Module_SP015

When a bat hits a ball, an
average force is applied
to the ball by the bat.
As a result, the ball’s
velocity changes from an
initial value of (top
drawing) to the final value
of (bottom drawing)

3.2 PRINCIPLE OF CONSERVATION OF
LINEAR MOMENTUM

a) Principle of conservation of linear momentum states that
the total momentum of an isolated system is constant.

b) An isolated system is a system for which the net external force is zero :

. That is, an isolated system is one on which there are no external
forces or for which the external forces are balanced and add to zero.

c) Mathematically, for an isolated system:

−+ 12 Momentum is conserved in
12
Before a 1D collision of two balls
12
During labelled 1 and 2:

After   


   

d) Since momentum is a vector quantity, the

equality is true for each components
of the momentum vector. That is,

(i) component:

2D collision (Oblique collision)

(ii) component: Apply in 2D collision (Oblique collision)
2D
collision
(Oblique
collision)

Refer example
12 ‒ 15

Collision

Collision is defined as an isolated event in which 2 or more bodies (the
colliding bodies) exert relatively strong forces on each other for a
relatively short time.

collision

Elastic Inelastic

Elastic collision

a) is defined as one in which the total kinetic energy of the system after the
collision is equal to the total kinetic energy before the collision.

b) Figure below shows the head-on collision of two billiard balls.

−+   

Before 1 2
   

During 12 Kinetic energy,    
After = ( )( )

   



1 2

Inelastic collision

a) is defined as one in which the total kinetic energy of the system is not the same
before and after the collision.

b) If the objects stick together after colliding, the collision is said to be completely inelastic.

c) Figure below shows the model of a completely inelastic collision of two billiard balls.

−+ 1 2 Caution!

Before:

During: 12 a) It is a common misconception that
After (stick together): 12
the only inelastic collisions are those in
which the colliding bodies stick together.

b) In fact inelastic collisions include
many situations in which the bodies do
not stick

Properties of elastic and inelastic collisions

elastic inelastic

Similarity Total momentum of the system is conserved.

  



Difference Total kinetic energy is    
conserved.
Total kinetic Total kinetic energy is NOT
energy    conserv ed.
before and  
after for the
system is
used to   
determine or   
prove types Some of the initial kinetic energy is
of collision. No loss of kinetic energy in the transformed into another type of
(Refer energy such as thermal or potential
Example 8) collision
energy.
The total kinetic energy after the collision is
less than the total kinetic energy before the
collision.

TOPIC 4 FORCES

4.1 Basic of forces and free body MODE Face to Non Face to
diagram (FBD) face face
Lecture SLT SLT
4.2 Newton’s laws of motion Tutorial
1 1

3 3

Prepared by ChongYL/KMJ/session 20192020

4.1 Basic of forces and free body diagram (FBD)

o Force is defined as physical quantity which Forces
causes an object to move, stop, change
its direction or change its physical form. Weight,

o A force is a push or pull on the object.

Push Force Tension, A force has
Pull Force an agent.
Normal force, Something
o A force is a vector quantity. It has both a tangible
magnitude and a direction. Friction, and
External force identifiable
o SI unit of force, is kg m s2 or Newton (N) (pull or push), causes the
force.

4.1.1 Weight of a body,

Definition: Force exerted on a body due to gravitational pull.

Formula: m is mass of the body (in kg)
g is acceleration due to gravity (Earth: 9.81 m s–2)

Direction: The weight vector always points vertically downward.
Unit : Newton (N)
Remarks Pay attention to the direction
o Weight also known as gravitational force of weight. Weight always
o varies slightly with altitude because weight depends on the
point downwards!
strength of the gravity (g).
o The greater the distance from the earth, the less the strength Weight ≠ mass
Mass is the amount of
of gravity, the less the weight a body have. matter that is contained by
the object.

4.1.2 Tension, Frictionless
pulley

Contact force exerted by a cord as it Object
Definition: pulls on an object.

Direction: It is always directed away from the Tension in a massless string is
object and along the cord. unchanged by passing over a
A B
Unit: Newton (N) frictionless pulley. Tension of the
string is the same on both sides
o The cord has negligible mass, of a pulley.
unbreakable, un-stretchable, and
frictionless

Remarks: o The tension is the same at all
points in the rope. (Same string

possessed same tension.) Direction of
tension force is
o e.g. of cord: string, chain, wire, always away
cable or etc. from the object.

