FIGURE 5.4 shows a cart moving to the right passes point A at a speed of 20.0 m
s1.
(a) What is the speed of the cart at point C?
(b) Will the cart reach point D? Prove your answer using calculation (Ignore

friction).

7. A 2 kg block is projected at 3 m s1 up a 15 incline for which k  0.2 . Use the

work energy theorem to calculate the distance it travels before coming to rest.

8. A constant horizontal force of 2.0 x 103 N is acting on an object of mass 5.0

x 103 kg on a horizontal surface. The initial velocity of the object is 4.0 m s1. By

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Kolej Matrikulasi Negeri Sembilan

using work energy theorem, calculate the velocity of the object after it has moved
300 m;
(a) if the horizontal surface is smooth.
(b) if the horizontal surface is rough and exerts an opposing force of 400 N to

the motion of the object.

9. A 1500 kg car accelerates uniformly from rest to reach 10.0 m s-1 in 5.00 s.
Determine
(a) the average power delivered by the engine.
(b) the instantaneous power delivered by the engine at t = 2.00 s.

10. A block of mass 100 kg is being dragged at a constant speed of 5.0 m s1 by an
applied force of 120 N. The force is applied by pulling on a string making an angle
of 60o to the floor. Determine the rate at which work is done by the applied force.

ANSWERS:

1. (a) 2F.3s4co1s013 8J0 (b) (i) 120 J (ii) 58.86 J
2. W
 

3. (a) 0 J (b) 46.23J

4. (a) 6.25 J (b) 11.25J

5. 180 J

6. (a) 14.28 m s-1 (b) Yes. Because the cart still has a velocity of 2.78 m s-1 at point D

7. 1.01 m

8. (a)16 m s-1(b) 14.4 m s-1

9. (a) 15 kW (b) 12 kW

10. 300 W

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Kolej Matrikulasi Negeri Sembilan

TOPIC 6
CIRCULAR MOTION

6.1 Uniform circular motion

a) Describe uniform circular motion.
b) Convert units between degree, radian and revolution or rotation.

6.2 Centripetal force
a) Define centripetal acceleration.
b) Solve problems related to centripetal force for uniform circular motion cases:
horizontal circular motion, vertical circular motion and conical pendulum
(exclude banked curve).

28

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

1. For an object to move in a uniform circular motion, it must move with

A. constant speed
B. constant velocity
C. constant momentum
D. constant linear acceleration

2. A body is moving in a circular motion. Which row in the table below correctly
describes the linear speed, angular velocity and linear acceleration of the
body?

Linear speed Angular velocity Linear acceleration
A. Constant Constant Varying
B. Constant Constant Zero
C. Constant Varying Constant
D. Varying Constant Varying

3. Object moving along a circular path is

A. in equilibrium
B. not in equilibrium
C. not moving with constant speed
D. in random motion

4.

FIGURE 6.1

FIGURE 6.1 shows a particle moves with uniform speed, v in a circle of radius,
r. The period of the circular motion is T. What is the acceleration of the particle
when it moves from one end X of a diameter to the other end Y?

A. Zero B. v 2

C. 2v r
T D. v

2T

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Kolej Matrikulasi Negeri Sembilan
5.

FIGURE 6.2

A particle of mass m is moving with uniform velocity in a vertical circular track
of radius r as shown in FIGURE 6.2. The reaction of the track is

A. Zero at P B. Maximum at P
C. Equal to mg at Q D. Equal to mg at S

ANSWERS:

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

STRUCTURED QUESTIONS (C4, PLO 4, CTPS 3, MQF LOD 6)

1. If an object of mass 3.5 kg is travelling in a circular path with a radius of 3.14 m at
a speed of 3.46 m s, what will be the centripetal force on that object?

2.

FIGURE 6.3

A 1500 kg car is moving on a flat, horizontal curved road as shown in FIGURE
6.3. If the radius of the curve is 35 m and the coefficient of static friction between
the tyres and dry road is 0.5.

(a) Calculate the maximum speed of the car to successfully make a turn.

(b) Suppose the car travels on this curve on a wet day and begins to skid
when its speed reaches 8 m s. Calculate the coefficient of static friction.

3. The frequency and angular velocity of a second-hand clock is?

4. An object is moving at a constant velocity on a horizontal circular path of radius 6
m. If the frequency of the object is 0.2 Hz, what is the centripetal acceleration
acting on the object?

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Kolej Matrikulasi Negeri Sembilan
5. A person is staying in a country situated at the equator. The radius of earth is

6400 km and is rotating 24 hours per revolution about its axis. Calculate
(a) the angular velocity of the earth’s rotation.
(b) the speed of the person as the earth rotates.
6.

