A spring is attached on one end to the bottom of an insulated container that is filled with an ideal gas at 300 K. A basket is connected to the other end of the spring. At rest, the basket sits 1 meter above the bottom of the container. A ball of 1 kg is put in the basket while holding the basket in position (Fig. 1a). When the basket is let go, the weight of the ball initially pushes the spring down due to gravity (Fig. 1b), but then the ball rolls out of the basket and falls to the bottom of the box. As a result, the spring wildly oscillates (Fig. 1c), but ultimately comes to rest (Fig. 1d).

Figure 1. A ball was inside a basket that is connected to a container by a spring but falls off to the bottom.

Data: For the spring, the force = , where is a spring constant and is the displacement from the elongation at which the spring has zero force. = 50 /. The box is large so that its temperature can remain constant. No plastic deformation takes place in the ball when it falls. The gravitational acceleration = 10 / , . With the initial state being the state where the basket with the ball is held at 1 m above the bottom of the box (Fig. 1a), determine whether the following statements are true or false. For full credits, explain why.

a. (True or False) The internal energy of a system decreases in this process if the system consists of the ball, basket, and spring.

b. (True or False) The internal energy of a system decreases in this process if the system consists of the basket and spring.

c. (True or False) The entropy of a system decreases in this process if the system consists of the ball, basket, and spring.

d. (True or False) The entropy of a system decreases in this process if the system consists of the basket and spring.

e. Calculate the change in the entropy for the system consisting of the ball, basket, and spring