4.1.3 Normal Force,

Definition: Normal force is defined as a
reaction force that is exerted by the
surface to an object in contact with
the surface.

Direction: Normal force is always perpendicular
to the surface.

Unit: Newton (N)
Remarks:
Normal force, NOT always has
to be the same as Weight, .

The surface pushes outward against the
bottom of the object. The normal force is
perpendicular to the surface.

4.1.4 Friction,

Definition: Friction is defined as a force that opposes the relative motion of two
Direction: surfaces in contact.
Unit:
acts PARALLEL to the surface in contact and in the OPPOSITE direction of the
Remarks: motion (or tendency of motion)

Newton (N)

o Friction is directly proportional to the reaction force.
o Equation :

where friction force ; : coefficient of friction ; : normal force
o Coefficient of friction, is defined as the ratio between frictional force to

normal force.

o depends on the nature of the surfaces.

o There are two types of friction: (i) Static friction, (ii) Kinetic friction,
o In general thus

4.1.4.(a) Static Friction force, (at rest)

is the force that keeps an object “stuck” Object tends to
slide down. Thus to
Definition: on a surface and prevents its motion. Rough prevent it slide
surface down, static friction
(frictional force before the object start is acting upwards

moving, )

Static friction is parallel to surface in
Direction: contact and points opposite the direction

of tendency of motion.

Remarks: May have different values up to some
maximum.



Just before an object starts to slide (verge of

motion), is maximum

( )

: coefficient of static friction
: Normal force

4.1.4.(b) Kinetic Friction force, o The agent for friction is
rough surface.
Definition: The frictional force exists between 2 object, when there
is relative motion between at the interface of the o In our syllabus, the
surface contact. surface is always
smooth unless stated
Formula: : coefficient of kinetic friction rough surface or given
: Normal force value of .

kinetic friction is parallel to surface in contact and points Rough surface
Direction: opposite direction of velocity (“the motion”).

Rough surface 1.0 kg does not have
any friction force
because it does not
contact with any rough
surface

NON FACE TO FACE SLT

1) Fig. (a) & (b) For small applied forces

, the magnitude of the force of static

friction ⃗ equals the magnitude of the
applied force. No movement.
2) Fig. (c) When the magnitude of the

applied force exceeds the magnitude
of the maximum force of static friction

⃗ , the block can breaks free and
begin to move.
3) Once the block start to move, the force
of friction change to kinetic friction. If
the force larger than the kinetic friction,
the block can accelerates to the right.

4.1.5 External Force,

Definition A force exerted on a system by an agency
outside the system

Depending on the direction of application
Direction as stated in the question.

Unit Newton (N)

Remarks External force can either be push or pull
force exerted on the object.

CAUTION!

Do NOT add in external force by your own.

Forces and motion problems generally have two A force has an agent.
basic steps:
Something tangible and identifiable
1) Identify all the forces acting on the object causes the force.
2) Apply Newton’s laws and kinematics to
4 criteria questions for
determine the motion.
identifying forces:
Identifying Forces
is the primary goal 1) Have mass and on earth
in subtopic 4.1 gravity pull?  Weight

It is important to identify correctly all the forces 2) contact with surface?  Normal
acting on the object. It is equally important not to
include forces that do not really exist. Force

3) Rough surface or is
mentioned?  Frictional Force

4) string/chain/cord/rope/wire?

 Tension

For external force, just redrawn as
stated in question !

Free body Diagram (FBD)

A diagram used to show ALL forces acting on upon an object in
a given situation.

Drawing a free-body diagram

1) Identify all forces acting on the object.
2) Draw a coordinate system. Use the axes defined in your pictorial

representation. If those axes are tilted, for motion along an incline, then the
axes of the free-body diagram should be similarly tilted.
3) Represent the object as a dot at the origin of the coordinate axes.

4) Draw vectors representing each of the identified forces. Be sure to label
each force vector. CAUTION ! All force vectors are drawn from the

point outward in the direction in which the forces are acting.

Case 1 : Horizontal surface Case 2 : inclined plane

smooth rough

Case 3 : Hanging object Case 4 : Pulley

knot = 0.34

::

Knot: :

4.2 Newton’s laws of motion

Newton’s first law Net force also refer as Mass vs Weight

resultant force,  
 

states “if there is no net force acting on an 1 1 kg object weigh only
kg one-sixth as much as it
object ( ), object that is at rest will did on earth, since gravity
remain at rest, or an object that is moving will is weaker. But its mass
will be the same.

continue to move in straight line with
constant velocity.

