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## 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/s^{2}

1N = kg m/s^{2}

**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/s^{2})^{ }

**Questions and Answers**

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

**Answer:**

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? **

**Answer:**

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?**

**Answer:**

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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