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2.1 LINEAR MOTION

Physical Definition, Quantity, Symbol and unit
Quantity
Distance is the total path length traveled from one
Distance, l location to another.
Quantity: scalar SI unit: meter (m)

(a) The distance in a specified direction.
(b)the distance between two locations measured along
Displacement, the shortest path connecting them in a specific
l direction.
(c) The distance of its final position from its initial
position in a specified direction.

Quantity: vector SI unit: meter (m)

Speed is the rate of change of distance
Speed,v
Speed = Distance traveled
Time taken

Quantity: scalar SI unit: m s-1

Velocity is the rate of change of displacement.
Velocity, v
Velocity = Displacement
Time taken

Direction of velocity is the direction of displacement
Quantity : Vector SI unit: m s-1

Average v = Total distant traveled, s Example: A car moves at
speed Total time taken , t an average speed /
velocity of 20 ms-1
On average, the car moves
Average v = Displacement, s a distance / displacement
velocity Time taken, t of 20 m in 1 second for the
whole journey.

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Uniform Speed that remains the same in magnitude regardless of
speed its direction.

Uniform Velocity that remains the same in magnitude and
velocity direction.

An object has (a) the direction of motion changes or the motion is
a non-uniform not linear.
velocity if: (b)The magnitude of its velocity changes.

Acceleration, When the velocity of an object changes, the object is
a said to be accelerating.

v−u Acceleration is defined as the rate of change of
a= velocity.
t
Acceleration = Change in velocity
unit : ms-2
Time taken

= final velocity, v – initial velocity, u
Time taken, t

acceleration
is positive • The velocity of an object increases from an initial
velocity, u, to a higher final velocity, v

Deceleration The rate of decrease in speed in a specified direction.

acceleration The velocity of an object decreases from an initial
is negative. velocity, u, to a lower final velocity, v.

Zero An object moving at a constants velocity, that is, the
acceleration magnitude and direction of its velocity remain
unchanged – is not accelerating
Constant Velocity increases at a uniform rate.
acceleration When a car moves at a constant or uniform acceleration
of 5 ms-2, its velocity increases by 5 ms-1 for every
second that the car is in motion.



1. Constant = uniform
2. increasing velocity = acceleration
3. decreasing velocity = deceleration
4. zero velocity = object at stationary / at rest
5. negative velocity = object moves at opposite
direction
6. zero acceleration = constant velocity
7. negative acceleration = deceleration

Comparisons between distance Comparisons between speed and
and displacement. velocity

Distance Displacement Speed Velocity
Total path length The distance The rate of change The rate of change
traveled from between two of distance of displacement
one location to locations Scalar quantity Vector quantity
another measured along
the shortest path It has magnitude It has both
connecting them but no direction magnitude and
in specific direction
direction SI unit : m s-1 SI unit : m s-1
Scalar quantity Vector quantity

It has magnitude It has both
but no direction magnitude and
direction
SI unit meter SI unit : meter

Fill in the blanks:
1. A steady speed of 10 m/s = A distance of .. ……….is traveled
every ………..
2. A steady velocity of -10 m/s = A …………. Of 10 m is traveled every
………..to the left.
3. A steady acceleration of 4 ms-2 = Speed goes up by 4 m/s every
……….
4. A steady deceleration of 4 ms-2 = speed goes ……….. by 4 m/s
every ……….
5. A steady velocity of 10 m/s = ……………………………………………
…………………………………………………………………………………



Example 1 Example 2
Every day Rahim walks from his Every morning Amirul walks to
house to the junction which is 1.5 Ahmad’s house which is situated
km from his house. Then he turns 80 m to the east of Amirul’s house.
back and stops at warung Pak Din They then walk towards their
which is 0.5 km from his house. school which is 60 m to the south
of Ahmad’s house.
(a) What is the distance traveled
by Amirul and his
displacement from his
house?

(b)If the total time taken by
Amirul to travel from his
house to Ahmad’s house and
then to school is 15 minutes,
(a) What is Rahim’s displacement what is his speed and
from his house velocity?
• when he reaches the junction.

• When he is at warung Pak
Din.

(b)After breakfast, Rahim walks
back to his house. When he
reaches home,
(i) what is the total distance
traveled by Rahim?

(ii) what is Rahim’s total
displacement from his
house?

Example 3
Syafiq running in a race covers 60 m in 12 s.
(a) What is his speed in m/s
(b) If he takes 40 s to complete the race, what is his distance covered?



Example 4
An aeroplane flys towards the
north with a velocity 300 km/hr in
one hour. Then, the plane
moves to the east with the
velocity 400 km / hr in one hour.

