Question

A spring with spring constant k is attached to the floor, standing vertically. You place a box of mass m on the spring and, from rest, release it. The spring bounces up and down a few times and comes to rest (both its velocity and acceleration are zero). Find the thermal energy generated in this process in terms of m, g, and k.

Answer Options:

A. mg/k

B. m^2 g/k

C. m^2 g^2/k

D. m^2 g^2/ 2k

E. mg/2k

Answer 1

The thermal energy generated in this process is equal to (1/2)kx^2, where k is the spring constant and x is the displacement of the spring. The correct answer is E. mg/2k.

Step-by-step explanation:

To find the thermal energy generated in this process, we need to understand that the thermal energy is equal to the initial potential energy of the spring when the block was released. The potential energy stored in the spring is given by the formula PE = (1/2)kx^2, where k is the spring constant and x is the displacement of the spring from its equilibrium position. Since the box was released from rest, the displacement will be equal to the maximum amplitude of the oscillations. Therefore, the thermal energy generated is equal to (1/2)kx^2.

Now, let's solve the problem using the given options. The correct option is E. mg/2k.