EP015 Note #KMKK

PHYSICS 1
EP 015

KOLEJ MATRIKULASI KEJURUTERAAN KEDAH

KHAIRUL NIZAM BIN AB HAMID, AMAR SHAH BIN ALI, MOHD HAILMY BIN RAZALI,
MOHD HUSAINE BIN MUKHTAR, ISMAIL BIN YAACOB, RAZIAH BT MOHD NOOR,
NORMADIAH BT SHAFIE, SYAZLINA BT ABDUL RASHID, SITI AISHAH BT TAHIR,
RAHAYU BT YAHAYA, JAMILAH BT MORAD, FATIN AZIMAH BT SAAD

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CONTENTS PAGE

TITLE 4
14
CHAPTER 1: PHYSICAL QUANTITIES AND MEASUREMENTS 29
CHAPTER 2: KINEMATICS OF LINEAR MOTION 42
CHAPTER 3: MOMENTUM AND IMPULSE 53
CHAPTER 4: FORCES 71
CHAPTER 5: WORK ENERGY AND POWER 82
CHAPTER 6: CIRCULAR MOTION 91
CHAPTER 7: GRAVITATION 105
CHAPTER 8: ROTATION OF RIGID BODY 116
CHAPTER 9: SIMPLE HARMONIC MOTION 138
CHAPTER 10: MECHANICAL AND SOUND WAVES 149
CHAPTER 11: DEFORMATION OF SOLIDS 165
CHAPTER 12: FLUID MECHANICS 173
CHAPTER 13: HEAT CONDUCTION AND THERMAL EXPANSION 185
CHAPTER 14: GAS LAWS AND KINETIC THEORY OF GASES 198
CHAPTER 15: THERMODYNAMICS 203
PRE-LAB EXPERIMENT 1: MEASUREMENT AND UNCERTAINTY 207
PRE-LAB EXPERIMENT 2: FREE FALL AND PROJECTILE MOTION 211
PRE-LAB EXPERIMENT 3: EXPERIMENT 3: ENERGY 214
PRE-LAB EXPERIMENT 4: ROTATIONAL MOTION OF A RIGID BODY 217
PRE-LAB EXPERIMENT 5: SIMPLE HARMONIC MOTION (SHM)
PRE-LAB EXPERIMENT 6: STANDING WAVES

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1.1 Dimensions of Physical Quantities EXAMPLE

a) Define dimension Determine a dimension and the S.I. unit for
b) Determine the dimensions of derived the following quantities:
a. Velocity
quantities. b. Acceleration
c) Verify the homogeneity of equations
Solutions:
using dimensional analysis.

a. Velocity  change in displacement
time interval
Dimension is defined as a technique or
method which physical quantity can be v L  LT1
expressed in terms of combination of
basic quantities. T

[Basic Quantity] Dimensional Unit b. [ ] = [ ]
[mass] or [m] Symbol
[ ]
M kg
[ ] = − = −


[length] or [l] L m
T
[time] or [t] A@I Principle of Homogeneity
 s
N
[electric current] Dimension on the L.H.S. = Dimension on the R.H.S
or [I]
A

[temperature] or K 1. For constant and dimensionless quantity
[T] mole the dimension is 1 ex : [n] = 1 , [23] = 1

[amount of 2. Dimension can’t be added or subtracted
3. The validity of the equation is ONLY
substance] or [N]
determined by EXPERIMENT

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EXAMPLE

Determine whether f  1 g QUANTITY
2π l , where f, l and
g represent the frequency, length and

acceleration due to gravity respectively are SCALAR VECTOR
QUANTITY QUANTITY
dimensionally correct or not
Magnitude Magnitude and
Solutions: direction
Mass, work,
Dimension on the LHS; distance, speed Momentum, force,
displacement, velocity
[ ] = [1] = −1
[ ]

Dimension on the RHS; Representing Vectors

1 g    1 g 1 l  1  Symbols;
 l   2π 2 2
  i. printed bold (eg: A) or
2π ii. use an arrow over a letter (eg: ⃗ )
 Arrow;
     1 L 1 i. its length indicates the magnitude
1 LT 2 2 2  T1 ii. direction of the arrow represents direction

∴Dimension on the L.H.S. = Dimension on the R.H.S of the vector
 Magnitude of the vector A is written as | |
Therefore the equation above is homogeneous or
dimensionally correct.

