Question

A block is connected to a spring that is suspended from the ceiling. Assuming air resistance is ignored, describe the energy transformations that occur within the system consisting of the block, the Earth, and the spring when the block is set into vertical motion.

Short answer

The potential energy of earth-block system increases during upward motion and decreases during downward motion. The increase or decrease of potential energy transformed into decrease or increase in kinetic energy.

Step-by-step solution

Define energy transformation of block and spring for upward motion

The block is initially at rest so there is no energy transformation of block. When block undergoes in upward vertical motion then spring compresses and potential energy of the block-Earth system increases. The kinetic energy of the block decreases in upward motion due to increase in potential energy of Earth-block system.

Define energy transformation of block and spring for downward motion

When block undergoes in downward vertical motion then spring stretches and potential energy of the block-Earth system decreases. The kinetic energy of the block increases in downward motion due to decrease in potential energy of Earth-block system.

Therefore, the potential energy of earth-block system increases during upward motion and decreases during downward motion. The increase or decrease of potential energy transformed into decrease or increase in kinetic energy.