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
kinetic and elastic
gravitational and elastic
gravitational, kinetic, and elastic

Explanation:

• Gravitational energy: Since the ball is above the tabletop (zero - gravitational - energy level), it has gravitational potential energy \(U_g = mgh\) (where \(h>0\)).
• Kinetic energy: The spring has not yet brought the ball to a halt, so the ball is still in motion. Kinetic energy is given by \(K=\frac{1}{2}mv^{2}\), and since \(v

eq0\), \(K
eq0\).

• Elastic energy: The spring is being compressed. The elastic potential energy of a spring is \(U_e=\frac{1}{2}kx^{2}\), and since \(x > 0\) (spring is compressed), \(U_e

eq0\).

Answer:

Gravitational, kinetic, and elastic