1.2 Scalars and Vectors EXAMPLE

a) Define scalar and vector quantities. The magnitude of B is twice from magnitude A.
b) Resolve vector into two perpendicular | | = 2| |
or
components ( and axes). | ⃗⃗ | = 2| ⃗ |
c) Illustrate unit vectors ( ,̂ ,̂ ̂ ) in
A
Cartesian coordinate.
d) State the physical meaning of dot B

(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.

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Resolving Vectors EXAMPLE
Any type of vector may be expressed in terms of
its component. The magnitudes of the 3 displacement vectors
shown in drawing. Determine the magnitude &
⃗ directional angle for the resultant that occurs
when these vectors are added together.

⃗ A
B

⃗

with the aid of trigonometry C=8 m

Solutions:

⃗ Vector x-component y-component
A
⃗ = + 10 cos 45 = + 10 sin 45
B = + 7.07 = + 7.07
⃗ ⃗ = ⃗ = − 5 cos 30
⃗ = ⃗ C = − 4.33 = + 5 sin 30
=0 = + 2.50
Resultant =−8
= + 2.74 m
= + 1.57 m

cos = Magnitude of resultant vector :
ℎ

sin = | | = √ 2 + 2

ℎ

Magnitude of vector A :  (2.74)2  (1.57)2
| | = √ 2 + 2  3.16 m

Direction of vector A :

Direction of vector A : = −1 | |

= −1 | |

= tan−1 |1.57|

!! θ is always measured from x axis. 2.74
!! Any component that points along the negative
x or y axis get a ‘− sign’.   29.81 above  x
!! Add by component if more than one vector
involved.

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Unit Vectors Dot (scalar) Product

⋅ = | || | cos

where;
= vector A
= vector B
| | = magnitude of vector A
| | = magnitude of vector B
= angle between vector A and vector B

Definition dimensionless vector having a  Scalar quantity
magnitude of exactly 1 and  Example of physical quantity; = ⋅
points in a particular direction  Its value is maximum if = 0°
 Its value is minimum if = 90°
iˆ  ˆj  kˆ  1  Commutative law applied to dot product;

Notation − ̂ or i ⋅ = ⋅
−
Vector (Unit − ̂ or j PHYSICAL MEANING OF ⋅
vector) ̂ or k the magnitude of A
Magnitude of multiplied by the
vector = ̂ + ̂ + ̂ component of B
| | = √ 2 + 2 + 2 parallel to A

EXAMPLE or
the magnitude of B
Please write the vector S below in the term of unit multiplied by the
vector and its magnitude. component of A
parallel to B

Dot (scalar) Product Calculation

⋅ = ( ̂ + ̂ + ̂ )( ̂ + ̂ + ̂ )

S Note:

̂ ⋅ ̂ = ̂ ⋅ ̂ = ̂ ⋅ ̂ =(1)(1)cos 0 =1
̂ ⋅ ̂ = ̂ ⋅ ̂ = ̂ ⋅ ̂ =(1)(1)cos 90 =0

Solutions: Therefore:
unit vector ; = (4 ̂ + 3 ̂ + 2 ̂ )m ⋅ = ( + + )

magnitude ; | | = √42 + 32 + 22 = 5.39

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EXAMPLE PHYSICAL MEANING OF ×
the magnitude of A
Given 2 vectors: multiplied by the
component of B
= (3 ̂ + 2 ̂ − 4 ̂ ) perpendicular to A
= (−5 ̂ + 8 ̂ − 2 ̂ )
or
Calculate the magnitude of B
(a) the value of ⋅ multiplied by the
(b) the angle θ between 2 vectors component of A
perpendicular to B

