Verified answer

A) When released the ball only has Gravitational PE = mgh

GPE = 0.650kg x 9.80N/kg x 2.50m .... ►GPE = 16.0 J

B) After bouncing .. 75%(3/4) of its orignal GPE is returned, so .. 25%(1/4) of 16.0J is 'lost' .. .. 1/4 of 16.0J ►= 4.0J 'lost'

The 4.0J not returned as GPE has been converted to sound, and (mostly) to heat due to it's impact with the ground.

The ball gets slightly warmer as it's particles vibrate more due to the impact.

Mechanical energy is expressed in two forms: kinetic and potential. Kinetic energy is energy manifested in the motion of a massive object, while potential energy is when an accelerative field is applied to an object that has not yet reached its terminal point/velocity. To express this in simpler terms: kinetic energy is moving energy, potential energy is the ability to move. In the case of the ball, its initial suspension gives it an initial potential energy, which is converted to kinetic energy as it falls.

Potential energy is calculated as E = m*a*d, where E is the energy in Joules, m is the mass of the object in kilograms, a is the acceleration being applied to the object in m/s^2 (acceleration due to gravity in this case, which is 9.81m/s^2), and d is the distance the object will travel before being stopped.

A.) Just after the ball is released, none of its energy has been made kinetic yet, thus its energy is entirely in terms of potential energy, thus E = m*a*d will tell us 100% of the ball's initial energy. Applying our formula, we see E = 0.65kg*9.81m/s^2*2.5m = 15.94J of energy.

B.) If the ball returns to 75% of its height, which is 2.5m*0.75 = 1.875m, we can see that the energy is now E = 0.65kg*9.81m/s^2*1.875m = 11.96J of energy, which is 75% of the energy it initially had. In a system, energy can neither be created nor destroyed, so the energy doesn't simply disappear. This energy is actually dispersed within the ball itself as a result of its collision with the ground, and is usually felt in terms of sound energy.