(a) What is the average speed
of the plane?
(b)What is the average
velocity of the plane?
(c) What is the difference
between average speed and
average velocity of the
plane?

Example 5
The speedometer reading for a
car traveling north shows 80
km/hr. Another car traveling at
80 km/hr towards south. Is the
speed of both cars same? Is the
velocity of both cars same?

A ticker timer

Use: 12 V a.c power supply
1 tick = time interval between two dots.
The time taken to make 50 ticks on the ticker tape is 1 second.
Hence, the time interval between 2 consecutive dots is 1/50 = 0.02 s.
1 tick = 0.02 s



Relating displacement, velocity, acceleration and time using ticker tape.

FORMULA
VELOCITY Time, t = 10 dots x 0.02 s
= 0.2 s
displacement, s = x cm
velocity = s = x cm
t 0.2 s

ACCELERATION Initial velocity,
u = x1
0.2
final velocity,
v = x2
0.2
elapse time, t = (5 – 1) x 0.2 s = 0.8 s acceleration,
or t = (50 – 10) ticks x 0.02 s = 0.8 s a=v–u
t

TICKER TAPE AND TYPE OF MOTION
CHARTS
Constant velocity
– slow moving

Constant velocity
– fast moving

Distance between the dots
increases uniformly
the velocity is of the object is
increasing uniformly
The object is moving at a
uniform / constant
acceleration.



Distance between the dots
decrease uniformly
The velocity of the object is
decreasing uniformly
The object is experiencing
uniform / constant
deceleration

Example 6
The diagram above shows a ticker tape
chart for a moving trolley. The frequency
of the ticker-timer used is 50 Hz. Each
section has 10 dots-spacing.
(a) What is the time between two dots.
(b) What is the time for one strips.
(c) What is the initial velocity
(d) What is the final velocity.
(e) What is the time interval to change
from initial velocity to final velocity?
(f) What is the acceleration of the
object.

THE EQUATIONS OF MOTION

u = initial velocity
v = final velocity
t = time taken
s = displacement
a = constant accleration



2.2 MOTION GRAPHS

DISPLACEMENT – TIME Velocity is obtained from the gradient of
GRAPH the graph.

A – B : gradient of the graph is +ve and
constant ∴ velocity is constant.
B – C : gradient of the graph = 0 ∴ the
velocity = 0, object at rest.
C – D : gradient of the graph –ve and
constant. The velocity is negative and
object moves in the opposite direction.

VELOCITY-TIME GRAPH Area below Distance / displacement
graph
Positive Constant Acceleration
gradient (A – B)
Negative Constant Deceleration
gradient (C – D)
Zero Constant velocity / zero
gradient acceleration
(B – C)

GRAPH s versus t v versus t a versus t
Zero
velocity

Negative
velocity

Constant
velocity



GRAPH s versus t v versus t a versus t
Constant
acceleration

Constant
deceleration

Example 6 Example 7

Contoh 11

Based on the s – t graph above:
(a) Calculate the velocity at (a) Calculate the acceleration at:
(i) AB (ii) BC (iii) CD (i) JK (ii) KL (iii) LM

(b) Describe the motion of the object at:
(i) AB (ii) BC (iii) CD
(b) Describe the motion of the object at:
(i) JK (ii) KL (iii) LM
(c)Find:
(i) total distance

(ii) total displacement Calculate the total displacement.
(d) Calculate
(i) the average speed
(c) Calculate the average velocity.
(ii) the average velocity of the
moving particle.


2.3 INERTIA

Inertia The inertia of an object is the tendency of the
object to remain at rest or, if moving, to continue
its motion.

Newton’s first law Every object continues in its state of rest or of
uniform motion unless it is acted upon by an
external force.
Relation between The larger the mass, the larger the inertia
inertia and mass
SITUATIONS INVOLVING INERTIA
SITUATION EXPLAINATION
When the cardboard is pulled away quickly, the
coin drops straight into the glass.
The inertia of the coin maintains its state at rest.
The coin falls into the glass due to gravity.

Chili sauce in the bottle can be easily poured out if
the bottle is moved down fast with a sudden stop.
The sauce inside the bottle moves together with
the bottle. When the bottle stops suddenly, the
sauce continue in its state of motion due to the
effect of its inertia.

Body moves forward when the car stops suddenly
The passengers were in a state of motion when the
car was moving. When the car stopped suddenly,
the inertia in the passengers made them maintain
their state of motion. Thus when the car stop, the
passengers moved forward.