Solutions: Cross (vector) Product Calculation

(a) ⋅ = (3 ̂ + 2 ̂ − 4 ̂ )(−5 ̂ + 8 ̂ − 2 ̂ ) ̂ ̂ ̂
× = | |
 (3)(5)  (2)(8)  (4)(2)

=9

(b) | | = √32 + 2 + (−4)2 = 5.39 = | | ̂ − | | ̂ + | | ̂
| | = √(−5)2 + 8 + (−2)2 = 9.64

From = [ − ] ̂ − [ − ] ̂ +
[ − ] ̂
⋅ = | || | cos

= cos−1 ⋅ = 80.03° Note:
| || |

̂ × ̂ = ̂ × ̂ = ̂ × ̂ = 0

Cross (vector) Product ̂ × ̂ = ̂ ̂ × ̂ = − ̂

× = | || | sin ̂ × ̂ = ̂ ̂ × ̂ = − ̂

where; ̂ × ̂ = ̂ ̂ × ̂ = − ̂
= vector A
= vector B Direction of Cross (vector) Product
| | = magnitude of vector A
| | = magnitude of vector B
= angle between vector A and vector B

 Vector quantity
 Example of physical quantity;

= ×
 Its value is maximum if = 90°
 Its value is minimum if = 0°
 Commutative law applied to cross product;

× = −( × )

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EXAMPLE
Given 2 vectors:

= (3 ̂ + 2 ̂ − 4 ̂ )
= (−5 ̂ + 8 ̂ − 0 ̂ )
Calculate
(a) the value of ×
(b) the value | × |
Solutions:
(a)
̂ ̂ ̂
× = | 3 2 −4|
−5 8 0
= [2(0) − [(−4)(8)]] ̂ − [3(0) − [(−4)(−5)]] ̂

+ [3(8) − [(2)(−5)]] ̂
= 32 ̂ + 20 ̂ + 34 ̂
(b) | × | = √322 + 202 + 342 = 50.79

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CHAPTER 1
PHYSICAL QUANTITIES AND MEASUREMENTS
LEARNING OUTCOMES
1.1 Dimensions of Physical Quantities
a) Define dimension
b) Determine the dimensions of derived quantities.
c) Verify the homogeneity of physics equations using dimensional analysis.
1.2 Scalars and Vectors
a) Define scalar and vector quantities.
b) Resolve vector into two perpendicular components ( and 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.

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1.1 DIMENSIONS OF PHYSICAL QUANTITIES

1. Dimension is define 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 equations.
D. technique or method to construct an equation.

2. What is the dimension of Force?

( − )

3. The pressure of a liquid with density and moving with a velocity is given by

= − 1 2
2
where is a dimensional quantity. What are the dimensions of ?

( − − )

4. Show that the dimensions of the following equations are homogeneous:
(i) Pressure, = ℎ
(ii) Impulse, = ( − )
Here is mass, is time, is initial velocity, is final velocity, is acceleration due to
gravity, ℎ is height, is density and is force.

5. Check the homogeneity of equation using dimension analysis technique :

(i) = , unit for G is −1 3 −2 , F=force , m and M = mass , r = radius
2

(homogenous)

(ii) = , unit for Y is kg −1 −2 , T = Tension , l = length , A = area , x =
2

elongation

(not homogenous)

1.2 SCALARS AND VECTORS

1. Which statement is always true for vector quantity?
A. Only diection matters
B. Only magnitude matters
C. It must have magnitude and direction
D. Only units matter

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2. The unit vectors along the , are ̂, ,̂ ̂ respectively. Which of the
following cross products of vectors is correct?
A. ̂ × ̂ = ̂
B. ̂ × ̂ = ̂
C. ̂ × ̂ = 0
D. ̂ × ̂ = ̂

3. ⋅ means
A. Direction of vector M and vector Z is perpendicular to each other.
B. Direction of vector M and vector Z is parallel to each other.
C. Direction of scalar M and Scalar Z is perpendicular to each other.
D. Direction of scalar M and vector Z is parallel to each other.

