FORCE AND LAWS OF MOTION

Sir Issac Newton

(1643 -1727)

Galileo Galilei

(1564 – 1642)

1. Force

2. Effects of Force

3. Balanced Forces

4. Unbalanced Forces

5. Newton’s First Law of Motion (Inertia)

6. Momentum

7. Newton’s Second Law of Motion

8. F = ma

9. Applications of Second Law of Motion

10.Newton’s Third Law of Motion

11.Applications of Third Law of Motion

12.Law of Conservation of Momentum

Created by C. Mani, Education Officer, KVS Silchar Region

Force

A push or pull on a body is called force.

Push

Pull

F

F

Push or Pull?Pull

Push or Pull?

Push

Push

A body at rest can be moved by a force.

Effects of Force

A body in motion can be stopped by a force.

F

F

A body in motion can be changed in its direction of motion by a force.

F F

A body (spring) can be changed (stretched) in its shape or size by a force.

A body (spring) can be changed (compressed) in its shape or size by a force.

F F

Effects of Force: Revisit

1. A force can move a stationary body.

2. A force can stop a moving body.

3. A force can change the speed of a moving body.

4. A force can change the direction of a moving body.

5. A force can change the shape (and size) of a body.

Force

A force is an influencing agency which tends to move a stationary body or which tends to stop a moving body or which tends to change the velocity (speed or and direction) of a moving body or which tends to change the shape (and size) of a body.

Balanced ForcesIf the resultant of all the forces acting on a body is zero, the forces are called balanced forces.

F F

Reaction (R) (Exerted by the table)

Weight (W) (Force of gravity)

The block on the table is acted upon by many forces.

Force ‘F’ applied by the left hand is being balanced by the force ‘F’ applied by the right hand.

The weight ‘W’ of the block is balanced by the Reaction ‘R’ on the block.

Note:

1. When a body at rest is acted upon by balanced forces, the body is not displaced. i.e. the body remains stationary.

2. When balanced forces act on a body moving with constant velocity (uniform motion), they do not produce any acceleration on the body. i.e., the body continues to move with the same speed and direction.

Eg. When rain drops fall from clouds at a greater height, the drops at first gain velocity due to gravity of the earth.

After falling through some height, a stage called equilibrium occurs when downward weight of the drops is balanced by the upward forces such as upthrust and viscous force.

The net force acting on the drops will be zero and hence no more acceleration is produced on the drops.

Therefore, the rain drops move with constant velocity which was last gained by the drops just before reaching equilibrium condition.

Can you imagine the speed of the rain drops while reaching the surface of the earth, if they continue to move only under the action of gravity?

Suppose the clouds are at the height (h) of 3 km (3000 m). Acceleration due to gravity (g) is 9.8 m/s2. Initial velocity (u) = 0 m/s.

Then, final velocity is given by v2 = u2 + 2gh

i.e. v2 = 02 + 9.8 x 3000 => v = 171.5 m/s = 617 km/h

A rain drop with such a high velocity is faster than a bullet and can pierce through a human skull !

3. Though the balanced forces cannot produce motion in a stationary body or stop a moving body, they can, however, change the shape of the body.

Eg. When a ball is pressed between the hands the forces are balanced but the ball is changed in its shape and size.

Unbalanced ForcesIf the resultant of all the forces acting on a body is not zero, the forces are called unbalanced forces.

Unbalanced forces can move a stationary body or they can stop a moving body.

When we talk of a force acting on a body, we usually mean an unbalanced force. When the total force on the plane

is in one direction, the force is called “unbalanced”.

An unbalanced force changes the motion of the plane. For instance, when thrust is greater than drag, it is the unbalanced force that causes the plane to speed up, or accelerate.

In addition, as the velocity of the plane increases, the lift force increases and becomes the unbalanced force that causes the plane to fly.

ThrustLift

Weight

Drag

Weight of the block is balanced by the reaction by the table on the block.

As long as the applied force F is less than the frictional force, the block is not moved.

When the applied force is just equal to the friction, the body may move with uniform velocity.

When the applied force is greater than the friction, the body moves with acceleration.

F ≤ f

Reaction (R)

Weight (W)

f

F > f

NEWTON’S LAWS OF MOTIONF

The block remains at rest…..

unless and until it is acted upon by an external force.

F

The ball continues to be in uniform motion……

unless and until it is acted upon by an external force.

