Final answer:
When comparing the work done for ball bouncing back and ball making a crater, we need to consider gravitational potential energy and elastic potential energy.
Step-by-step explanation:
When comparing the work done for a ball that bounces back to a portion of its original height and a ball that makes a crater in the sand, we need to consider two factors: the gravitational potential energy and the elastic potential energy.
For the ball that bounces back, as it falls towards the floor, its gravitational potential energy decreases. When it hits the floor and bounces back, the gravitational potential energy is converted to elastic potential energy. Some of the energy is lost due to internal friction and heat, resulting in a smaller bounce.
On the other hand, for the ball that makes a crater in the sand, as it falls towards the sand, its gravitational potential energy also decreases. However, when it hits the sand, the energy is dissipated as sound, heat, and deformation of the sand particles. The work done in this case is mainly dissipated as heat and deformation.