How do I calculate the energy required to hold a weight at arm's length?

Question

I am interested in the energy consumed/produced by muscles. It will be higher with a heavier weight but by how much?

Answer 1

You perform no work holding an object steady because your arm could just as easily be replaced by a shelf. You only perform work when you move an object against a force.

Your muscles will consume energy as they strain against the weight of the object, but no energy will be transferred to the object.

- An elderly Professional Engineer

Answer 2

Deep Thought is absolutely correct; however, he overlooked explaining why he was talking about "work" instead of energy. Energy, by definition, is the capability to do work or cause a change.

Thus, energy is a sort-of potential (a capability) for moving or changing things. Thus, potential energy represents work that could be done, but only if the mass in question moves; so that kinetic energy is used up.

In your example, nothing is moving or changing. No work is performed; so no energy is expended.

There is energy in your body being expended because electro-chemical changes are being effected when holding that weight up. Even though you are expending no energy on that weight, you are exerting an upward force on it with your hand. But, as Deep Thought pointed out, that is not work/energy expended on moving the weight.

Because the weight is not moving, we can say the upward force from your hand is exactly equal to the weight (W = mg) of that weight. So we have f = F - W = 0 = ma; where f is the net force on the weight, F is the upward force of your hand, and W is the weight of the weight acting downward.

When f = ma = 0, where m = mass and a = acceleration, a = 0 because m>0. Thus, when f = 0, the weight and your hand are not accelerating; so, starting at rest, there is no motion and, therefore, no work/energy being expended.

Bottom line, things have to move or change for work to be expended. But forces can still be exerted even when there is no work.

Answer 3

Sounds like leverage or torque. Force or Weight x Distance.
eg. 10 lbs x 2 ft = 20 Ft-lbs.
Or possibly examine "potential energy".