How to calculate the demand of energy necessary to hold an object?

[LCSphysicist]

Homework Statement

How to calc the demand of energy necessary to hold an object in certain space of time?

Relevant Equations

All below

I was just think how we could calc the power that we need to do {obviously, in general/average, since varies from person to person} to hold an object
But we know the force we need to apply is equal mg.
I am pretty sure that this question is very comprehensive and because of this it becomes difficult to answer, we would need to know something about the muscles of our arm.
I could imagine the muscles contraying like a spring oscillating, do you know any articles that say about it?

 

[etotheipi]

You are correct to link it to muscle contractions. When you hold something in front of you in a stationary position, your muscles undergo isometric contractions. This is the energy-requiring process that results in you being able to maintain tension and exert the contact force on the object (so whilst this contact force from your hand does no work on the object, you still expend energy within your muscles as the muscle cells continually contract and relax).

That is as much as I know. I am not sure how you could go about calculating a numeric value, but I will think about it. I found https://journals.physiology.org/doi/pdf/10.1152/jappl.1976.41.2.136, which might be a starting place.

 

[etotheipi]

In fact, Feynman touched upon this in his lectures,

Spoiler: Expand

It is a fact that when one holds a weight he has to do “physiological” work. Why should he sweat? Why should he need to consume food to hold the weight up? Why is the machinery inside him operating at full throttle, just to hold the weight up? Actually, the weight could be held up with no effort by just placing it on a table; then the table, quietly and calmly, without any supply of energy, is able to maintain the same weight at the same height!

The physiological situation is something like the following. There are two kinds of muscles in the human body and in other animals: one kind, called striated or skeletal muscle, is the type of muscle we have in our arms, for example, which is under voluntary control; the other kind, called smooth muscle, is like the muscle in the intestines or, in the clam, the greater adductor muscle that closes the shell. The smooth muscles work very slowly, but they can hold a “set”; that is to say, if the clam tries to close its shell in a certain position, it will hold that position, even if there is a very great force trying to change it. It will hold a position under load for hours and hours without getting tired because it is very much like a table holding up a weight, it “sets” into a certain position, and the molecules just lock there temporarily with no work being done, no effort being generated by the clam.

The fact that we have to generate effort to hold up a weight is simply due to the design of striated muscle. What happens is that 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 into the muscle, large numbers of twitches are maintaining the weight, while the other fibers relax. We can see this, of course: when we hold a heavy weight and get tired, we begin to shake. The reason is that the volleys are coming irregularly, and the muscle is tired and not reacting fast enough.

Why such an inefficient scheme? We do not know exactly why, but evolution has not been able to develop fast smooth muscle. Smooth muscle would be much more effective for holding up weights because you could just stand there and it would lock in; there would be no work involved and no energy would be required. However, it has the disadvantage that it is very slow-operating.

Feynman Vol. I, Chap. 14

Perhaps you could think of each individual fiber as a spring, and determine some effective spring constant. Then find the work needed to contract the fiber to maximum contraction in a single cycle (assume this is dissipated as heat when the fiber relaxes). Then you can multiply up by the number of contractions per second and the number of fibers in the muscle to get an estimate for the chemical energy required per second.

The key part would be how to determine that effective spring constant. That I am not sure.