A boy runs away from a cow in a zig zag motion.
The cow has a large inertia making it difficult to
change direction.



• The head of hammer is secured tightly to its
handle by knocking one end of the handle, held
vertically, on a hard surface.
• This causes the hammer head to continue on its
downward motion when the handle has been
stopped, so that the top end of the handle is
slotted deeper into the hammer head.

• The drop of water on a wet umbrella will fall
when the boy rotates the umbrella.
• This is because the drop of water on the surface
of the umbrella moves simultaneously as the
umbrella is rotated.
• When the umbrella stops rotating, the inertia of
the drop of water will continue to maintain its
motion.
Ways to reduce 1. Safety in a car:
the negative (a) Safety belt secure the driver to their seats.
effects of inertia When the car stops suddenly, the seat belt
provides the external force that prevents the
driver from being thrown forward.
(b)Headrest to prevent injuries to the neck
during rear-end collisions. The inertia of the
head tends to keep in its state of rest when
the body is moved suddenly.
(c) An air bag is fitted inside the steering wheel.
It provides a cushion to prevent the driver
from hitting the steering wheel or dashboard
during a collision.
2. Furniture carried by a lorry normally are tied up
together by string. When the lorry starts to
move suddenly, the furniture are more difficult
to fall off due to their inertia because their
combined mass has increased.
Relationship • Two empty buckets which are hung with rope
between mass from a the ceiling.
and inertia • One bucket is filled with sand while the other
bucket is empty.
• Then, both pails are pushed.
• It is found that the empty bucket is easier to



push compared to the bucket with sand.
• The bucket filled with sand offers more
resistance to movement.
• When both buckets are oscillating and an
attempt is made to stop them, the bucket filled
with sand offers more resistance to the hand
(more difficult to bring to a standstill once it has
started moving)
• This shows that the heavier bucket offers a
greater resistance to change from its state of
rest or from its state of motion.
• An object with a larger mass has a larger inertia.

2.4 MOMENTUM

Definition Momentum = Mass x velocity = mv
SI unit: kg ms-1

Principle of In the absence of an external force, the total
Conservation of momentum of a system remains unchanged.
Momentum

Elastic Collision Inelastic collision

Both objects move The two objects combine and
independently at their move together with a
respective velocities after the common velocity after the
collision. collision.
Momentum is conserved. Momentum is conserved.
Kinetic energy is conserved. Kinetic energy is not
Total energy is conserved. conserved.
Total energy is conserved.



Total Momentum Before = total Total Momentum Before = Total
momentum After Momentum After
m1u1 + m2u2 = m1v1 + m2v2 m1u1 + m2u2 = (m1 + m2) v

Explosion
Before explosion both object stick
together and at rest. After collision,
both object move at opposite direction.

Total Momentum Total Momentum
before collision after collision :
Is zero m1v1 + m2v2
From the law of conservation of
momentum:
Total Momentum = Total Momentum
Before collision after collision
0 = m1v1 + m2v2
m1v1 = - m2v2

-ve sign means opposite direction
EXAMPLES OF EXPLOSION (Principle Of Conservation Of Momentum)
When a rifle is fired, the bullet of mass m,
moves with a high velocity, v. This creates
a momentum in the forward direction.
From the principle of conservation of
momentum, an equal but opposite
momentum is produced to recoil the riffle
backward.

Application in the jet engine:
A high-speed hot gases are ejected from the
back with high momentum.
This produces an equal and opposite
momentum to propel the jet plane forward.



The launching of rocket
Mixture of hydrogen and oxygen fuels burn
explosively in the combustion chamber.
Jets of hot gases are expelled at very high
speed through the exhaust.
These high speed hot gases produce a large
amount of momentum downward.
By conservation of momentum, an equal but
opposite momentum is produced and acted
on the rocket, propelling the rocket
upwards.
In a swamp area, a fan boat is used.
The fan produces a high speed movement of
air backward. This produces a large
momentum backward.
By conservation of momentum, an equal but
opposite momentum is produced and acted
on the boat. So the boat will move forward.

A squid propels by expelling water at high
velocity. Water enters through a large opening
and exits through a small tube. The water is
forced out at a high speed backward.
Total Mom. before= Total Mom. after
0 =Mom water + Mom squid
0 = mwvw + msvs
-mwvw = msvs
The magnitude of the momentum of water and
squid are equal but opposite direction.
This causes the squid to jet forward.



