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# Newton’s Second Law of Motion

## Key Concepts:

• Newton’s second law of motion
• Relate force, mass and acceleration

### Introduction:

In this session we are going to learn about second law of motion of Newton.

## Explanation:

### Newton’s second law of motion

Newton’s second law of motion states that the rate of change of momentum of a body is directly proportional to the applied force and takes place in the direction in which force acts. Force is equal to the product of mass and acceleration.

F = ma

#### Few of the applications are:

• A fielder pulls his hand backward while catching a cricket ball coming with a great speed, to reduce the momentum of the ball with a little delay. This reduces the effect of the force exerted by the ball on his hands.
• Seat belts prevent injuries when brakes are applied in a fast-moving car. A car has a large momentum due to its large velocity, which is reduced to zero in a very short time, hence provided with seat belts.
• For athletes, during long and high jump, sand bed or cushioned bed is provided to allow a delayed change of momentum to zero to prevent the athletes from being injured due to rapid change in momentum to zero.
• A karate player breaks slab of bricks in a single blow as when hands move they carry velocity and when they touch slab the velocity is reduced to 0 in a very short time. Hence, the force exerted is very high and the slab breaks in a single blow.

### One Newton:

One Newton is defined as that force necessary to provide a mass of one kilogram with an acceleration of one meter per second per second squared.

1 Newton (N) = 1kg × 1m/s2

1N = kg m/s2

### Derivation of Second Law of Motion

Let the mass of a moving object be m and F be the force acting on it.

Let the velocity of the object change from u to v in the interval of time t.

Momentum = p = Mass × velocity

Initial momentum = mu

Final momentum = mv

Change in momentum = mv – mu = m(v–u)

Rate of change of momentum = m(v–u)/t

Force ∝ Rate of change of momentum

F ∝ m(v–u)/t

F ∝ ma (because a = (v–u)/t)

F = kma,

where k is the constant of proportionality

F = ma

(k = 1, m = 1kg, a = 1m/s2)

Question 1: How much force is  needed to produce an acceleration of 20 m/s² in a body of mass  500 g?

m = 500 g = 0.5 kg

a  = 20 m/s²

F = ?

F = m × a

= 0.5 – 20

= 10 N

Question 2: A body of mass 5 kg is moving  with a uniform velocity of 10 m/s. It is acted upon by a force of 20 N. What will be its acceleration?

M = 5 kg

u = 10 m/s, F = 20 N

F = ma

a =  F/m

= 20/5

= 4 m/s²

Question 3: A body of mass 2 kg is kept at rest. A constant force of 6 N starts acting on it. what will be its acceleration?

m = 2 kg

u = 0 m/s

F = 6 N

a = F/m

= 6/2

= 3 m/s²

## Summary:

• 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 force acts.”
• F = ma where F is the force applied, m is the mass of the object and a is the acceleration
of the object
• One Newton is defined as that force necessary to provide a mass of one kilogram with an
acceleration of one meter per second per second.

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