Newton’s first law give the idea of inertia:

Inertia • is defined as the tendency of a A bigger mass
body to resist change in needs a bigger
motion. force to overcome
its inertia and
• depends on mass change its
motion.

Newton’s First Law  Equilibrium of a particle

a) A particle is said to be in equilibrium c) Two types of equilibrium of a particle.
when the vector sum of all forces
acting on a particle (point) equals i. Static equilibrium ( )
to zero. body at rest (stationary).

b) It is easier to work with the equation i. Dynamic equilibrium ( )
in terms of its component: body moving at a uniform

(constant) velocity.

Keywords constant , at rest, in equilibrium, static,
for at the verge of motion, just begin to slide,
static equilibrium, dynamic equilibrium, all
Newton’s
First Law forces acting are balanced.

Newton’s second law a) Newton’s second law can
also be w  ritten as:
The rate of change of momentum of a
moving body is proportional to the net   
force and is in the same direction as the net
  
force acting on it.
It can be represented by,  

  Mass is constant,

  Therefo  re,
 
  
 

 where   : net force
 
: mass

: acceleration

b) Rearrange : ∑   ⃗ o One newton

c) The acceleration of an object is (1 N) is defined
directly proportional to the net force as the amount
acting on it and inversely of net force
proportional to its mass. that gives an
acceleration
d) The direction of net force is in of 1 m s−2 to a
the same direction as body with a
acceleration. mass of one
kilogram
Keywords for accelerates, unbalanced
Newton’s forces, resultant (net)
force acting
Second Law

Tips to write 1) Identify the direction of
Newton’s
second law 2) { Force(s) IN direction of } – { Force(s) OPPOSITE to }
equation

Newton’s third law When you push on the wall, it
will push back with the same
force

Every action force has a reaction force that is
equal in magnitude but opposite in
direction.

Reaction Action

When two bodies interact, the action is also called normal force
and reaction forces act on different Reaction
bodies. They do not cancel out.

FF

Action

NON FACE TO FACE SLT

PROBLEM SOLVING STRATEGY
TO APPLY NEWTON’S LAWS

1. Draw free body diagram showing ALL the forces acting on the object.

o Identify the object whose is considered and represent the object by a point (●)

To identify the forces acting, ask yourselves 5 Questions.
 Is there mass of object, under gravity pull ? Got mass  Weight,
 Is the object in contact with a surface? In contact  Normal Force,

 Is the coefficient of friction given (μ) or is it mentioned that the surface is rough?

Got μ / rough surface  Frictional ( or )
 Is there string/chain connected to the object? Got string/chain 

Tension,

 Is there any external forces acting on the object as stated in question given?

Got external forces 

Hint: external F (if any) you just need to redraw as stated in question.

22

NON FACE TO FACE SLT

PROBLEM SOLVING STRATEGY
TO APPLY NEWTON’S LAWS

2. Choose a system of coordinates ( and axes) so that calculations may be
simplified.
*Tips : always let the direction of motion to be one of the axes

3. Resolve the forces into and components
4. Apply the suitable Newton’s law to both axes to solve for the unknown

quantities.

a) Axis parallel to motion :

if system in equilibrium (static or dynamic)   
 

if system accelerate   
 

b) Axis perpendicular to motion :  
 

23

Figure shows a 0.4 kg ① FBD ⃗ ④ Apply Newton’s law to solve the problem.
block being pushed ⃗
against a rough vertical Refer keyword: remains stationary apply Newton
wall by a force F at angle first law for both and axis.
45° with respect to the
horizontal. The block Along axis :
remains stationary. If the ③ resolve ∑   = 0
coefficient of static forces (if any) 45 − = 0
friction, μs = 0.20, what is N = 0.7071 …(1)
the magnitude of F?
Along axis:
⃗ 45 ⃗ ∑   = 0
45 + − = 0
⃗ 45 + − = 0
0.7071 + 0.20 − 0.4(9.81) = 0 …(2)
45°
Put (1) into (2)
0.7071 + 0.20(0.7071 ) − 0.4(9.81) = 0
⃗ 45 0.7071 + 0.1414 − 3.924 = 0
0.8485 = 3.924
② choose axes
N

