Why does holding something up cost energy while no work is being done?

Question

I read the definition of work as $$W ~=~ \vec{F} \cdot \vec{d}$$ $$\text{ Work = (Force) $\cdot$ (Distance)}.$$
If a book is there on the table, no work is done as no distance is covered. If I hold up a book in my hand and my arm is stretched, if no work is being done, where is my energy going?

Answer 1

While you do spend some body energy to keep the book lifted, it's important to differentiate it from physical effort. They are connected but are not the same. Physical effort depends not only on how much energy is spent, but also on how energy is spent.

Holding a book in a stretched arm requires a lot of physical effort, but it doesn't take that much energy.

• In the ideal case, if you manage to hold your arm perfectly steady, and your muscle cells managed to stay contracted without requiring energy input, there wouldn't be any energy spent at all because there wouldn't be any distance moved.

• On real scenarios, however, you do spend (chemical) energy stored within your body, but where is it spent? It is spent on a cellular level. The only way your muscle cells can stay contracted is by receiving electrical impulses. This electrical energy comes from the chemical energy contained within your molecules. What happens on a cellular level is that the cells contract and relax very quickly, thus resulting in a macroscopic contracted muscle. Since the cells are moving and applying a force, they are doing work. Since they are not efficient machines, they are also releasing a lot of heat. So, finally, the Chemical energy stored within your body is released by the cell as both work and heat.*

Both on the ideal and the real scenarios we are talking about the physical definition of energy. On your consideration, you ignore the movement of muscle cells, so you're considering the ideal case. A careful analysis of the real case leads to the conclusion that work is done and heat is released, even though the arm itself isn't moving.

* Ultimately, the work done by the cells is actually done on other cells, which eventually dissipates into heat due to friction and non-elasticity. So all the energy you spend is invested in keeping the muscle tension and eventually dissipated as heat.

Answer 2

This is about how your muscles work -- the're an ensemble of small elements that, triggered by a signal from nerves, use chemical energy to go from less energetical long state to more energetical short one. Yet, this obviously is not permanent and there is spontaneous come back, that must be compensated by another trigger. This way there are numerous streches and releases that in sum gives small oscillations that create macroscopic work on the weight.

Answer 3

Perhaps an analogy is in order. Lets hold up the book by using an electromagnet (say we put a piece if steel under it ). If the coils were made of superconducting material it would take no energy input to maintain the position/field strength. But if we use ordinary wire, ohmic loses within the coil must be made up for by externally supplied electrical energy.

Answer 4

The reason is that you need to spend energy to keep muscle stretched.

The first thing you need know is that the work $W=F \Delta x$ is the energy transfer between objects. Hence, there are no work done on the book when it is put on the table because there are no movement.

When your arm muscle is stretched, however, it consumes energy continuously to keep this state so you feel tire very fast. This energy comes from the chemical energy in your body and most of them are converted into heat and lost to the surrounding. In this situation, no energy is transferred to the book, so no work is done.

You can feel the different energy consumption when your arm is stretched in different angle. A particular case is that you put the book on your leg when you sit on a chair so your muscle is relaxed and the energy spent is less.

There are also a special type of muscle, smooth muscle, requires very little energy to keep its state so that it can always keep it stretched and you won't get tire:

Tonic smooth muscle contracts and relaxes slowly and exhibits force maintenance such as vascular smooth muscle. Force maintenance is the maintaining of a contraction for a prolonged time with little energy utilization.

Answer 5

When a physicist talks about work, they are using the word in the technical sense of the equation you quote. To a biologist, though, work might be defined as energy expended to carry out a task. In your example, your arm will not naturally stay in the position described. Your body (mostly your muscles) must expend energy to hold your arm (and the book) in a set position, unsupported by anything but your own physiology.

So, by the biologist's definition, your muscles are doing work to hold up the book and your arm (muscle fibers are contracting and relaxing based on a host of chemical processes at the cellular level). But by the physicist's technical definition, no work is being done.

Answer 6

Consider an analogy,

We get tired after STANDING for some time,without doing any work*. The reason behind this is same as the reason of why we dont do any work holding any object above our heads, but this case is easier to comprehend,

when we stand we r actually resisting the tendency of falling on the ground,muscles are holding on to the structure of our body so that we dont collapse on the ground like some non living thing,

these muscles have fibers which have have streached themselves ,which requires energy,

Similarly when we hold something above our head we r doing the same thing, resisting that collapsing tendency , which causes elongment in the muscles which requires energy.

Answer 7

Energy is being expended maintaining it in position. Earth's gravity is applying a force downwards, the book is being accelerated down gravitation force.

A force is being applied to the hand and arm which must be resisted and thus energy expended.

The arm and book are not a closed system.