How do we lose calories while treading on a treadmill even the displacement is 0?

Question

How do we lose calories while treading on a treadmill even the displacement is 0?

Since, $W = F\cdot d$

Here $d = 0$

Hence, $W = 0$

Answer 1

Your muscles still have to expend energy to contract. The macroscopic kinetic energy of your center of mass is not the only relevant energy here.

A simpler case to consider that doesn't involve moving body parts is holding a book at a constant height. You are not doing work on the book, yet you will expend energy to keep the book up (see Why does holding something up cost energy while no work is being done?). The $0$ work just means there is no energy transfer between you and the book, but there can still be energy expenditure elsewhere.

Answer 2

It says you're a new contributor -- welcome to PSE!

BioPhysicist basically said it, so I'll just rephrase it in a different way. In a treadmill, the relevant reference frame is the band that keeps going backwards. So to do zero work, you would stand still, and because the band is going backwards, you would go along with it.

When running on a treadmill, you lose calories each time you push your foot off the band and move your body forwards and upwards.

Answer 3

The other answers give valid arguments, but I'd like to add that (as correctly pointed out by @Alchimista in the comments) the term $d$ (more precisely $\Delta r$) represents the displacement of the point of application of force. In this case, you exert a force on the treadmill band, and the band (the point of application) also moves backward so $W$ is infact non-zero! This can also contribute to the expenditure of chemical potential energy in your body (from previous meals and such).

Hope this helps

Answer 4

The fact that the displacement is zero (relative to the Earth) means the net work by all forces on you are zero. But what matters for the calories you burn is what work you do, not the work done by external forces (otherwise you could lose weight by standing on a moving walkway!). You have done non-zero work in order to stay still with respect to the Earth. If you did not do any work, the treadmill would have moved you backward with respect to the Earth. The work done by your muscles to resist the motion of the treadmill accounts for the calories you burned.