NON FACE TO FACE SLT

Figure below shows a ① FBD ④ Apply Newton’s law to solve the problem.
block sliding down on an
incline at 37° with the ⃗ Along axis : System accelerate
horizontal. The coefficient ∑   = ma along inclined
of kinetic friction between plane ( ) apply
the block and the incline 37 − = Newton second
plane is 0.20.
Calculate the 37 − = …(1) law for axis.
acceleration of the block.
Along axis: Axis perpendicular to
Identify direction of motion ( ) ∑   = 0 motion ( ) apply
− 37 = 0 Newton first law.
= 37 …(2)

② choose axes Put (2) into (1):
37° 37 − ( 37) =
③ resolve forces (if any) ⃗ 9.81 37 − 0.2 9.81 37 =

37° m s−2

37 NON FACE TO FACE SLT



Two objects are connected by ① FBD ④ Apply Newton’s law to solve the problem.

a light string that passes over a : : Consider :
⃗
frictionless pulley as in the Along axis : accelerate
∑   = upwards apply
figure. The kinetic friction acts − = Newton second law
for axis.
on is 4.5 N. Given m1 = − 2(9.81) = 2
2.00 kg, m2 = 6.00 kg and  =
55, calculate the ② choose axes − 2 = 19.62 …(1)
(i) acceleration of the objects,
(ii) tension in the string

Consider : System
accelerate
Identify direction of motion ( ) Along inclined plane ( ) axis : along inclined
∑   = plane ( )

55 − − = apply Newton
6 9.81 55 − − 4.5 = 6 second law for

⃗

+ 6 = 43.72 …(2) axis.

③ resolve Solve (1) & (2) using mode EQN
forces (if
any) = . N

= . m s−2
NON FACE TO FACE SLT

Topic 5
Work, Energy and Power

Subtopic :
5.1 Work
5.2 Energy and Conservation of Energy
5.3 Power

MODE Face to face Non Face to face
Lecture SLT SLT
Tutorial 1.5
1.5
7
7

Learning outcomes

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

5.1 Work

(a) Define work done bysa constant force, (c) State and apply work-energy theorem
W F
Lecture : C2,PLO1, MQF LOD1)
(Lecture : C2,PLO1, MQF LOD1) (Tutorial : C4, PLO4, CTPS3, MQF LOD6)

(b) Apply work done by a constant force 5.3 Power
and from a force-displacement
graph. (a) Define and use average power,

(Tutorial : C4, PLO4, CTPS3, MQF LOD6) W
t
5.2 Energy and Conservation of Energy Pav 

(a) State the principle of conservation and instaPntanFeouvs power
of energy.

(Lecture : C2,PLO1, MQF LOD1) (Lecture : C2,PLO1, MQF LOD1)
(Tutorial : C4, PLO4, CTPS3, MQF LOD6)
(b) Apply the principle of conservation of
energy (mechanical energy and heat
energy due to friction)

(Tutorial : C4, PLO4, CTPS3, MQF LOD6)

5.1 Work

5.1.1 Work done by a constant force

Definition F sin θ Only || does
work on the body
does no work
on the body.

scalar product between force θ
and displacement of a body. || F cos θ

the product of the magnitude Equation
of displacement times the
component of the force (s)
parallel to the displacement.

: Magnitude of force
: displacement of a body

: angle between ⃗ and ⃗

o Work is a scalar quantity. Work does not have direction.
However, it can have
o SI unit of work is Nm or
Joules (J). positive, zero or negative value
depending on the angle θ between
o 1 J can be defined as work
F and s.
done by a force of 1 N which
results in a displacement of W > 0 (positive) W < 0 (negative)
1 m in the direction of force.
If : If :

0< < 90 90< <180
then cos > 0 then cos < 0

(positive value) (negative value)

means: means:

work done on the work done by the

system (by the external system where energy
force) where energy is is transferred from
transferred to the
the system.

system.

Situation Work done Example (LO 5.1 b) Non Face-to-face SLT

= 5 = A person pulls a 50-kg crate 40 m along a horizontal
= 5 10 0 floor by a constant force = , which acts at °
= 10 = Nm angle as shown in figure below. The floor is rough and
= 5 exerts a friction force = . Determine work done
= by each forces.
60° = 5 10 60
=25 Nm
= 10
= 5 = 37°
= 5 10 90
= Nm
= 40
=
= 5 10 120
= − Nm
= 10 Nm Nm
= Nm
120° = 5 10 180 & is ⊥ to s
= 5 = − Nm = 90°
cos = 0
= 10
Nm
= 5