Example Example

Car A of mass 1000 kg moving at
20 ms-1 collides with a car B of mass
1200 kg moving at 10 m s-1 in same
direction. If the car B is shunted
forwards at 15 m s-1 by the impact, Before collision After collision
what is the velocity, v, of the car A MA = 4 kg MB = 2 kg
immediately after the crash? UA = 10 m/s to the left
UB = 8 m/s to the right
VB = 4 m/s to the left.
Calculate the value of VA .

Example Example

A man fires a pistol which has a
A truck of mass 1200 kg moving at
mass of 1.5 kg. If the mass of the
30 m/s collides with a car of mass
bullet is 10 g and it reaches a
1000 kg which is traveling in the
velocity of 300 m/s after shooting,
opposite direction at 20 m/s. After
what is the recoil velocity of the
the collision, the two vehicles move
pistol?
together. What is the velocity of
both vehicles immediately after
collision?



2.5 FORCE

Balanced Force Example:
When the forces acting on
an object are balanced, they
cancel each other out.
The net force is zero.

Effect :
the object at is at rest [
velocity = 0]
or moves at constant
velocity [ a = 0]

Weight, W = Lift, U Thrust, F = drag, G

Unbalanced Force/ When the forces acting on an object are not
Resultant Force balanced, there must be a net force acting
on it.
The net force is known as the unbalanced
force or the resultant force.

Effect : Can cause a body to
- change it state at rest (an object will
accelerate
- change it state of motion (a moving
object will decelerate or change its
direction)

Force, Mass & Acceleration
Newton’s Second The acceleration produced by a force on an object
Law of Motion is directly proportional to the magnitude of the net
force applied and is inversely proportional to the
mass of the object. The direction of the
acceleration is the same as that of the net force.

Force = Mass x Acceleration
When a net force, F, acts F = ma
on a mass, m it causes
an acceleration, a.


Relationship aαF
between a & F The acceleration, a, is directly
proportional to the applied force, F.

Relationship a∝
1
between a and m
m The acceleration of an object is
inversely proportional to the mass,

Experiment to Find The Relationship between Force, Mass & Acceleration

Relationship a&F a&m
between
Situation

Both men are pushing the Both men exerted the same
same mass but man A strength. But man B moves
puts greater effort. So he faster than man A.
moves faster.
Inference The acceleration The acceleration produced
produced by an object by an object depends on
depends on the net force the mass
applied to it.

Hypothesis The acceleration of the The acceleration of the
object increases when object decreases when the
the force applied mass of the object
increases increases

Variables:
Manipulated : Force Mass
Responding : Acceleration Acceleration
Constant : Mass Force

Apparatus Ticker tape and elastic cords, ticker timer, trolleys,
and Material power supply and friction compensated runway and
meter ruler.


Procedure : An elastic cord is hooked An elastic cord is hooked
- Controlling over the trolley. The over a trolley. The elastic
manipulated elastic cord is stretched cord is stretched until the
variables. until the end of the end of the trolley. The
trolley. The trolley is trolley is pulled down the
pulled down the runway runway with the elastic
with the elastic cord cord being kept stretched
being kept stretched by by the same amount of
the same amount of force force

- Controlling Determine the Determine the acceleration
responding acceleration by analyzing by analyzing the ticker
variables. the ticker tape. tape.
v−u v−u
Acceleration a = Acceleration a =
t t

Repeat the experiment by Repeat the experiment by
- Repeating using two , three, four using two, three, four and
experiment. and five elastic cords five trolleys.

Recording
data

Analysing
data



1. What force is required to move a 2. Ali applies a force of 50 N to
2 kg object with an acceleration move a 10 kg table at a constant
of 3 m s-2, if velocity. What is the frictional
(a) the object is on a smooth force acting on the table?
surface?
(b) The object is on a surface where
the average force of friction
acting on the object is 2 N?

3. A car of mass 1200 kg traveling 4. Which of the following systems
at 20 m/s is brought to rest over a will produce maximum
distance of 30 m. Find acceleration?
(a) the average deceleration,
(b) the average braking force.

2.6 IMPULSE AND IMPULSIVE FORCE

Impulse The change of momentum m = mass
mv - mu u = initial
Unit : kgms-1 or Ns velocity
Impulsive The rate of change of momentum in a v = final
Force collision or explosion velocity
t = time
Unit = N
Effect of Impulsive force Longer period of time →Impulsive
time is inversely force decrease
proportional to Shorter period of time →Impulsive
time of contact force increase


Situations for Reducing Impulsive Force in Sports
Situations Explanation
Thick mattress with soft surfaces are used in
events such as high jump so that the time
interval of impact on landing is extended, thus
reducing the impulsive force. This can prevent
injuries to the participants.

