Final answer:
The initial potential energy (PE) of the 0.68kg ball lifted to 2.4m is calculated using PE = mgh, giving approximately 15.97 Joules. Energy is lost when the ball bounces back up to 0.58m due to air resistance and energy absorption by the ball and ground.
Step-by-step explanation:
When the student lifts the 0.68kg bouncy ball to a height of 2.4m and then releases it, the ball has a certain amount of gravitational potential energy (PE) at that height. The energy is calculated using the formula PE = mgh, where m is the mass of the object, g is the acceleration due to gravity, and h is the height.
The initial potential energy of the ball can be calculates as follows:
PE = (0.68 kg) × (9.8 m/s²) × (2.4 m) = 15.9744 J. Therefore, the initial potential energy of the ball is approximately 15.97 Joules.
Upon releasing the ball, it falls due to gravity, converting its potential energy into kinetic energy. When the ball bounces back up to a height of 0.58m, it does not reach its original height because some energy is lost due to various factors like air resistance and energy absorbed by the ball's material and the surface it bounces on, which converts some of the kinetic energy into heat or sound. Thus, the ball's potential energy at its peak during the bounce will be lower than the initial potential energy due to these energy losses.