NEWTON’S FIRST LAW OF MOTION

A body at rest will remain at rest, and a body in uniform motion will continue to be in uniform motion, unless and until it is compelled by an external force to change its state of rest or of uniform motion.

Inertia

Inertia is the inherent property of a body due to which it resists a change in its state of rest or of uniform motion.

Inertia can be understood in parts, viz. inertia of rest and inertia of motion.

Mass is a measure of the inertia of a body.

Heavier objects have more inertia than lighter objects.

Eg. 1. A stone of size of a football has more inertia than football.

2. A cricket ball has more inertia than a rubber ball of the same size.

Inertia of rest

Examples of Inertia of rest:

1. A passenger in a bus jerks backward when the bus starts suddenly because the passenger tends to be in inertia of rest whereas the bus is moved away forcefully.

2. When a bed sheet is flicked away suddenly dust particles fall away as they tend to be in inertia of rest.

3. When a branch of a tree carrying a mango is suddenly flicked mango falls off due to inertia of rest.

Examples of inertia of motion:

1. A passenger in a bus jerks forward when the bus stops suddenly because the passenger tends to be in inertia of motion whereas the bus is stopped forcefully.

2. An athlete after reaching the finishing point can not stop suddenly or if he stops suddenly then he falls toppling head down.

3. A car takes some time and moves through some more distance before coming to rest even after the application of brakes.

4. A rotating fan continues to do so for some more time even after the current is switched off.

5. An oscillating simple pendulum bob does not halt at the mean position but continues to move further.

6. When a car or bus turns around a sharp corner, we tend to fall sideways because of our inertia to continue to move in a straight line.

7. It is dangerous to jump out of a moving bus because the jumping man’s body is in the state of inertia of motion but the legs are suddenly stopped by the ground and hence he topples down.

MOMENTUMMomentum is the quantity of motion in a body and it depends on its mass and velocity.

Momentum of a body is defined as the product of its mass and velocity.

i.e. Momentum = mass x velocity or p = m x v

Momentum is directly proportional to mass.

If a cricket ball and a tennis ball move with same velocity, momentum of

cricket ball is more because its mass is larger than that of the tennis ball.

Momentum is directly proportional to velocity.

If two cricket balls move with different velocities, then the momentum of

the ball with greater velocity possesses more momentum.

If a body is at rest, its velocity is zero and hence its momentum is zero.

But, every moving body possesses momentum.

Momentum is a vector quantity.

SI unit of momentum is kg m/s or kg ms-1.

CGS unit of momentum is g cm/s g cms-1.

NEWTON’S SECOND LAW OF MOTION

The rate of change of momentum of a body is directly proportional to the applied force, and takes place in the direction in which the force acts.

Force α Time taken

Change in momentum

F αΔp

t

F αmv - mu

t

F αm(v – u)

t

F α m x at

(v – u)since a =

If force of 1 N applied on a body of mass 1 kg produces an acceleration of 1 m/s2 on the body, then

F = K m a

1 = K x 1 x 1

or K = 1

F = m a Force = mass x acceleration

The acceleration produced in a body is directly proportional to the force acting on it and inversely proportional to the mass of the body.

Acceleration a =F

m

Force is a vector quantity.

Force can cause acceleration or deceleration.

Eg.: Accelerator of a car accelerates it and brakes decelerate it.

SI unit of force is ‘newton’.

One ‘newton’ is defined as that force which when acting on a body of

mass 1 kg produces an acceleration of 1 m/s2 in it.

100 g

Place an 100 g on your outstretched palm. The force you feel is nearly 1 newton !

Applications of Newton’s Second Law of motion

1. A cricket player (fielder) moves his hands backwards on catching a fast moving cricket ball.

A fast moving cricket ball has a large momentum.

In stopping the cricket ball, its momentum has to be reduced to zero.

When a player moves his hands back, the time taken to stop the ball increases and hence the rate of change of momentum decreases.

i.e. the force exerted by the ball on the hands decreases. So, the hands of the player do not get hurt.

2. A high jumping or long jumping athlete is provided either a cushion or a heap of sand on the ground to fall upon.

The cushion or sand helps to increase the time in which the momentum comes to zero. This decreases the rate of change of momentum and hence the force. So, the athlete does not get hurt.

3. Packing materials like thermocoal, corrugated sheets, bubbled plastic sheet, straw, paper strands, etc. are used while packing glassware, chinaware, electronic devices, etc.

