Question

Describe the Newton's second law of motion and deduce first law from it.

Answer 1

It is known that a definite force 'F' is applied to different bodies, then magnitude of acceleration is different in different cases. Thus, a numerical quantity is asigned to each body known as mass. The mass of two bodies are such that

F = m₁a₁ = m₂a₂

or, m₁/m₂ = a₂/a₁

Now if force also varies then it is found that acceleration produced id proportional to the force applied and inversely proportional to the mass of the body.

Thus, a = K F/m

It is convenient to choose unit of force such that constant K = 1. Thus we have, F = ma

If there are large number of forces

acceleration is directly proportional to the force acting on it and parallel in direction to this force regardless of the direction of velocity.

The acceleration for a given force is inversely proportional to the mass of the body.

In terms of momentum (P = mv), the second law of momentum is stated that the rate of change in momentum is directly proportional to the external force acting on the body.

(constant of proportionality is 1)

First law from second law: According to second law of motion

F = ΔP/Δt

If F = 0, then ΔP = 0   (∵ Δt ≠ 0)

or, Δ(mv) = 0 or, mΔv = 0

Δv = 0 (∵ m ≠ 0)

⇒ v = constant

Thus, in the absence of external force, a body will remain in its state of motion. It is first law of motion.