Goal keepers will wear gloves to increase the
collision time. This will reduce the impulsive
force.

A high jumper will bend his legs upon landing.
This is to increase the time of impact in order to
reduce the impulsive force acting on his legs.
This will reduce the chance of getting serious
injury.
A baseball player must catch the ball in the
direction of the motion of the ball. Moving his
hand backwards when catching the ball
prolongs the time for the momentum to change
so as to reduce the impulsive force.

Situation of Increasing Impulsive Force
Situations Explanation
A karate expert can break a thick wooden slab
with his bare hand that moves at a very fast
speed. The short impact time results in a large
impulsive force on the wooden slab.

A massive hammer head moving at a fast
speed is brought to rest upon hitting the nail.
The large change in momentum within a short
time interval produces a large impulsive force
which drives the nail into the wood.



A football must have enough air pressure in it
so the contact time is short. The impulsive
force acted on the ball will be bigger and the
ball will move faster and further.

Pestle and mortar are made of stone. When a
pestle is used to pound chilies the hard
surfaces of both the pestle and mortar cause
the pestle to be stopped in a very short time. A
large impulsive force is resulted and thus
causes these spices to be crushed easily.

Example 1
A 60 kg resident jumps from the first
floor of a burning house. His
velocity just before landing on the
ground is 6 ms-1.
(a) Calculate the impulse when his
legs hit the ground.
(b) What is the impulsive force on
the resident’s legs if he bends
upon landing and takes 0.5 s to
stop?
(c) What is the impulsive force on
the resident’s legs if he does not
bend and stops in 0.05 s?
(d) What is the advantage of bending
his legs upon landing?

Example 2
Rooney kicks a ball with a force of
1500 N. The time of contact of his
boot with the ball is 0.01 s. What is
the impulse delivered to the ball? If
the mass of the ball is 0.5 kg, what is
the velocity of the ball?



2.7 SAFETY VEHICLE

Component Function
Headrest To reduce the inertia effect of the driver’s head.
Air bag Absorbing impact by increasing the amount of time the
driver’s head to come to the steering. So that the
impulsive force can be reduce
Windscreen The protect the driver
Crumple Can be compressed during accident. So it can increase
zone the amount of time the car takes to come to a complete
stop. So it can reduce the impulsive force.
Front Absorb the shock from the accident. Made from steel,
bumper aluminium, plastic or rubber.
ABS Enables drivers to quickly stop the car without causing
the brakes to lock.
Side impact Can be compressed during accident. So it can increase
bar the amount of time the car takes to come to a complete
stop. So it can reduce the impulsive force.
Seat belt To reduce the inertia effect by avoiding the driver from
thrown forward.



2.8 GRAVITY

Gravitational Objects fall because they are pulled towards the Earth
Force by the force of gravity.

This force is known as the pull of gravity or the earth’s
gravitational force.

The earth’s gravitational force tends to pull everything
towards its centre.

Free fall An object is falling freely when it is falling under the
force of gravity only.
A piece of paper does not fall freely because its fall is
affected by air resistance.
An object falls freely only in vacuum. The absence of
air means there is no air resistance to oppose the
motion of the object.
In vacuum, both light and heavy objects fall freely.
They fall with the same acceleration ie. The
acceleration due to gravity, g.
Acceleration Objects dropped under the influence of the pull of
due to gravity with constant acceleration.
gravity, g This acceleration is known as the gravitational
acceleration, g.
The standard value of the gravitational acceleration,
g is 9.81 m s-2. The value of g is often taken to be 10
m s-2 for simplicity.
The magnitude of the acceleration due to gravity
depends on the strength of the gravitational field.

Gravitational The gravitational field is the region around the earth in
field which an object experiences a force towards the centre
of the earth. This force is the gravitational attraction
between the object and the earth.

The gravitational field strength is defined as the
gravitational force which acts on a mass of 1 kilogram.
F
g= Its unit is N kg-1.
m


Gravitational field strength, g = 10 N kg-1
Acceleration due to gravity, g = 10 m s-2

The approximate value of g can therefore be written
either as 10 m s-2 or as 10 N kg-1.

Weight The gravitational force acting on the object.
Weight = mass x gravitational acceleration
W = mg SI unit : Newton, N and it is a vector quantity

Comparison Mass Weight
between The mass of an object is The weight of an object is
weight & the amount of matter in the force of gravity acting
mass the object on the object.
Constant everywhere Varies with the magnitude
of gravitational field
strength, g of the location
A scalar quantity A vector quantity
A base quantity A derived quantity
SI unit: kg SI unit : Newton, N
The
difference
between a
fall in air and
a free fall in
a vacuum of
a coin and a
feather.

