Dynamics
Name: ________________
Class: _________________
Index: ________________
Learning Objectives
1) State each of Newton's 1st and 2nd laws of motion.
2) State Newton’s 3rd law of motion.
3) Describe the effect of balanced and unbalanced forces on a body.
4) Describe the ways in which a force may change the motion of a body.
5) Show an understanding that mass is the property of a body which resists change in
motion.
6) State that a gravitational field is a region in which a mass experiences a force due to
gravitational attraction.
7) Define gravitational field strength g as gravitational force per unit mass.
8) Identify forces acting on an object and draw free body diagram(s) representing the
forces acting on the object (for cases involving forces acting in at most two
dimensions)
9) Describe and use the concept of weight as the effect of a gravitational field on a
mass.
10) Define linear momentum as the product of mass and velocity.
11) Define force as rate of change of momentum.
12) Recall and solve problems using the relationship F = ma, appreciating that
acceleration and force are always in the same direction.
13) Apply the relationship between resultant force, mass and acceleration to new
situations or to solve related problems.
14) Describe the motion of bodies with constant weight falling with or without air
resistance, including reference to terminal velocity.
What’s a Force?
It’s a push or a pull that one object exerts on another. It can change the state of motion
of an object. It may change the shape of an object.
S.I. unit of a force is the newton (N). Examples of forces include friction, weight &
air resistance.
Forces are vectors and can be added by considering both direction and magnitude
Forces Acting on a Body
2N
4N
Net Force
6N
4N
0N
4N
6N
10 N
4N
6N
7N
3N
4N
No net
force
Example
Addition of Vectors
How large must force X on the car (Porsche 911) be such
that the resultant force on the car is ZERO?
X
800 N
300 N
Work out the answer!
Addition of Vectors
How large must force X on the car (Porsche 911) be such that the
resultant force on the car is ZERO?
X
800 N
300 N
When resultant force is zero, the forces balance out.
Force X + 300 N = 800 N
Force X = 800 - 300 N
Force X = 500 N (to the left)
Newton’s First Law of Motion
An object at rest will remain at rest and an object in motion will
continue in motion at constant speed in a straight line in the absence
of a resultant force acting on it.
Note:
No net force does not
mean there are no forces
acting on it but just that
they are balanced.
An object at rest will remain at rest and an object in motion will
remain in constant speed in straight line in absence of net force
acting on it.
Think about a stationary ball lying on the ground:
Unless you kick it (exert net force), it will remain at rest.
There are forces acting on the ball, but these forces balance out and
hence there is no net force.
Force exerted by ground on ball
ground
Weight of ball
An object at rest will remain at rest and an object in motion will remain
in motion at a constant speed in straight line in absence of net force
acting on it.
Assuming no friction and air resistance,
When a ball is kicked into motion, it will travel in straight line at
constant speed, v.
It will continue its motion in straight line at constant speed. (ideal
situation)
Constant
speed
Unbalanced forces
To change motion of an object (speed, direction etc), a
net force is needed.
When the forces do not balance out, there is a net force.
When this happens,
1) A stationary object will start to move or moving object
stops.
2) The speed of moving object changes
(acceleration/ deceleration).
3) Moving object changes its direction of motion.
Newton’s Second Law of Motion
States that the resultant force acting upon an object is equal
to the product of the mass and the acceleration of the object;
the direction of the force is the same as that of the object’s
acceleration.
F=ma
where F = resultant force or net force (N);
m = mass of the object which the net force is acting
on (kg);
a = acceleration of the object (ms-2)
Definition of the newton (N)
a = 1 m/s2
One newton is defined as the force
required to produce an acceleration of 1
m/s2 in a body with a mass of 1 kg.
1 kg
Example 1:
A boy pushes a large box of mass 5 kg with a force of 20 N.
What is the acceleration of the box?
a=?