These materials help to increase the time in which the momentum comes to zero when jolting and jerking take place. This decreases the rate of change of momentum and hence the force. So, the articles do not get broken.

NEWTON’S THIRD LAW OF MOTION

To every action there is an equal and opposite reaction.

Note:

• Action and reaction are just forces.

• The forces always occur in pairs.

• Action and reaction do not act on the same body.

• Action and reaction act on different bodies but simultaneously.

• Though action and reaction forces are equal in magnitude but they do not produce equal acceleration in the two bodies on which they act.

The statement means that in every interaction, there is a pair of forces acting on the two interacting objects. The size of the forces on the first object equals the size of the force on the second object. The direction of the force on the first object is opposite to the direction of the force on the second object. Forces always come in pairs - equal and opposite (action-reaction) force pairs.

F F0 20 40 8060 100

0 204080

60

100

Reaction = 58 gwt

Action = 58 gwt

0 204080 60

100

0 20 40 8060 100

Examples / Applications of Newton’s Third Law of motion

F

F

Reaction

Action

FF

Force on bullet (Action)

Force on gun (Reaction)

Recoil of a gun

Identify Action and Reaction

Reaction

ActionWeight

Vertical component of reaction

Horizontal component of reaction

Reaction

Weight

Forward Motion

Action

Reaction

Horse and Cart Problem

A horse is urged to pull a cart. The horse refuses to try, citing Newton’s third law as his defence. “The pull of me on the cart is equal but opposite to the pull of the cart on me. If I can never exert a greater force (action and reaction are always equal) on the cart than it exerts on me, how can I ever set the cart moving?”, asks the horse.

How would you reply?

WC

RC

TCH THC

Action

Reaction R

H

V

f

Why don’t you educate the Horse properly?

Weight of the cart ‘WC’ is balanced by Reaction ‘RC’ on the cart offered by the ground.

Forward pull of the horse on the cart ‘THC’ is balanced by the Reaction pull of the cart on the horse ‘TCH’.

If the horse pushes the ground in a slanting manner (Action), the Reaction offered by the ground is resolved into Vertical and Horizontal components.

The Vertical component ‘V’ balances the weight of the horse ‘WH’.

If the Horizontal component ‘H’ is greater than the Friction ‘f’, then the horse-cart system will move forward with acceleration.

WH

LAW OF CONSERVATION OF MOMENTUM

When two or more bodies act upon one another, their total momentum remains constant provided no external forces are acting on them.

Suppose a big and a small car move in the same direction with different velocities.

Let the mass of the bigger car be ‘m1’ and its initial velocity is ‘u1’.

Let the mass of the smaller car be ‘m2’ and its initial velocity is ‘u2’ such that u2 < u1.

Suppose both the cars collide for a short time ‘t’.

Due to the collision, the velocities will change.

Let the velocities after the collision be v1 and v2 respectively.

Suppose that during collision, the bigger car exerts a force F1 on the smaller car and in turn, the smaller car exerts a force F2 on the bigger one.

When the force F1 acts on the smaller car, its velocity changes from u2 to v2.

According to Newton’s third law, F1 = - F2

F1 = m2a2

F1 = m2 xv2 – u2

tWhen the force F2 acts on the bigger car, its velocity changes from u1 to v1.

F2 = m1a1

F2 = m1 xv1 – u1

t

m2 xv2 – u2

tm1 x

v1 – u1

t= -

Cancelling t on both sides, we get

m2(v2 – u2) = m1(v1 – u1) m2v2 – m2u2 = m1v1 – m1u1 m1u1 + m2u2 = m1v1 + m2v2

Total momentum before collision = Total momentum after collision

Initial momentum of the bigger car = m1u1

Initial momentum of the smaller car = m2u2

Final momentum of the bigger car = m1v1

Final momentum of the smaller car = m2v2

Recoil of a Test Tube (Activity)

Wait…..water is getting heated !

Here, the event of popping up of the cork is considered as collision. Total momentum before collision is zero. Total momentum after collision also must be zero. Hence, the velocities of the test tube and the cork are adjusting themselves. i.e. the cork and the tube fly away in opposite directions; also note that the velocity of the cork (lighter) is faster than that of the test tube (heavier).

Acknowledgement

The objects copied from various sites:

1. Pictures of Galileo, Newton

2. Apple Tree

3. Aeroplane

4. 5 Rupee coin

5. Rocket

6. Body of the car

7. Spirit Lamp