Both the
coin and the At vacuum state: At normal state:
feather are There is no air resistance. Both coin and feather will
released The coin and the feather fall because of gravitational
simulta- will fall freely. force.
neously from Only gravitational force Air resistance effected by
the same acted on the objects. the surface area of a fallen
height. Both will fall at the same object.
time. The feather that has large
area will have more air
resistance.
The coin will fall at first.


(a) The two sphere are (b)The two spheres are
falling with an falling down with the
acceleration. same acceleration

The distance between The two spheres are at
two successive images the same level at all
of the sphere increases times. Thus, a heavy
Two steel showing that the two object and a light object
spheres are spheres are falling with fall with the same
falling under increasing velocity; gravitational
gravity. The falling with an acceleration.
two spheres acceleration.
are dropped Gravitational
at the same acceleration is
time from independent of mass.
the same
height.

Motion graph for free fall object
Free fall object Object thrown upward Object thrown upward
and fall

Example 1
A coconut takes 2.0 s to fall to the
ground. What is
(a) its speed when it strikes the
ground
(b) the height of the coconut tree.



2.9 FORCES IN EQUILIBRIUM

Forces in When an object is in equilibrium, the resultant force acting
Equilibrium on it is zero.
The object will either be
1. at rest
2. move with constant velocity.
Newton’s
3rd Law
Examples( Label the forces acted on the objects)

Resultant A single force that represents the combined effect of two of
Force more forces in magnitude and direction.

Addition of Forces
Resultant force, F = ____ + ____

Resultant force, F = ____ + ____



Two forces acting at a point at an angle [Parallelogram method]

STEP 1 : Using ruler and protractor, STEP 3
draw the two forces F1 and F2 from a Draw the diagonal of the
point. parallelogram. The diagonal
represent the resultant force, F in
magnitude and direction.

STEP 2
Complete the parallelogram

scale: 1 cm = ……

Resolution of A force F can be resolved into components
Forces which are perpendicular to each other:
(a) horizontal component , FX
(b) vertical component, FY
Inclined Plane

Fx = F cos θ Component of weight parallel to the plane
= mg sin θ
Fy = F sin θ Component of weight normal to the plane
= mg cos θ


find the resultant force

(d) (e)

Lift
Stationary Lift Lift accelerate upward Lift accelerate
downward

Resultant Force = Resultant Force = Resultant Force =

The reading of The reading of The reading of
weighing scale = weighing scale = weighing scale =



Pulley

1. Find the
resultant force, F

2. Find the
moving mass,m

3. Find the
acceleration,a

4. Find string
tension, T



2.10 WORK, ENERGY, POWER & EFFICIENCY

Work Work done is the product of an applied force
and the displacement of an object in the
direction of the applied force

W = Fs W = work, F = force s = displacement

The SI unit of work is the
joule, J 1 joule of work is done when a force of 1 N
moves an object 1 m in the direction of the
force

Calculation of Work
The displacement , s of the
The displacement, s of the object is in the object is not in the
direction of the force, F direction of the force, F

W = Fs s F

W = (F cos θ) s
W=Fs
Example 1 Example 2 Example 3
A boy pushing his bicycle A girl is lifting up a 3 kg A man is pulling a crate of fish
with a force of 25 N flower pot steadily to a along the floor with a force of
through a distance of 3 m. height of 0.4 m. 40 N through a distance of 6 m.

Calculate the work done What is the work done in
by the boy. What is the work done by pulling the crate?
the girl?



No work is done when:
The object is stationary The direction of motion of No force is applied on the
the object is perpendicular object in the direction of
to that of the applied force. displacement (the object
moves because of its
own inertia)
A satellite orbiting in
space. There is no
friction in space. No
force is acting in the
A student carrying his bag A waiter is carrying a tray direction of movement of
while waiting at the bus of food and walking the satellite.
stop

Concept Definition Formula & Unit
Power The rate at which work is W
done, or the amount of work P=
t
done per second. p = power, W = work /
energy t = time
Energy Energy is the capacity to do work.
An object that can do work has energy
Work is done because a force is applied and the
objects move. This is accompanied by the transfer
of energy from one object to another object.
Therefore, when work is done, energy is transferred
from one object to another.
The work done is equal to the amount of energy
transferred.