5 kg
20 N
1N
Example 1:
A boy pushes a large box of mass 5 kg
with a force of 20 N.
What is the acceleration of the box?
a = 4 m/s2
Given F = 20 N, m = 5 kg
Since F = m a,
5 kg
20 N = (5 kg) a
a = 20 N / 5 kg
= 4 m/s2
20 N
Example 2:
A car of mass 1000 kg accelerates from rest to 20 m/s in a time of 5
seconds. Calculate the forward thrust of the car.
u = 0 m/s, v = 20 m/s, t = 5 s
Forward thrust
m = 1000 kg
Example 2:
A car of mass 1000 kg accelerates from rest to 20 m/s in
a time of 5 seconds. Calculate the forward thrust of the
car.
Given, m = 1000 kg
u = 0 m/s, v = 20 m/s, t = 5 s
a = (v – u) / t
= (20-0)/5
= 4 m/s2
F=ma
F = (1000 kg)(4 m/s2)
F = 4000 N
4000 N
m = 1000 kg
Example 3:
The force on an aircraft of mass 725 kg due to the engine
is 15 000 N. The air resistance on the plane is 9925 N.
Find the acceleration of the plane.
Example 3:
The force on an aircraft of mass 725 kg due to the engine is 15 000 N.
The air resistance on the plane is 9 925 N.
Find the acceleration of the plane.
Net F = 15 000 N – 9 925 N = 5 075 N (to right)
Given m = 725 kg
F=ma
5 075 N = (725 kg) a
a = (5 075 N) / (725 kg)
a = 7 m/s2 (to right)
Inertia
Newton’s first law tells us that objects have in-built resistance to any
change in their motion.
A stationary object only starts to move when you apply a resultant
force.
A moving object keeps moving at a steady speed in a straight line. To
change the speed or direction, you need to apply another resultant
force.
The reluctance to change velocity is called inertia. The inertia of an
object depends on its mass. A bigger mass needs a bigger force to
overcome its inertia and change its motion.
Your personal experience:
1) What overcomes your inertia as the car accelerates?
2) What happens as you turn a corner?
3) What happens when the car decelerates?
1) What overcomes your inertia as the car accelerates?
You can feel the car seat pushing against your back to move you forward.
2) What happens as you turn a corner?
Your body tries to keep moving in a straight line, while the car turns the corner. You
feel as if you are being pushed into the side of your seat.
3) What happens when the car decelerates?
Your inertia keeps you moving and you lurch forward. If the car brakes suddenly
and you are not properly restrained, you will keep moving forward at high speed
until the airbag, steering wheel or windscreen forces a change in your motion!
Gravitational Field Strength
Gravity is a force that attracts objects with mass towards each other. The
weight of an object is the force acting on it due to gravity. The
gravitational field strength of the Earth is 10 N/kg.
Weight is not the same as mass. Mass is a measure of how much stuff is
in an object. Weight is a force acting on that stuff.
You have to be careful. In physics, the term weight has a specific
meaning, and is measured in Newtons. Mass is measured in kilograms.
The mass of a given object is the same everywhere, but its weight can
change.
Weight is the result of gravity. The gravitational field strength of the
Earth is 10 N/kg (ten newtons per kilogram). This means an object
with a mass of 1kg would be attracted towards the centre of the Earth
by a force of 10N. We feel forces like this as weight.
You would weigh less on the Moon because the gravitational field
strength of the Moon is one-sixth of that of the Earth. But note that
your mass would stay the same.
Weight
A special case of Newton’s Second Law (F = m a)
is for an object being pulled by gravity.
When F = Weight of object = W (in newton, N);
When m = mass of object = m (in kilogram, kg);
When a = acceleration due to gravity = g (in m/s2 or N/kg)
w=mg
F=ma
Question:Scenario 1:
When the resultant force acting on an object is zero,
does it mean that the object is necessarily stationary?
Object is stationary at first with no forces acting on it.