4.
B

y 3.7 km

40o x
FIGURE 1
30o

5.2 km
A

Two displacement vectors A and B are shown in FIGURE1 above. Find
(i) the resultant displacement in form of unit vector.

(− . ̂ − . )̂
(ii) magnitude and direction of the resultant displacement

( . , . ° − )

5. The speed of a boat crossing a river in still water is 2.0 −1. Find the magnitude and
direction of the resultant velocity of the boat when the current downstream is 1.5 −1.

( . − , . ° ( − ))

6.

FIGURE 2
Based on FIGURE 2 above, calculate the resultant vector of P and Q.

( . − , . °( − ))

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7.
F=6N

60°

s = 5.0 m ( )
FIGURE 3 (-28, 58.7°)
Based on FIGURE 3, find the scalar product (F.s)

8. If = (6 ̂ + 8 ̂) and = (2 ̂ − 5 ̂), find
(i) ⋅
(ii) The angle between A and B?

9. If = (2 ̂ + 6 ̂ − 5 ̂ ) and = (3 ̂ − 4 ̂ + 8 ̂ ) ,find ×

( ̂ − ̂ − ̂ )

10. Copy the diagram below and show the direction of the vector product ×

A

B

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CHAPTER 2
KINEMATICS OF LINEAR MOTION

LEARNING OUTCOMES

2.1 LINEAR MOTION

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

2. Discuss 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

1. Apply equations of motion with uniform acceleration:

v = u + at, s  ut  1 at 2 , v² = u² + 2as.
2

2.3 PROJECTILE MOTION

1. Describe projectile motion launced at an angle,θ as well as special cases when θ = 0˚ and
θ = 90˚ (free fall).

2. Solve problems related to projectile motion.
3. Determine the acceleration due to gravity, g using free fall and projectile (Experiment 2)

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2.1 LINEAR MOTION

1. A ball which has been dropped vertically downward on to the floor rebounds upward. If
the direction of the velocity is considered as positive when the ball is moving downward,
which of the following graphs shows the variation of velocity with time?

v v
A. C.

v0 t v0 t

B. 0 t D. t
0

2. A piece of rock slides on the surface of ice and travels a distance x in time t under
uniform deceleration. Which of the following will result in a straight line graph?

A. x against t

B. x against t2

x
C. t against t

D. x against t2
t

3 An object falling down under gravity from top of a building. Which of the following
graph is will present the object falls to ground.

AV B CD

tt t t

4. Distinguish between
(i) Instantaneous speed and average speed
(ii) Speed and velocity

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5. A student stays 6.0 km from the main road. His school is 12 km from the junction P as
shown in the figure

School

12.0 km

House Junction P

6.0 km

He takes 10.0 minutes to travel from his house to the junction P, and another 15 minutes

from the junction to his school which is 12 km and from the junction P as shown. Assume

that the student travel with constant speed from the house to the junction P and from
junction P to the school. Calculate the student’s:

(i) Average speed from his house to the school (43.2 km h-1)
(ii) Average velocity from his house to the school (32.16 km h-1, 63.4˚)

6. FIGURE shows how the velocity of a car undergoing linear motion varies with time t.
a) Determine:

i) the displacement undergone by the car. (3047.5 m)

ii) the distance undergone by the car
b) Sketch a graph of acceleration, a against time t.

