What is the maximum compression of a spring with a stiffness of 500 N / m, if a ball with a mass

What is the maximum compression of a spring with a stiffness of 500 N / m, if a ball with a mass of 5 kg falls on it from a height of h = 2 m?

Initial data: k (stiffness of the deformed spring) = 500 N / m; m (mass of the ball that fell on the spring) = 5 kg; h (height from which the ball fell) = 2 m.

Reference values: g (acceleration due to gravity) = 10 m / s2.

The potential energy of the ball as a result of the fall will pass into the potential energy of the spring and the equality will be true: 0.5 * k * Δl ^ 2 = m * g * h, whence Δl = √ (2m * g * h / k).

Calculation: Δl = √ (2 * 5 * 10 * 2/500) = 0.63 m or 63 cm.

Answer: 2) The maximum spring compression will be 63 cm.