Final answer:
When comparing the work done on a ball that bounces back to a portion of its original height and a ball that makes a crater in the sand, there are a few differences to consider. The ball that bounces back experiences an elastic collision with the ground, while the ball that makes a crater transfers its energy into work done on the sand. The work done on each ball is different due to the different outcomes of their collisions.
Step-by-step explanation:
When comparing the work done on a ball that is dropped and bounces back to a portion of its original height, and a ball that is dropped and makes a crater in the sand, there are a few differences to consider.
1. The ball that bounces back experiences an elastic collision with the ground, meaning that some of the initial potential energy is converted back into kinetic energy. This results in the ball bouncing back up to a certain height, although it will not reach its original height due to energy losses from air resistance and other factors.
2. The ball that makes a crater in the sand does not bounce back up. Instead, it transfers some of its initial potential energy into kinetic energy as it falls, and then into work done on the sand to create the crater. This means that the work done on the ball in this case is equal to the work done on the sand to create the crater.
In summary, the work done on the ball that bounces back is different from the work done on the ball that makes a crater because of the different outcomes of their collisions.