= 10

(b) A person

(a) A person holding cos moving the
a briefcase does briefcase
no work on it
because there is horizontally
no motion (
). at a

(c) When the briefcase is lowered, the work done on constant
the briefcase by the generator is negative
because F and s are in opposite direction. speed,

Work done by forces that oppose the force F

direction of motion, such as friction will be does no

negative. work on it

because F

is

cos

o If there is more than one force acting on a body,

The total, or net, work is defined +
+
as work done by all the forces acting +
on the body or scalar sum of all those OR
quantities of work.
Total work also refer as nett
work,

5.1.2 Work done from a force−displacement graph

F/N

0 s1 Work

s2 s/m

Work done = the area under force-displacement graph

5.2 Energy and Conservation of energy

Work done to lift the box
is changed to potential
energy at final position.

Doing work involves a transfer of energy
from one form to another form.

Energy is defined as the stored
ability to do work.

o Scalar quantity
o S.I unit for energy is joule (J)
o 2 types of mechanical energy:

(1) Potential Energy, U
(2) Kinetic Energy, K

Kinetic Energy, K

Definition:

Energy of a body due to its motion

Equation : 1
2
K  mv 2

K : kinetic energy of a body

m : mass of a body
v :speed of a body

Is a scalar quantity; it depends on only the
body’s mass and speed and not its direction

of motion.

Potential Energy, U

Energy stored in a body or system
because of its position, shape and state.

Gravitational Elastic
potential energy, U potential energy , U

Definition: Definition

Energy stored in a body or system because of its Energy stored in elastic materials as the result of
position their stretching or compressing.

Equation: Equation:

U  mgh U  1 kx2
2
U: gravitational potential energy
m: mass of a body U: elastic potential energy
g: acceleration due to gravity k: spring constant
h: height of a body from the initial position. x: compression or extension of the spring

Force-extension graph (F-x graph) for spring

Spring is a device which can store elastic potential energy due to its compression
or stretching; releasing the spring transforms it into kinetic energy.

Hooke’s Law Fxs is negative  
is positive Fs F

The force required to compress or x

stretch a spring is: (Negative sign indicates direction x0 Fxs  0
 0
Fs  kx of restoring force, is always
opposite to the direction of the
amount of stretching or

where compression , (Equilibrium position)

Fs : the restoring force of spring  x 0 Fxs is positive
F Fs is negative
k : the spring constant or force constant
x
x : the amount of stretch or compressio n (x f -xi )

• Caution:

– For calculation, ignored negative sign and use : Fs  kx  F where F : applied force

– Dimension of spring constant, k :

k   Fs   MT 2
x

– The unit of k is kg s2 or N m1

• From the Hooke’s law (without “” sign), a restoring force, Fs against extension

of the spring, x graph is shown in Figure below

Fs Work done to stretch a spring a distance :

F W  area under the Fs  x graph

W  1 Fx W  1 kxx Work done
2 2 is stored as
elastic

0 xx W  1 kx2 U potential
2 energy in
spring

Work Energy Theorem

o Consider a block with mass, moving • By using an equation of linear motion:
along the horizontal surface (frictionless)
under the action of a constant net force, v2  u2  2as

undergoes a displacement, : a  v2 u2 (2)
2s
• By substituting eq. (2) into (1),

Fnett  m v2 u2 
2s

Fnett s  1 mv2  1 mu2
2 2

Fnetts  K f  Ki

 F  Fnett  ma (1) {Work energy
theorem}

Work Energy Theorem

states “the work done by the net force on a body equals the
change in the body’s kinetic energy”.

o When Wnet is positive, o When Wnet is o When Wnet is 0, the
the kinetic energy negative, the kinetic kinetic energy stays
increases (the final energy decreases (Kf the same (Ki = Kf)
kinetic energy Kf is is less than Ki) and and the speed is
greater than the the speed is less unchanged
initial kinetic energy after the (constant).
Ki) and the particle is displacement.
going faster at the
end of the
displacement

Principle of conservation of Principle of conservation of
energy mechanical energy

states “in an isolated (closed) states “In a conservative
system, the total energy of system (for example no
that system is always friction), the total mechanical
constant”. energy (Kinetic + Potential) is
constant.“

Energy can be transferred Conservative system means

from one form to another, such as only conservative forces such as
from mechanical energy to heat
gravitational and elastic
energy but it cannot be forces are acting on the system.
destroyed or created



Highest position, A :  
 

Position B :  
 

Lowest position,C :  
 



′