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7. The speed of the car travelling along a straight road decrease uniformly from 12 ms-1 to
8 ms-1 over 88.0 m. Sketch the velocity –time graph for the motion of the car and use the

graph to calculate:
i. the time taken for the speed to decrease from 12 ms-1 to 8 ms-1

(8.8 s)

ii. the decelaration of the car
(0.455 ms-2)

iii. the time taken for the car to come to stop from the speed of 12 ms-1

(26.4 s)

2.2 UNIFORMLY ACCELERATED MOTION

1. A car accelerates from rest at a rate of 4.0 m s-2. (40 ms-1)
i) Calculate it velocity after 10 s? (6 s)

ii) How long does it take to travel 72 m? (128 m)

iii) How far has it traveled after 8.0 s?

2. The speed of a car traveling along a straight road decreases uniformly from 12.0 m s-1 to
8.0 m s-1 over 88.0 m. Calculate the

i) acceleration of the car
(-0.455 ms-2)

ii) time taken for the speed to decrease from 12.0 m s-1 to 8.0 m s-1

(8.79 s)
iii) time taken for the car to come to rest

(26.4 s)

iv) total distance traveled by the car during this time

(158 m)

3. A stationary airplane accelerates 5 ms-2 and travel for 40 s before it takes off. Find
i) the minimum length of the runway
(4000 m)
ii) the velocity of the airplane at take off
(200 ms-1)

4. Just as a car starts to accelerate from rest with acceleration 1.4 m s-2, a van moving with a
constant speed of 12 ms-1 passes it in a parallel lane.
i) How long does it takes before the car overtakes the van.

(17.1 s)
ii) What is the distance taken before the car overtakes the van.

(204.7 m)
iii) What is the speed of the car while overtaking the van.

(24 ms-1)

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5. A bullet is shot from a gun at a speed of 245 ms-1 towards a pieces of polystyrene with
5.5 cm thickness and emerges with a speed of 220 ms-1. Calculate:
i) the deceleration through the polystyrene
(-1.06 x 105 m s-2)
ii) time taken to get through the polystyrene
(2.36 x 10-4 s)

2.3 PROJECTILE MOTION

1. A student drops a stone from a second floor window, 15 m above the ground.

a) How long does it takes for the stone to reach the ground?

(1.75 s)

b) Calculate the velocity before it hits the ground.

(17.2 m s-1)

2. A golf ball is struck with an initial velocity of 24 m s-1 at an angle of 30º to the ground as
shown in FIGURE 2.1. How far it does travels horizontally before striking the ground?

u = 24 m s-1

30º

GROUND

FIGURE 2.1 (50.9 m)

3. An archer standing on a cliff 50 m high shoots an arrow at an angle of 30° above the
horizon with a speed of 80 m s-1.

a) How long is it in the air?

(9.25 s)

b) How far from the base of the cliff the arrow lands?

(640 m)

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

(85.87 m s-1)

26

4. a)

h

Ground
FIGURE 2.2

A rocket is launched vertically upwards from the ground as shown in FIGURE 2.2 with
initial velocity 35 m s-1. It is accelerating at 5.0 m s-2. The engine suddenly broke down at
height h = 20 km from the ground. Neglecting air resistance, calculate the

i ) speed of the rocket at height 20 km (448.6 m s-1)
ii) maximum height achieved by the rocket (30.26 km)
iii) time of flight of the rocket. (207 s)

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5. A u  5 m s1

1 B
m

Cx
FFIIGGURUER2.E3 2.3

In the FIGURE 2.3, a ball is dropped from the edge of a table with initial horizontal velocity of

5 m s-1. The height of the table is 1 m. Calculate the

i) time taken for the ball to reach point B (0.45 s)
ii) horizontal distance x (2.25 m)
iii) magnitude and direction of its velocity at point B. (6.68 m s-1 and -41.4o or 318.50)

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30

In an Inelastic Collision
31

32

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Definition SUMMARY
Equation Momentum
Graph
Impulse
Definition
Equation Elastic Collision
Graph

Inelastic Collision

Principle of Conservation
of Momentum

Principle of Conservation
of Energy

Conservation of
Kinetic Energy

Coefficient of Restitution

34

CHAPTER 3
MOMENTUM AND IMPULSE

LEARNING OUTCOMES
3.1 Momentum and Impulse
1. Define momentum and impulse, J   p  Ft .

