Question

A block of mass m moving at a speed v compresses a spring through a distance x before its speed is halved. Find the spring constant of the spring.

Answer 1

Let the velocity of the body at A be v
So, the velocity of the body at B is v/2
Energy at point A = Energy at point B
So, ½ mv_A²= ½ mv_B² + ½ k_x²⁺
= ½ kx² = ½ mv_A² - ½ mv_B² = kx² = m (v_A²⁺ - v_B²) = kx² = m(v²-v²/4)  
    K=  3mv²/3X²