Where does the energy go when punching a ball in the air causing it to "float"? Here is a link to a video of a people punching a ball so it appears to float: https://www.youtube.com/watch?v=v7wqrUFREK0
When the arms are continuously punching the ball, it does not change the height, therefore the ball doesn't gain any gravitational potential energy. Also, it barely moves at all, so there is either no kinetic energy, or a minute amount, but this still doesn't explain where all the energy from the arms and fists go to, because that little bit of movement cannot result from all that energy. So my question here is, where does the kinetic energy from the fists go to? What is the energy converted to?
 A: I'm going to neglect the changes of kinetic and gravitational potential energy changes of the ball for this explanation. What is happening when you punch the ball like in the video is an example of an inelastic collision. When you punch a ball, your arm actually bounces back with some speed, so not all of the energy is lost immediately. Part of the energy has been transferred to the air as sound, and part of it has been transferred to the ball, causing rapid vibrations in the ball. Some of these vibrations "radiate away" as sound for a short period of time after the punch. A small amount can result in permanent deformations in the ball. The rest of the vibrations stay with the ball as "heat." Similar vibrations occur in your hand, propagating up your arm and into the rest of your body, most of which heat it up.
Now your arm has bounced back and still has some energy. To get ready for the next punch (with the same arm), you then decelerate your arm to a halt (or at least to a low speed), doing negative work on your arm in the process. A fraction of this energy may be stored temporarily in your arm as potential energy (as in a spring), to be converted to kinetic energy during your next punch. However, your body is unable to store the rest of this energy in a useful form, so it is lost as heat. This deceleration can also be viewed as an inelastic collision. Moreover, not only can you not recover this energy, since you contract your muscles to supply (at least part of) the force to decelerate your arm, you spend energy in the process, some of which is also lost as heat in your muscles.
Then you spend energy to accelerate your arm, punch the ball, and this repeats.
A: Let's consider the more obvious situation of punching a wall. Now the wall certainly does not move, so it's not gaining gravitational potential energy & kinetic energy. Where does the kinetic energy from the fists go to?
Some of it goes to heat, some goes to sound, and the rest is preserved as kinetic: the hand rebounds from the wall (the same way a ball bounced on a wall rebounds), and that contains some energy. 