2. Solve problem related to impulse and impulse-momentum theorem,
J   p  Ft = mvf - mvi

3. Use the graph of force-time, F-t to determine impulse.

3.2 Conservation of Linear Momentum

1. State the principle of conservation of linear momentum.

2. Apply the principle of conservation of momentum in elastic and inelastic collisions in 1D

& 2D collisions.

3. Differentiate elastic and inelastic collisions.

4. Define and use the coefficient of restitution, ek= –( v2  v1 )
u2  u1

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3.1 MOMENTUM AND IMPULSE

1 The units for Impulse are
A. N/s
B. Ns
C. N
D. m/s

2 A change in momentum is called an ____________.
A. impulse
B. amperes
C. force
D. power

3 A 20 N of force acted on a body of mass 2 kg for 2 s. What is the change of velocity of the

body? (20 m s-1)

4

Determine the impulse from the graph given below

( 80Ns )

36

5

The figure showed a sphere of mass 0.40kg moving with a horizontal velocity of 18 ms-1
hits a vertical wall. After 0.02s, the sphere rebounded backward with its initial velocity.
Determine

a) The impulse of the sphere
b) The average force exerted by the sphere on the wall.
c) Is the collision elastic or inelastic? Justify your answer.

(14.4Ns, 720N)

6 An object of mass 0.25kg move at a velocity of 24 ms-1 along a straight line. After it has
collided with another object, it moves at a velocity 40 ms-1 in the opposite direction.
Determine
a) The impulse acting on the object

b) The average force applied on the object if impulsive force has acted for t=4ms
(− − , − )

7

Before After

FIGURE 3.1 shows an object of mass 0.20 kg moving with a velocity of 20 m s-1 and
strikes a vertical wall with an impulse of 6.0 N s. The object rebounds from the wall with
velocity v. Calculate v.

(-10 m s-1)

37

3.2 CONSERVATION OF LINEAR MOMENTUM

1 Momentum is the product of __________ and velocity.
A. weight
B. mass
C. direction
D. force

2 A bullet traveling at 500 m/s is brought to rest by an impulse of 50 Ns. What is the mass
of the bullet?
A. 10 kg
B. 0.1 kg
C. 25 kg
D. 2500 kg

3 Which two quantities can be expressed using the same units?
A. momentum and energy
B. energy and force
C. impulse and force
D. impulse and momentum

4 A 2 kg cart has a momentum of 16 kg m/s. What is its velocity?
A. 8 m/s
B. 32 m/s
C. 0.125 m/s
D. 18 m/s

5 Momentum is a ____________________ quantity
A. science
B. scalar
C. vector
D. energy

6 Momentum is large when mass is large, _____________ is large, or both are large.
A. speed
B. direction
C. velocity
D. energy

38

7 Which object has the least momentum?
A. 0.25 kilogram softball moving at 20 m/s
B. 7.25 kilogram bowling ball moving at 1 m/s
C. 2 kilogram rock moving at 3 m/s
D. 2 kilogram rock resting on a stump

8 If an eagle and a bumblebee are both traveling at 10 km/hr, which has the greater
momentum?
A. eagle
B. bumblebee
C. both
D. neither

9 Which has more momentum: a 5kg fish swimming at 100 m/hr or a 25kg fish at rest?
A. the 5kg fish
B. the 25kg fish
C. both
D. neither

10 A biker with a mass of 75 kg moves along the path with a constant velocity of 5 m/s. What
is the biker's momentum?
A. 25 m/s