FIGURE 6.4
A ball of mass moves with constant velocity in a horizontal circular path of radius,
r. The ball is attached to a string of length 24 cm and makes a conical pendulum
as shown in FIGURE 6.4.
(a) Sketch a free body diagram showing the forces acting on the object.

(b) If   30o , calculate:

(i) radius, r
(ii) velocity, v
7.

FIGURE 6.5
A particle moves in a horizontal circle of radius 15 cm inside an inverted smooth
hollow hemisphere as shown in FIGURE 6.5.
(a) Sketch a free body diagram showing the forces acting on the object.
(b) Calculate the speed of the particle.

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Kolej Matrikulasi Negeri Sembilan
8.

FIGURE 6.6
An airplane is flying in a horizontal circle at a speed of 480 km/h. The wings are
tilted 40° to the horizontal as shown in FIGURE 6.6. Assume that the required
force is provided entirely by an “aerodynamic lift” that is perpendicular to the wing
surface.
(a) Sketch a diagram to illustrate the forces acting on the passenger in the plane.
(b) Determine the radius of the circle in which the plane is flying?
9.

FIGURE 6.7
FIGURE 6.7 shows a 1.34 kg ball connected by two massless strings to a vertical,
rotating rod. The strings are tied to the rod and are taut. The tension in the upper
string is 35 N.
(a) Sketch the free body diagram for the ball.
(b) Determine:

(i) the tension in the lower string.
(ii) the net force on the ball.
(iii) the speed of the ball.
10. An object of mass, m is attached to a string of length, l . The object is moving with
constant speed, v in a vertical circle. The maximum tension in the string is Tmax
and g is the acceleration due to gravity.
(a) Sketch a diagram illustrating the forces acting on the object when it is at the
top of the circle and at the bottom of the circle.
(b) Write expressions for the centripetal force acting on the object (in terms of
m, v and l ).
(c) If the string breaks, at which position will this be likely to occur?

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Kolej Matrikulasi Negeri Sembilan

(d) If m  50 g , l  60 cm and v  10 m s1; calculate the value of Tmax.

11. A Ferris wheel with diameter 18 m and rotates at the rate of 4 rpm. Calculate:

(a) the acceleration of a rider on the wheel.

(b) the magnitude and direction of the force which the seat exerted on a 40 kg
rider at the:
(i) lowest point of the wheel.
(ii) highest point of the wheel.

12. A roller-coaster car has a mass of 1200 kg when fully loaded with passengers. As
the car passes over the top of a circular track of radius 18 m (upside down
position) its speed is not changing. What are the magnitude and direction of the
force of the track on the car at the top of the hill if the car’s speed is 14 m s?

ANSWERS:

1. 13.34 N

2. (a) 13.10 m s (b) 0.19

3. 1.67×10 Hz; 0.10 rad s

4. 9.53 m s

5. (a) 7.27×10 rad s (b) 465.28 m s

6. (b) (i) 12 cm (ii) 0.8244 m s

7. (b) 0.92 m s

8. (b) 2.16×103 m

9. (b) (i) 8.71 N (ii) 37.9 N (iii) 6.45 m s

10. (d) 8.82 N

11 (a) 1.58 m s (b) (i) 455.6 N (ii) 329.9 N

12. 1294.67 N

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Kolej Matrikulasi Negeri Sembilan

TOPIC 7
GRAVITATION

7.1 Gravitational force and field strength

a) State and use the Newton’s law of gravitation, F  G Mm
r2

b) Define and use gravitational field strength, ag  G M .
r2

7.2 Gravitational potential energy
a) Define gravitational potential energy, U  GMm
r

7.3 Satellite motion in a circular orbit

a) Derive and use escape velocity, vesc  2GM  2gR
R

b) Derive and use equation for satellite motion:

i. Velocity, v  GM
r

ii. Period,T  2 r3
GM

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Kolej Matrikulasi Negeri Sembilan

(The mass of the Sun = 2.00×1030 kg, the mass of the Earth = 6.00×1024 kg, the mass of
the Moon = 7.35×1022 kg, radius of the Earth = 6.37×106 m)

OBJECTIVE QUESTIONS

(C2, PLO 1, MQF LOD 1)

1. A satellite is shifted to a higher orbit. Which of the following quantities decrease?
A. Gravitational force
B. Gravitational potential energy
C. Gravitational field strength
D. All of the above

2. If suddenly the gravitational force of attraction between the earth and a satellite
revolving around it becomes zero, then the satellite will
A. Continue to move in its orbit with the same velocity
B. Move tangentially to the original orbit with the same velocity
C. Become stationary in its orbit
D. Move towards the earth

3. The force of gravitation between two bodies in the universe does not depend on
A. the distance between them
B. the product of their masses
C. the sum of their masses
D. the gravitational constant

4. For a man standing inside a lift, when will his apparent weight be equal to real
weight?
A. When the life is moving upwards with a uniform acceleration.
B. When the lift is moving downwards with a uniform acceleration.
C. At rest or moving with uniform velocity.
D. Falling freely.

