Question

TUDUNUL AP Callegard AP Physics 1 FeburaryExamReview 24. A block of mass M is at rest on a ramp that is inclined at an angle with respect to the honzontal. Frictional forces are considered to be nonnegligible. The block is pushed against a spring and then held in place. The spring is compressed a distance of 21, and the spring is not secured to the block. The block is then released from rest, travels up the incline, and comes to rest arter traveling a distance D, as shown above. Which of the following claims correctly describes the energy of the system under consideration from when the block compressed the spring and when the block has traveled a distance D along the incline? Select two answers. (A) The mechanical energy of the system consisting of the spring increases by ku1. (B) The mechanical energy of the system consisting of the block does not change. The mechanical energy of the system consisting of the block and Earth increases by more than zero but less than ka O The mechanical energy of the system consisting of the spring, block, and Earth increases by ka?

Answer 1

24. Let us examine each of the statements.

A. The mechanical energy of the spring increases $\frac{1}{2}kx_1^2$ when it is first compressed but clearly, part of the energy is then transferred to the block so that it travels up. Therefore, this statement is incorrect.

B. The block starts from rest and ends at rest. However, it is at a greater height finally than it was initially. Therefore, the mechanical energy has increased. This statement is incorrect.

C. Considering the block and the earth to be the system, the friction force is internal to the system and can thus be neglected. Now, we have already determined that the energy of the spring is increased by  $\frac{1}{2}kx_1^2$ when it is first compressed and part of the energy is then given to the block. It can't be the whole energy $\frac{1}{2}kx_1^2$ because at the moment the block would have separated from the spring, the spring must have been stretched and thus have some energy to itself. Therefore, the block- earth system has gained some non-zero energy but less than $\frac{1}{2}kx_1^2$ . This statement is correct.

D. When we consider the block, spring and earth as a single system, the friction is once again internal. To start with, the action of compressing the spring introduced an energy of $\frac{1}{2}kx_1^2$ to the system. After that, there is no external non-conservative force acting on the system which can reduce this. Therefore, the energy of the system has increased by $\frac{1}{2}kx_1^2$ . This statement is correct.

C and D are correct