Where does the energy goes if the force is parallel to the displacement?

Question

So, we all know that if force is perpendicular to the displacement, then work done is 0. But to generate force, I have to use up some of my energy. Had the angle not been perpendicular, my energy would have transferred in increasing the velocity of the object but since the force angle is perpendicular, I wonder where my energy is going. My hypothesis is that it contributes to the potential energy of the object as evident from the following example: In circular motion, force is always perpendicular to the displacement, so it does 0 work, but at the same time we know that force is important to maintain the motion which is circular, therefore I think force contributes to the potential energy which keep the object in orbit.

Answer 1

But to generate force, I have to use up some of my energy.

In a physics sense, this is incorrect. No energy is required to create or maintain a force. Set a rock on the ground, and a force exists between the two. No energy is transferred to maintain the force.

Close a lid with a spring and latch it. The spring maintains a force on the lid indefinitely, with no energy transfer.

If you're trying to maintain a force with your muscles, yes that takes energy because the muscles slip. The displacement in the muscle fibers produces heat and causes the cells to consume energy.

Answer 2

You are performing work on a massive object. So if the velocity of that object changes because of this force, then the work goes into kinetic energy. If the velocity doesn't change, then you aren't performing any work. That's the case of a moving charge in a magnetic field. What does change, however, is the momentum of that charge, i.e. momentum conservation requires that the magnetic field is "anchored" to something that can absorb that momentum change. The mass of that "anchor" would have to be infinite for the momentum change to be associated with no change in energy. In other words, this is one of those cases where the idealization introduces a paradox because we are explicitly neglecting momentum conservation laws.

Answer 3

I wonder where my energy is going.

You are confusing physical effort with physics work. For example, you can push on a wall all day long and if it doesn't move you do no physics work. You do, however, expend energy. The same applies for holding, but not lifting, a heavy weight. Richard Feynman in his physics lectures described it this way:

The fact that we have to generate effort to hold up a weight is simply due to to the design of striated muscle. What happens is when a nerve impulse reaches a muscle fiber, the fiber gives a little twitch and then relaxes, so that when we hold something up , enormous volleys of nerve impulses are coming in to the muscle, large numbers of twitches are maintaining the weight, while other fibers relax. When we hold a heavy weight we get tired, begin to shake, ...because the muscle is tired and not reacting fast enough.

If you are supplying the centripetal force to maintain horizontal circular motion of a ball on a string, you do no physics work because your force acts inward whereas the velocity of the ball is directed tangent to a circle. But you are expending energy (doing physiological work internal to your body) just like you would do pushing on a fixed wall or holding a heavy weight in place. In this case, however, your physical effort is in keeping the ball from flying off in a straight line.

Hope this helps.