Newton’s Second Law of Motion

Introduction

Newton’s Second Law of Motion explains how force changes the motion of an object. It shows that when a force acts on a body, the body gets acceleration. The acceleration depends on the applied force and the mass of the body.

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 of the force.

For constant mass, this law is written as:

F = m × a

Here, F is the applied force, m is the mass of the body, and a is the acceleration produced.

Explanation

Momentum of a body is given by:

Momentum = m × v

According to Newton’s Second Law, applied force is proportional to the rate of change of momentum.

Force ∝ change in momentum / time

If the mass remains constant, then only velocity changes. So, the change in momentum depends on the change in velocity.

Therefore,

Force ∝ m × (change in velocity / time)

But change in velocity per unit time is acceleration.

So,

Force ∝ m × a

In SI system, the proportionality constant is taken as 1. Therefore,

F = m × a

This means acceleration is directly proportional to force and inversely proportional to mass.

Examples from Daily Life

  • Pushing an empty cart is easier than pushing a loaded cart because the empty cart has less mass.
  • If more force is applied to a body, it gets more acceleration.
  • A lighter object accelerates more than a heavier object when the same force is applied.

Illustration

Mass = Low Force High Acceleration Mass = High Same Force Low Acceleration

The same force produces greater acceleration in the cart of smaller mass and smaller acceleration in the cart of greater mass.

Important Points

  • Newton’s Second Law gives the relation between force, mass, and acceleration.
  • Applied force is equal to the rate of change of momentum.
  • For constant mass, the law becomes F = m × a.
  • Acceleration is directly proportional to force.
  • Acceleration is inversely proportional to mass.
  • The acceleration takes place in the direction of the applied force.

Conclusion

Newton’s Second Law of Motion explains how force affects the motion of a body. It gives a clear mathematical relation between force, mass, and acceleration and helps us understand many motions in daily life.

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