Question

how does the kinetic energy change if its momentum is halved

Answer 1

ke=p^2/2m is the answer

Answer 2

Given: Initial momentum = p₁

           Initial Kinetic Energy= E₁

           Final momentum p₂ =  p₁/2

           Mass of an object = m

To Find: Final Kinetic Energy, E₂

Solution:

Formula used-

• Kinetic Energy, E = (momentum)²/ 2 x mass
• E = p²/ 2m
• E ∝ p²

Therefore,

E₁ = (p₁)²/ 2m

E₂ = (p₂)²/ 2m

As, p₂ = p₁/2

So, E₂ = (p₁/2)² / 2m

On dividing E₁ and E₂

E₁/ E₂ = [(p₁)²/ 2m] / [(p₁/2)² / 2m]

E₁/ E₂ = 4/ 1

E₂ = E₁ / 4

This means, if momentum is halved, kinetic energy is reduced by 4 times its original value.