Final answer:
Energy transformations in a dropped ball bouncing half its original height include gravitational potential to kinetic to elastic potential and back to kinetic, with some energy lost as thermal energy.
Step-by-step explanation:
When a dropped ball bounces to one-half its original height, the energy transformations that take place are from gravitational potential to kinetic to elastic potential energy and back to kinetic energy. Initially, as the ball falls, its gravitational potential energy is converted to kinetic energy. Upon impact with the ground, some kinetic energy is lost—primarily as thermal energy due to the deformation of the ball and the ground. The remaining kinetic energy is stored temporarily as elastic potential energy as the ball deforms.
Then, as the ball recoils and rises, the elastic potential energy is converted back into kinetic energy and then into gravitational potential energy as the ball reaches a height that is half of the original height. However, some energy is not recovered due to energy losses, explaining why the ball does not reach its original height.