Work done on a pull up

Question

I use force to accelarate my body upwards and then I decelerate down. Both movements use energy, but the displacement is zero. I would say that the work done which is the energy used to move my body was not zero and maybe when going downward it has an opposite sign but still it feels like I used more energy to go up than down. Is the work zero because of 0 displacement?

Answer 1

When you ask about the work done, you need to specify by which force.

If you ask yourself, did gravity do work over the all motion? The answer is no: it did negative work when you went up and positive work when you went down, due to the displacement of your center of mass, for a net sum of 0. That is because gravity is a conservative force (a potential energy is defined and depends only on the initial e final condition, which being the same make up a difference of zero).

Let's assume you, as you probably are assuming, to be living in an external gravitational uniform field. Then we may ask, did you do any work going up and down? Or, putting it differently, did the bar holding you up do any work? The answer is no, that is because the displacement of the point on which the force is applied, your hands, is none.

Then you may ask, where did the energy needed to fight gravity come from, when gravity makes a negative work on you while you pull up, subtracting energy from the system. Well, it comes from chemical potential energy inside your muscles, which gets converted in gravitational potential energy. Sadly, this process doesn't reverse when you pull down, even though gravity does a positive work, pumping energy. All this energy gets converted into heat, due to the functioning of your body. This loss happens even when you pull up, in the conversion from chemical to gravitational potential energy, so that you spend more energy than it would be necessary if the dynamic was ideal.

I want to stress on the fact that the only force you apply is on the bar, and for slow enough movements it is always equal to the force of gravity, and it doesn't do any work.

Answer 2

The net work done by you would be zero if you were a conservative force, like the force of gravity or the restoring force of a spring, because you begin and end at the same location. But you are not a conservative force. You burn energy converting the chemical potential energy in your cells both accelerating up and down.

But the fact is even if you did not decelerate down but simply tried to maintain your upward position you would continue to burn calories in that upward position even though there is no subsequent displacement. That's because there is a difference between physics work and physiological work. Physiological work can involve a force with no displacement. Physics work doesn't.

Richard Feynman in his lectures on physics described it this way for the example of holding but not moving a weight:

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.

Hope this helps.