Energy needed to hold up a weight

Everybody knows that you get tired if you try and hold up a weight for a period of time. The greater the weight and the longer the time the more tired you feel. Feeling tired means that you have expended some energy. Now it is easy to see that you will have given the weight some gravitational potential energy when you lifted it up but that is a finite and precisely measured amount (mgh).

Why is it that you are expending energy just to keep the weight in position without moving it?

Muscles are composed of a large number of individual cells and when the muscle as a whole is under tension these muscle cells contract. To do this they need energy and this energy is obtained from breathing which brings a supply of food and oxygen to the cells. The cell breaks down ATP to release energy. It is this need for a continual supply of energy top our muscle cells that makes us feel tired when we hold up a weight.

This contraction cannot be maintained without continual addition of energy and so the muscle continually relaxes and contracts. This can take place at a frequency of between 5 and 10 Hz. The contraction of the muscle as a whole is a sort of average of these small fluctuations within each cell. Although it seems as if you are holding your arm steady it is actually making tiny movements as the muscles contract and relax.

You may have seen this movement magnified in weightlifting contests where the lifter's muscles start to twitch when under great stress.


Note: we have used the word weight here since it is the force that we have to balance when lifting a mass in a gravitational field.