Potential m = mass
Energy Gravitational potential energy h = height
is the energy of an object due g = gravitational
to its higher position in the acceleration
gravitational field.
E = mgh

Kinetic Kinetic energy is the energy of m = mass
Energy an object due to its motion. v = velocity

E = ½ mv2



Principle of Energy can be changed from one form to another, but
Conservation it cannot be created or destroyed.
of Energy The energy can be transformed from one form to
another, total energy in a system is constant.

Total energy before = total energy after

Example 4 Example 5
A worker is pulling a wooden block of A student of mass m is climbing up a
weight,W,with a force of P along a flight of stairs which has the height of h.
fritionless plank at height of h. The He takes t seconds..
distance traveled by the block is x.
Calculate the work done by the worker to
pull the block.

What is the power of the student?

Example 6 Example 7
A stone is thrown upward with initial
-1
velocity of 20 ms . What is the maximum
height which can be reached by the
stone?

A boll is released from point A of height
0.8 m so that it can roll along a curve
frictionless track. What is the velocity of
the ball when it reaches point B?

Example 8 Example 9



A trolley is released from rest at point X
along a frictionless track. What is the A ball moves upwards along a frictionless
velocity of the trolley at point Y? track of height 1.5 m with a velocity of
-1
6 ms . What is its velocity at point B?

Example 10
A boy of mass 20 kg sits at the top of a
concrete slide of height 2.5 m. When he
slides down the slope, he does work to
overcome friction of 140 J. What is his
velocity at the end of the slope?



2.12 ELASTICITY

Elasticity A property of matter that enables an object to
return to its original size and shape when the
force that was acting on it is removed.

No external force is applied.
Molecules are at their equilibrium separation.
Intermolecular force is equal zero.

Compressing a solid causes its molecules to be
displaced closer to each other.
Repulsive intermolecular force acts to push the
molecules back to their original positions.

Stretching a solid causes its molecules to be
displaced away from each other.
Attractive intermolecular force acts to pull back
the molecules to their original positions.

Stretching a wire by an Its molecules are slightly displaced away from
external force: one another.
Strong attractive forces act between the
molecules to oppose the stretching
When the external force is removed:
The attractive intermolecular forces bring the
molecules back to their equilibrium separation.
The wire returns to its original position



Hooke’s Law The extension of a spring is directly proportional
to the applied force provided the elastic limit is
not exceeded.

F = kx

F= force on the spring
x = extension
k = force constant of the spring

Force extension graph Based on the graph:
Relationship between F & x :
F is directly proportional to x

The gradient of the graph represent = force
constant of the spring, k

Area under the graph equal to the work done to
extent the spring:
= elastic potential energy = ½ Fx = ½ kx2

The elastic limit of a The maximum force that can be applied to a
spring spring such that the spring will be able to be
restored to its original length when the force is
removed.
If a force stretches a spring beyond its elastic
limit, the spring cannot return to its original length
even though the force no longer acts on it.
The Hooke’s law is not obeyed anymore.

Force constant of the The force required to produce one unit of
spring, k extension of the spring.
F
k= unit N m-1 or N cm-1 or N mm-1
x

k is a measurement of the stiffness of the spring
The spring with a larger force constant is
harder to extend and is said to be more stiff.
A spring with a smaller force constant is easier
to extend and is said to be less stiff or softer.


Factors that effect elasticity
Factor Change in factorHow does it affects the
elasticity
Length Shorter spring Less elastic
Longer spring More elastic
Diameter of spring Smaller diameter More elastic
wire Larger diameter Less elastic
Diameter spring Smaller diameter Less elastic
Larger diameter More elastic
Type of material Springs made of different materials
Elasticity changes according to the type of
material

Arrangement of the spring
In series In parallel

The same load is applied to each The load is shared equally among the
spring. springs.
Tension in each spring = W Tension in each spring =
W
Extension of each spring = x 2
Total extension = 2x Extension of each spring =
x
If n springs are used: 2
The total extension = nx If n springs are used:
x
The total extension =
n
Example 1
The original length of
each spring is 10 cm.
With a load of 10 g, the
extension of each
spring is 2 cm.
What is the length of the
spring system for (a),
(b) and (c)?



SECTION A

QUESTION 1

Figure 1.1 shows a car moving along a straight line but hilly road.

Figure 1.1
Figure 1.2 shows how the velocity of the car
varies with time as it travels from A to E. The car
travels at 60 kmh-1 from A to B for two minutes.

