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Dynamics

Learning Objectives1) 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 Acting on a Body Net Force

6 N

2 N

6 N

6 N

4 N

4 N

3 N

4 N

4 N

4 N

0 N

10 N

7 N

Forces are vectors and can be added by considering both direction and magnitude

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?

300 N

800 NX

Work out the answer!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?

300 N

800 NX

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

Weight of ball

ground

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), anet 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 = m a

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)

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 1 N

a = 1 m/s2

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?

5 kg 20 N

a = ?

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?

Given F = 20 N, m = 5 kg

Since F = m a,

20 N = (5 kg) a

a = 20 N / 5 kg = 4 m/s2

5 kg20 N

a = 4 m/s2

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.

Forward thrust

u = 0 m/s, v = 20 m/s, t = 5 s

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

a = (v – u) / t = (20-0)/5 = 4 m/s2

F = m a

F = (1000 kg)(4 m/s2)

F = 4000 N

u = 0 m/s, v = 20 m/s, t = 5 s

m = 1000 kg

4000 N

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 = m a 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 = m gF = m a

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?

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.

5 N 8 N3 N

1 N

1 N

Question:

When the resultant force acting on an object is zero,does it mean that the object is necessarily stationary?

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.

Velocity = 3 m/s

Question:

When the resultant force acting on an object is zero,does it mean that the object is necessarily stationary?

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.

5 N

8 N

3 N 1 N

1 N

Velocity = 3 m/s

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 = weightforce exerted by vehicle on ground

R = Reaction Forceforce exerted by ground on vehicle

Name the action-reaction forces:

pendulum

string

Weight exerted by pendulum on string

Tension exerted by string on pendulum

Friction

Friction is a contact force that slows down moving objects. Friction always acts in the opposite direction to the forceapplied to the object.It acts in direction opposite to motion

Quiz QuestionsWhen 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 Nis 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.

or

20 N5 N

20 N

5 N

Question :

A box is pushed with a force of 20 N and a frictional force of 5 Nis acting against the first force. The box has a mass of 10 kg.

(ii) State the resultant force acting on the box.

20 N5 N

Question :

A box is pushed with a force of 20 N and a frictional force of 5 Nis acting against the first force. The box has a mass of 10 kg.

(ii) State the resultant force acting on the box.

Resultant Force = F = 20 N + ( - 5 N) = 15 N (to right)

20 N5 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.

(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 N5 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?

4 kg15 N

a = 0.8 m/s2

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?

4 kg15 Na = 0.8 m/s2

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 itaccelerates at 0.8 m/s². b) The same force is applied to the box on a frictionless floor.

What is the new acceleration produced?

4 kgO N

a = ? m/s2

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 itaccelerates at 0.8 m/s². b) The same force is applied to the box on a frictionless floor.

What is the new acceleration produced?

4 kgO N

a = ?

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 = m a

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

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

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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