SP015 : TUTORIAL FLIPBOOK 1/4

PHYSICS UNIT KMNS

PHYSICS
TUTORIAL
BOOKLET

SP015

2021/2022

Flipbook 1/4
(Topic 1-4)

PHYSICS UNIT PHYSICS UNIT

COPY RIGHT PHYSICS UNIT KMNS

CONTENTS i
ii
THE GREEK ALPHABET iv
LIST OF SELECTED CONSTANT VALUES
LIST OF SELECTED FORMULAE 1
TOPIC 1: PHYSICAL QUANTITES AND MEASUREMENTS 7
TOPIC 2: KINEMATICS OF LINEAR MOTION 13
TOPIC 3: MOMENTUM AND IMPULSE 17
TOPIC 4: FORCES 23
TOPIC 5: WORK, ENERGY AND POWER 29
TOPIC 6: CIRCULAR MOTION 36
TOPIC 7: GRAVITATION 40
TOPIC 8: ROTATIONAL OF RIGID BODY 46
TOPIC 9: SIMPLE HARMONIC MOTION 53
TOPIC 10: MECHANICAL WAVES AND SOUND 60
TOPIC 11: DEFORMATION OF SOLIDS 65
TOPIC 12: HEAT CONDUCTION AND THERMAL EXPANSION 69
TOPIC 13: GAS LAW AND KINETIC THEORY 74
TOPIC 14: THERMODYNAMICS

THE GREEK ALPHABET

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

i

LIST OF SELECTED CONSTANT VALUES
SENARAI NILAI PEMALAR TERPILIH

ii

LIST OF SELECTED CONSTANT VALUES
SENARAI NILAI PEMALAR TERPILIH

iii

LIST OF SELECTED FORMULAE
SENARAI RUMUS TERPILIH

iv

LIST OF SELECTED FORMULAE
SENARAI RUMUS TERPILIH

v

LIST OF SELECTED FORMULAE
SENARAI RUMUS TERPILIH

vi

Physics Unit, KMNS SP015

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( ̂, ,̂ ̂ ) in Cartesian coordinate.
d) State the physical meaning of dot (scalar) product: ⃗ ∙ ⃗⃗ =
e) State the physical meaning of cross (vector)product: ⃗ × ⃗⃗ = ̂
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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Physics Unit, KMNS SP015

OBJECTIVE QUESTIONS

(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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Physics Unit, KMNS SP015

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. P

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

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Physics Unit, KMNS SP015

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 = + 1 2 is homogeneous.
2

3. Verify the homogeneity of equation 2 = 2 + by using dimensional
analysis.

4. The viscous force, F when a metal sphere is going its way downward is given

by the equation:

=

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.

5. y

8N

12 N 30° x

50°
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
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Physics Unit, KMNS SP015

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.

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°
19° x

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.

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Physics Unit, KMNS SP015

ANSWERS:

4. Value a =1, b = 1, c = 1, the equation is =
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 +ve 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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Physics Unit, KMNS SP015

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:
= +
= + 1 2

2

2 = 2 + 2

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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Physics Unit, KMNS SP015

OBJECTIVE QUESTIONS

(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. 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

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

FIGURE 2.1

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Physics Unit, KMNS SP015

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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Physics Unit, KMNS SP015

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

1. Object B Object C
Object A
Displacement 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.
(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 above,
(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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Physics Unit, KMNS SP015

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

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Physics Unit, KMNS SP015

(a) the speed of the rocket at height 20 km.
(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 x B
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) s

9. (a) 9.23 s (b) 639 m (c) 85.76 m s–1

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

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Physics Unit, KMNS SP015

TOPIC 3
MOMENTUM AND IMPULSE

3.1 Momentum and impulse
a) Define momentum and impulse ⃗ = ⃗ ∆ .
b) Solve problem related to impulse and impulse-momentum theorem,
⃗ = ∆ = ⃗ − ⃗ .
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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Physics Unit, KMNS SP015

OBJECTIVE QUESTIONS

(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.

C. D.
.

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. A car is moving to the right in a constant velocity. Then it change the direction
without changing the speed. What do you think about its 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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Physics Unit, KMNS SP015

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

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Physics Unit, KMNS SP015

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
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 30
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 = 37 and β = 27.

ANSWERS:

1. −9.0 kg m s−1
2. −16.0 kg m s−1
3. 124.0 N
4. (b) (i) 480.0 N s (ii) 33.33 m s−1
5. (a) −16.0 kg m s-1 (b) −4000.0 N
6. 3.0 m s−1
7. 60.0 kg m s−1, 51.96 kg m s−1, 30.0 kg m s−1
8. 3.77 m s−1
9. −1.0 m s−1
10. 4.49 m s−1

16

Physics Unit, KMNS SP015

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.
≤ , ≤

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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Physics Unit, KMNS SP015

OBJECTIVE QUESTIONS

(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

18

Physics Unit, KMNS SP015

STRUCTURED QUESTIONS (C4, PLO 4, CTPS 3, MQF LOD 6)
1.

v

Rough Surface

200

FIGURE 4.1

FIGURE 4.3

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.

19

Physics Unit, KMNS SP015

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.

20

Physics Unit, KMNS SP015
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.

21

Physics Unit, KMNS SP015

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. 31.68 N, 2.50o
5. F cos − mg sin

6. 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

22