Preventing the release of potential energy Suppose I pull on the string of a bow without releasing it. My muscles are converting chemical energy (from food) to let the bow string stay at this position but this energy is not stored in the bow, I mean no matter what time I release the bow, it will produce the same effect.
My question is where did this energy go?
How it is conserved?
I thought about heat but if all the energy I’m spending is converted to heat how did I produce a constant force to prevent the string from releasing.
 A: Whenever you are confused about energy involving a human the problem is the human and the solution is to get rid of the human.
For example, in your case we can replace the human with a rigid bar to hold the bow and a spring to pull the string. The elastic PE in the spring can be used to pull the bow, and once it gets to the final equilibrium position it can hold it indefinitely without further decrease in elastic PE. There is energy required to pull the bow, there is not energy required to hold the bow in place.
The energy required by the human to hold the bow steady is purely due to inefficiencies in the human body and all of that energy is wasted as heat.
A: If a stick was used to hold the bow in the drawn position it would be doing no work. The archer's arms likewise do no work on the bow, but they must still apply a force. To apply the force requires the muscle cells to remain contracted, and they use more energy when they are contracted, producing heat as well as the lactic acid that causes a feeling of tiredness and eventually reduces the muscles' efficiency.
A: In a static position, all the energy you use is converted to heat. To produce a constant force that does not move anything, you don't need to be expending energy. Place a book on a table; the table exerts a constant force on the book, but is not expending any energy. Only when the force is changing an object's velocity is when energy must be expended, because that energy is then converted into the object's kinetic energy.