5. An elephant and an ant are to be projected out of the earth into space. What is
the velocity needed to do so?
A. Elephant needs to be projected with a higher velocity.
B. Ant should be projected with a higher velocity.
C. Both should be projected with the same velocity.
D. Elephant cannot be projected to space.

ANSWERS:

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

35

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

1. Two objects with masses m1 and m2 respectively are a distance r apart. The
magnitude of the gravitational force between them is F . The masses are changed
to 2 m1 and 2 m2 and the distance is changed to 4 r . Find the magnitude of the new
gravitational force in terms of F .

2. A body is released close to the surface of a planet of mass M and radius R . It falls
freely under the gravitational attraction of the planet. What is its acceleration due to
gravity in terms of G, M and R?

3. During a solar eclipse, the Moon, Earth and Sun all lie on the same line with the
Moon between Earth and the Sun. Determine the
(a) force exerted by the Sun on the Moon.
(b) force exerted by Earth on the Moon.
(c) force exerted by the Sun on the Earth.
(The Sun-Earth distance = 1.496×1011 m, the Earth-Moon distance = 3.84×108 m)

4. A satellite is orbiting around the Earth with a distance of 2×106 m. Calculate the
gravitational acceleration of the satellite.

5. A point P is on a straight line joining the Earth and the Moon. The distance of point
P from the Earth’s center is x , and the distance between the Earth and the Moon
is r . If r  3.8 108 m and the gravitational field strength at P is zero, calculate the

value of x .

6. The escape velocity from the earth is 11.2 km/sec. Another planet is having a mass
1000 times and radius 10 times that of the earth, determine escape velocity at that
planet.

7. A satellite is placed in an orbit at a distance of 4.23107 m from the center of the
Earth. Calculate the speed of the satellite.

8. A satellite moves in a circular orbit around Earth at a speed of 5.0 103 m s-1.
Calculate the
(a) satellite’s altitude above the surface of the Earth.
(b) period of the satellite.

9. A satellite of mass 200 kg is launched from a site on the Equator into an orbit at
200 km above Earth’s surface. If the orbit is circular, calculate
(a) the orbital period of this satellite.
(b) the satellite’s speed.

10. The period of a satellite circling planet Nutron is observed to be 84 s when it is in
circular orbit with a radius of 8.0 x 106 m. Determine the mass of planet Nutron?

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Kolej Matrikulasi Negeri Sembilan

ANSWERS: (b) 1.995×1020 N (c) 3.576×1022 N

1. F (b) 2.01×104 s
4 (b) 7804.7 m s-1

2. MG
R2

3. (a) 4.404×1020 N
4. 100.05 m s-2
5. 3.42x108 m
6. 11.2 x 104 m/s
7. 3075.9 m s-1
8. (a) 9.63×106 m
9. (a) 5289.2 s
10. 4.29 x 1028 kg

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Kolej Matrikulasi Negeri Sembilan

TOPIC 8
ROTATION OF RIGID BODY

8.1 Rotational kinematics
a) Define and use:
i. Angular displacement, 

ii. Average angular velocity, av

iii. Instantaneous angular velocity, 
iv. Average angular acceleration, av

v. Instantaneous angular acceleration, .
b) Relate parameters in rotational motion with their corresponding quantities in

linear motion:

s  r ,

v  r ,

t  r ,

c  r 2  v2
r

c) Solve problems related to rotational motion with constant angular

acceleration.

    t ,

   t  1 t 2 and
2

 2    2

8.2 Eaq) uDileibfirniuemtoroqfuae,uniforrm Frig.id body

b) Solve problems related to equilibrium of a uniform rigid body.

8.3 Rotational dynamics
a) Define and use the moment of inertia of a uniform rigid body (sphere,
cylinder, ring, disc, and rod)
b) Determine the moment of inertia of a flywheel
(Experiment 4: Rotational motion of rigid body).

c) State and use torque,   I .

8.4 Conservation of angular momentum

a) Define and use angular momentum, L  I

b) State and use principle of conservation of angular momentum.

38

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

1. A rigid body is rotating about an axis passing through its center. Every point on the
body has
A. different angular speed but same linear speed.
B. same angular speed and angular acceleration.
C. same angular speed but different angular acceleration.
D. different angular speed but same angular acceleration.

2. Which of the following is true about a rotating rigid body

A. Its center of rotation is at rest.

B. The center of rotation is at the center mass.

C. All position on the body are moving the same linear velocity.
D. Every points in the body are moving with the same angular velocity.