Figure 1.2
(a) Describe the acceleration of the car as it
travels from A to E.
2
………………………………………………… m
…………………………….
(b) Compare the resultant force as it travels
along AB and CD.
1
………………………………………………… m
……………………………
(c) Give a reason to your answer in (b)

………………………………………………… 1
………………………… m
(d) Calculate the distance AB

2
m
(e) The velocity of a car increases if the
force exerted on the accelerator of a car
increases. Explain why the velocity of the
car increases from D to E although the
force on the accelerator of the car is the
same as a long C to D.
2
………………………………………………… m


……………………………

…………………………………………………
…………………………...

QUESTION 2 (SPM 1999)



(e) Why is it necessary to ha
capacity limit for the safe
A bus bus?
the traveled from Kota
QUESTION 3 ( SPM 2000) Lumpur at 9:00 pm. The cap
passenger in the bus is 40
………………………………
Figure 2 mass of the bus with the ca
……………………………
and the average frictional fo
Figure 2 shows a car of mass 1 000kg moving a bus tire and the road for the jo
………………………………
straight but hilly road. QRST and TU is the part The bus moves at average sp
……………………………
of the hill that have constant slope where the Kota Bharu before stopover a
slope of QRST is higher that the slope of TU. The at 12:00 mid night on the s
frictional force that acts along QRSTU is 2 000N. hour later the bus continue
The velocity if the car at P is Kuala Lumpur with average
80kmh-1 and takes 3 minutes to move from point The bus arrived at 6:00 am on
P to Q. The motion of the car along (a) Put in a table all the phys
PQRSTU represent by a velocity-time graph in involved in the informatio
Figure 3. two groups.

(b) Calculate the total distanc
the bus.

(c) Sketch a distance-time gr
the motion of the bus.

(d)
(i) What is the value of the tr
the bus when it moves at
speed?

(ii) ………………………………
……………………………
Give a reason for the ans

………………………………
www.physics4spm.com
……………………………
40


(a) Classify the physical quantity into two groups.

2m
(b) From the graph in Figure 3, explain the acceleration of the car from
point P to S.

…………………………………………………………………………………………

………………………………………………………………………………………… 2m
(c) (i) Compare the resultant force of the car when the move along PQ and
ST.
1m
……………………………………………………………………………………..
(ii) State a reason for your answer in c(i)
1m
……………………………………………………………………………………...
(d) Calculate the distance form point P to Q

2m


Figure 3(i)

Figure 3(ii)

Figure 3(i) shows a sky diver start to make a jump from an aircraft at a
certain height. Figure 3(ii) shows a velocity-time graph for the skydiver at
position S, T, U, V and W from the earth surface.

(a) (i) At which point the parachute start to open?

…………………………………………………………………………………… 1m
(ii) Give a reason for your answer in (a)(i)

…………………………………………………………………………………… 1m
(b) Calculate the acceleration of the diver at ST.



2m
(c) Sketch an acceleration-time graph for the motion of the skydiver at
point S, T, U, V and W at the space below.

3m
(d) Suggest one way that can the skydiver apply to reduce injuries on his
leg during landing. Explain your answer.

………………………………………………………………………………………...

……………………………………………………………………………………….. 2m


Figure 4(i)


Figure 4(i) show a gun fires a bullet of mass 5g to an object.

(a) (i) What happen to the gun during the shot?

1m
…………………………………………………………………………………..
(ii) Explain your answer in (a)(i)
1m

…………………………………………………………………………………...
(b) The bullet shot the object of mass 0.495kg.

(i) If the bullet speed is 400ms-1, what is the momentum of the
bullet?

2m

(ii) What is speed of the object after the bullet obscured into the
object after
the gunshot?
2m

(c) The object and the bullet that obscured in the object aloft at a
maximum height of H, as shown in Figure 4(ii).

Figure 4(ii)

(i) What is the value of kinetic energy of the object together with
the bullet
inside the object? 2m



(ii) Calculate maximum height, H achieved by the object?
2m

1m
(iii) In real situation it is possible to achieved maximum height, H.
Why?

……………………………………………………………………………………

……………………………………………………………………………………


Figure 5 shows a man standing on a stationary boat. He then jumps out of
the boat onto the jetty. The boat moves a way from the jetty as he jumps.

Figure 5

(a) State the physics principle that is involved in the movement of the boat
as the man jumps onto the jetty.

………………………………………………………………………………………… 1m
(b) Explain why the boat moves away from the jetty when the man jumps.

………………………………………………………………………………………… 1m
(c) The mass of the man is 50 kg and he jumps at a velocity 2ms-1. The
mass of the boat is 20kg. Calculate the velocity of the boat as the man
jumps.

2m
(d) Name one application of the physics principle stated in (a) in an
exploration of outer space.

………………………………………………………………………………………… m


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