Question

State Newton's third law of motion. How will you deduce it from the law of conservation of linear momentum? Why it is difficult to walk on stand?

Answer 1

Newton's third law of motion:- It states that every action, there is an equal and opposite reaction.

Let us consider two particles in an isolated system, their masses are m₁ and m₂ velocity are v₁ and v₂. Consider that they are moving along the same line and they interact. Their velocities change due to interaction. Thus, their momenta will also change in time Δt.

Let the change in momentum of the first particle

= ΔP₁ (Change in momentum of the second particle)

= ΔP₂

According to the law of conservation of linear momentum, in an isolated system with has no external force.

ΔP₁ + ΔP₂ = 0 or ΔP₁ = -ΔP₂

Dividing it by Δt, we have,

ΔP₂/Δt = -ΔP₁/ΔT

⇒ dP₂/dt = -dP₁/dt

⇒ F₂ = -F₁

That is force acting on m₂ = -force acting on m₁

or Action = -Reaction

This is Newton's third law of motion. When we press the sandy ground in backward direction, the sand gets pushed away and as a result, we get only very small reaction from the ground making it difficult for us to walk.