3. The torque in rotational motion corresponds to ___________ in linear motion.

A. mass B. momentum

C. acceleration D. force

4. The moment of inertia of a body does not depend on its

A. mass B. size

C. angular velocity D. axis of rotation

5. An ice skater is spinning with his arms folded in wards. Later the ice skater stretches
his arms outwards. Which of the following pairs of quantities will increase?
A. Kinetic energy and moment of inertia.
B. Angular momentum and kinetic energy.
C. Period of rotation and moment of inertia.
D. Angular momentum and period of revolution.

ANSWER:

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

39

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

1. A rigid body rotates about a fixed axis through a point in the body, with uniform
angular velocity of 600 r.p.m. The velocity then decreases at a constant retardation
to 300 r.p.m. 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.

2. A flywheel is accelerated uniformly from rest for 6.00 s. It is observed that at the
end of the 6.00 s, the flywheel rotates through an angle of 450 radians. Calculate
for the flywheel
(a) the average angular velocity during the 6.00 s.
(b) the angular velocity at the end of the 6.00 s.
(c) the angular acceleration.

3.

L

F1 FIGURE 8.1 F2

A heavy uniform plank of length L is supported by two forces F1 and F2 at a distance
L and L from its ends as shown in FIGURE 8.1 above. Find the ratio of F2 : F1
48

4. (a) 20 cm 30 cm
Q
P

M

FIGURE 8.2

A 1 m rod of mass 2 kg is pivoted at point P as shown in FIGURE 8.2 above.
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.

40

Kolej Matrikulasi Negeri Sembilan
(b)

20 N 50°

0.5 m F

FIGURE 8.3

A 10 kg uniform beam with 2.0 m long is pivoted at the center. A 20 N
perpendicular force is exerted 0.5 from center of the beam. If the beam is in
equilibrium, find F

5.
A

3m

B 50°

FIGURE 8.4

The FIGURE 8.4 above 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.
(a) Sketch 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.

6. To slow down a flywheel, a frictional torque of 8.0 N m is applied to the flywheel. If
the moment of inertia of the wheel is 10 kg m2 and its initial angular velocity is 12
rad s-1, calculate
(a) the angular displacement, in terms of number of revolutions, before it comes
to rest.
(b) the time taken.
(c) the angular velocity of the flywheel after it has completed 10 revolutions

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Kolej Matrikulasi Negeri Sembilan
7.

String

Wheel

FIGURE 8.5
FIGURE 8.5 above 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 is 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.

8. Cylinder

0.380 kg
FIGURE 8.6
A solid cylinder of radius 18.0 cm is free to rotate about a smooth horizontal axle.
A mass of 0.38 kg hangs from a string wound around the cylinder as shown in
FIGURE 8.6 above.
(a) When the system is released from rest, the mass takes 2.0 s to fall through
a height of 5.0 m. What is the moment of inertia of the cylinder?
(b) The cylinder is then replaced by a hollow cylinder of the same mass and
dimensions. What is the moment of inertia of the hollow cylinder?
(Moment of inertia: solid cylinder, I  1 MR2 ; hollow cylinder, I  MR2 )

2
9. (a) A disc of mass 1.6 kg and diameter 0.4 m is spinning with an angular

velocity of 0.4 revolutions per second. Then a 0.4 kg mass is dropped and
stuck on the rim of the disc. Calculate the new angular velocity. The moment
of inertia of the disc is I  1 MR2 .

2

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Kolej Matrikulasi Negeri Sembilan

(b) A skater is turning at 3.0 rad s1 with both arms outstretched, so that she
has a moment of inertia of 4.0 kg m2. Her arms are now drawn is so that her
new moment of inertia is 1.8 kg m2. Calculate her final angular velocity?

10 A horizontal disc rotates about an axis which passes vertically through the centre
of the disc with angular velocity of 100 r.p.m. A small particle of mass 10 g is
dropped onto the disc 9.0 cm from the axis and sticks to the disc. If the angular
velocity is reduced to 90 r.p.m. Determine the moment of inertia of the disc about
the axis.

ANSWER:

1. (a) - 5.2 rad s-2 (b) 45 revolutions (c) 6.0 s

2. (a) 75 rad s-1 (b) 150 rad s-1 (c) 25 rad s-2

3. 2/3

4. (a) 1.2 kg (b) 13.05 N

5. (a) DIY (b) RA =123.4 N, RB =294.3 N (c) 0.42

6. (a) 14.3 revolutions (b) 15 s (c) 6.6 rad s-1

7. 2.80 m s-2, 3.5 N

8. (a) 3.60 x 10-2 kg m2

(b) 7.20 x 10-2 kg m2

9. (a) 1.7 rad s-1 (b) 6.7 rad s-1

10. 7.3104 kg m2

43