Question

a ball is dropped from some height onto an unstrained vertical spring (mounted to a tabletop) and compresses it. consider an instant where the spring has not yet brought the ball to a halt, but is still in the process of compressing. what types of energies are associated with the spring - ball system at that instant? assume that the zero of gravitational energy is at the level of the tabletop. gravitational and kinetic gravitational, kinetic, and elastic kinetic and elastic gravitational and elastic

Explanation:

• Gravitational energy: Since the ball is above the tabletop (zero - level for gravitational energy), it has \(U_g = mgh\) (where \(h>0\)).
• Kinetic energy: The ball is still in motion (not yet halted), so \(K=\frac{1}{2}mv^{2}\) (\(v > 0\)).
• Elastic energy: The spring is compressed, so \(U_e=\frac{1}{2}kx^{2}\) (\(x>0\), \(k\) is the spring constant).

Answer:

B. Gravitational, kinetic, and elastic