B. 375 m/s
C. 25 kg m/s
D. 375 kg m/s

11 A particles P (mass 4 unit) and another particles Q (mass 9 unit) have head on collision

but they are separated after the collision. If the change in velocity of P and that of Q are

ΔVp and ΔVo respectively, the magnitude of ratio ΔVp / ΔVo is

A 4/9 C 3/2

B 2/3 D 9/4

12 If the kinetic energy of two masses of 3 kg and 5 kg is the same, what is the ratio of the

momentum of 3 kg mass to that of the 5 kg mass? C 5/3
A √3/5 D √ 5/3

B 3/5

39

13 Ball A of mass 800kg moving to the right at 5 ms-1 collides with another ball B of mass
500kg moving at 6 ms-1 in the opposite direction. After collision, Ball A bounces
backwards with velocity 0.2 ms-1.

Determine
a) The velocity of Ball B after collision.

b) Is the collision elastic or inelastic? Justify your answer.

(2.32 ms-1)

14 A tennis player receives a shot with the ball (0.060 kg) traveling horizontally at 50.0 m/s
and returns the shot with the ball traveling horizontally at 40.0 m/s in the opposite
direction.
a. What is the impulse delivered to the ball by the racquet?

b. What work does the racquet do on the ball?

(5.40 N s , -27 J)
15

AB C

FIGURE 3.2

Three blocks A, B, and C of masses m, 2m, and 3m respectively are placed on a horizontal
smooth plane as shown in FIGURE 3.2. Block A with speed 18 m s-1 collides and sticks

with block B. Both objects collide and stick with block C. Together they move with

common velocity v. Calculate v.
(3 m s-1)

16 A 4.0 kg rifle fires a 6 g bullet with a velocity of 500 ms-1.
a) Calculate the kinetic energy acquired
i) by the bullet
ii) by the rifle.

(750 J , 1.125 J)

b) Find the ratio of the distance the rifle moves backward to the distance the
bullet moves forward (assume it’s happen at same time interval).

(1.5  10-3)

40

17

FIGURE 3.3 An object of mass 2.0kg is placed at rest at the edge ofte smooth horizontal

table. The edge is 50cm above the floor. An object B of mass 1.5 kg moves towards object

A at constant speed 2ms-1. After colidong with object A, object B moves in the opposite

direction at speed 0.8ms-1.Determine the horizontal distance travelled by object A when it

reaches the floor. (Neglect air resistance) (0.67 m)

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CHAPTER 4
FORCES

LEARNING OUTCOMES
4.1 Basic of Forces and Free Body Diagram
1. Identify the forces acting on a body in different situations:

 Weight
 Tension
 Normal force
 Friction
 External force (pull or push)
2. Sketch free body diagram
3. Determine static friction and kinetic friction.
4.2 Newton’s Law of Motion
1. State Newton’s law of the mtion
2. Apply Newton’s law of the motion

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4.1 BASIC OF FORCES AND FREE BODY DIAGRAM

1. Three forces are acting on an object. If the object is at equilibrium, which of the
following statements is TRUE?
A. All three forces are acting at a point.
B. The forces formed a right angle triangle.
C. The resultant force is given by the hypotenuse of the triangle.
D. The resultant force is acting in the opposite direction to the forces.

2. 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.

3. A block A on a smooth inclined plane is connected to another block B by a string that
passes over a smooth pulley.

i) Draw and label the forces acting on the blocks A and B
ii) Draw free-body diagrams for the block A and B
4. A wooden box on a rough surface is pulled by a force F as shown in the figure.

F

(a) When the force F = 28 N, the box does not move. What is the static friction between

the box and the floor ? (28 N)

(b) The force F increased to 35 N, and the box still remains stationary. What is the static

friction between the box and the floor. (35 N)

(c) When the force F= 40 N, the box moves at a constant velocity across the surface.

What is the dynamic friction between the box and the floor. (40 N)

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