No force is acting on object,
the resultant force is then zero
(since no force is present in the first place).
The object remains stationary.
Question:
When the resultant force acting on an object is zero,
does it mean that the object is necessarily stationary?
1N
3N
8N
5N
1N
Scenario 2:
Object is stationary and forces act on it.
Forces acting on it cancel out each other,
the resultant force is then zero
(total horizontal force is zero, total vertical force is zero).
The object still remains stationary.
Question:
When the resultant force acting on an object is zero,
does it mean that the object is necessarily stationary?
Velocity = 3 m/s
Scenario 3:
Object is moving at constant speed with no forces acting on
it.
When the object is already moving at a certain velocity
& no other forces are acting on it,
- resultant force is zero
(since there are no forces present in the first place).
- The object is still moving at the same velocity.
Question:
When the resultant force acting on an object is zero,
does it mean that the object is necessarily stationary?
3N
1N
5N
Velocity = 3 m/s
8N
1N
Scenario 4:
When the object is already moving at a certain velocity
& all the forces cancel out each other,
The resultant force is zero
(since horizontal & vertical forces are zero).
The object is still moving at the same velocity.
Newton’s Third Law of Motion
For every action, there is an equal but opposite reaction.
Forces occur in action-reaction pair acting on different
bodies.
Newton’s Third Law of Motion
To every action force, there is an equal but opposite reaction.
If an object A exerts a force on an object B, then B exerts an
equal but opposite force on A.
W = weight
force exerted by vehicle on ground
R = Reaction Force
force exerted by ground on vehicle
Name the action-reaction forces:
string
Tension exerted by
string on pendulum
pendulum
Weight exerted by
pendulum on string
Friction
Friction is a contact force that slows down moving objects.
Friction always acts in the opposite direction to the force
applied to the object.
It acts in direction opposite to motion
Quiz Questions
When you are walking forward,
Is there friction between sole of your shoes & surface of the
floor?
What is the direction of friction?
Quiz Questions
When you are walking forward,
(i) Is there friction between sole of your shoes & surface of the
floor?
Yes, friction is present.
(ii) What is the direction of friction?
In order to move forward, foot pushes backwards.
Force applied on floor surface by foot backwards.
Reaction force acting on the surface is friction.
Thus, friction acts in the opposite direction to that of the force
applied.
Reducing Friction
Friction can be reduced by:
1. The use of ball bearings or rollers between the 2 contact
surfaces.
2. Apply a film of lubricant between surfaces in contact.
3. Smoothen the contact surfaces by polishing.
4. Choose material of low frictional resistance.
5. Insert a cushion of air between the contact surfaces.
Question
A box is pushed with a force of 20 N and a frictional force of 5 N
is acting against the first force. The box has a mass of 10 kg.
(i) Draw a force diagram to show the forces acting on the box.
Solution :
A box is pushed with a force of 20 N and a frictional force of 5 N
is acting against the first force. The box has a mass of 10 kg.
(i) Draw a force diagram to show the forces acting on the box.
20 N
5N
or
20 N
5N
Question :
A box is pushed with a force of 20 N and a frictional force of 5 N
is acting against the first force. The box has a mass of 10 kg.
5N
(ii) State the resultant force acting on the box.
20 N
Question :
A box is pushed with a force of 20 N and a frictional force of 5 N
is acting against the first force. The box has a mass of 10 kg.
5N
(ii) State the resultant force acting on the box.
Resultant Force = F = 20 N + ( - 5 N)
= 15 N (to right)
20 N
Question 3:
A box is pushed with a force of 20 N and a frictional force of 5 N
is acting against the first force. The box has a mass of 10 kg.
5N
(iii) Calculate the acceleration the box is experiencing.
F = 20 N – 5 N = 15 N (to right)
m = 10 kg
a = F / m = 15 N / 10 kg = 1.5 m/s2 (to right)
20 N
Effects of Forces on Motion
Question :
The frictional force between a box of mass 4 kg and the floor is 15 N.
It is pushed across the floor with a constant force such that it
accelerates at 0.8 m/s².
a) What is the force applied to the box?
a = 0.8 m/s2
15 N
4 kg
Question :
The frictional force between a box of mass 4 kg and the floor is 15 N.
It is pushed across the floor with a constant force such that it
accelerates at 0.8 m/s².
a) What is the force applied to the box?
a = 0.8 m/s2
15 N
4 kg
Net F = m a = (4 kg) (0.8 m/s2) = 3.2 N (to right)
Force applied to box = 15 + 3.2 = 18.2N (to right)
Question :
The frictional force between a box of mass 4 kg and the floor is 15 N.
It is pushed across the floor with a constant force such that it
accelerates at 0.8 m/s².
b) The same force is applied to the box on a frictionless floor.
What is the new acceleration produced?
a = ? m/s2
ON
4 kg
18.2 N
Question :
The frictional force between a box of mass 4 kg and the floor is 15 N.
It is pushed across the floor with a constant force such that it
accelerates at 0.8 m/s².
b) The same force is applied to the box on a frictionless floor.
What is the new acceleration produced?
a=?
ON
4 kg
Resultant Force = ma
a = resultant force/ m
= 18.2 / 4
= 4.55 ms-2
18.2 N
Momentum
Do you want to get in the way of a charging elephant or a speeding
bullet?
A speeding bullet is light
but it has high velocity.
A charging elephant is moving
relatively slow but it has great mass.
The speeding bullet is hard to stop as it has high velocity.
The charging elephant is hard to stop as it has great mass.
The mass and velocity of an object determines its momentum.
Momentum (p) = mass (m) x velocity (v)
kg ms-1
kg
ms-1
p = mv
Momentum is a vector quantity so we need to specify the direction. This
is always the same direction as the velocity of the object.
Example:
Calculate the momentum of an elephant of mass 2000 kg moving at 40
ms-1.
Momentum, p = mv = 2000 kg x 40 ms-1
= 80000 kg ms-1
Newton’s Second Law
When a resultant force acts on an object, its velocity changes. This
means that force causes a change in momentum.
F = (mv – mu) / t
= m x (v – u) / t
= m x
a
(kg) x (ms-2)
F =ma
One Newton (1 N) is the resultant force needed to give a mass of 1 kg
an acceleration of 1 ms-2.
Free Body Diagrams
Forces are caused by the interaction of two objects. Forces are vector
quantities and they are drawn as vector arrows. We only need to draw
a free body force diagram that shows all the forces acting on just one
object.
Man & Earth
Balanced beams
Suspended objects
Object resting against
rough and smooth surfaces
Moving objects
Further examples
Further examples
Terminal Velocity
At the point when the air resistance acting upwards is
equal to the force of gravity downwards (weight), there
is no acceleration and the object will fall with
“terminal velocity”. Since there is no acceleration, the
net force is zero.
A small dense object, like a steel ball bearing, has a
high terminal velocity. A light object, like a raindrop,
or an object with large surface area like a piece of
paper, has a low terminal velocity.
Terminal velocity
When object is thrown from a high height. What happens to its
speed??
-
At rest originally (0 ms-1)
Accelerates at 10ms-2 (gravitational acc) downwards
Velocity increases as object moves downwards
Air resistance starts acting on object upwards
Air resistance increases as object’s velocity increases
At a point,
air resistance upwards = force of gravity downwards
no net force, no acceleration
object falls at terminal velocity
Terminal velocity also occurs for….
 Falling body through column of motor oil due to
friction giving rise to resistance
Also, for Skydiving.
Reference:
Physics Insight “O” Level 2nd Edition. Loo Wan Yong, Loo Kwok Wai.
Advanced Physics for you. Keith Johnson, Simmone Hewett, Sue Holt, John Miller.
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