Question: A previous post ([What Is Energy? Where did it come from?](https://physics.stackexchange.com/q/3014/)) defines work qualitatively as "a process in which energy is transformed from one form to another form". And mathematically, work is defined as:

$$\Delta KE=\int\_{C} \vec{F}\cdot\mathrm d\vec{r}$$

But if you imagine lifting up a rock from the ground at constant speed, am I not doing work on the rock by converting the chemical energy stored in my muscles into the potential energy of the rock? I am confused because the kinetic energy of the rock does not change and yet I am still converting energy from one form to another, which is the qualitative definition of work. What's the right way to think about this and the concept of work in general?

Answer: 
I think maybe you are confused by an example that is often given to emphasize that the physics definition of "work" doesn't always match how it is used in everyday speech. If you move a rock *horizontally* at constant speed, then you are doing no work on the rock. Its kinetic and potential energy are both the same through the whole process. This is a common example because it certainly feels like you are doing work, and that is because maintaining constant tension in your muscles takes energy, which is converted into heat. Individual cells contract and then get tired and loosen up; you can't just lock your muscle at a certain length.

But lifting a rock upward is different, even if the velocity is constant. Then you really are doing work on it in the physics sense, because you are converting chemical energy to gravitational potential energy.
I think perhaps the easiest (perhaps way too didactic) method to understand it is in terms of currencies. For example, think of dollars (for potential energy), euros (for kinetic energy) and Yens (in the case of muscles chemical energy).

In the example of lifting up a stone (supposing somehow it was originally in motion), you are exchanging Yens for dollars (meanwhile increasing the stone's potential energy), but you do nothing with the entire system's total energy (no one is actually changing the total amount of euros in your pocket). In this simple
metaphor, your total capital is constant and therefore the Energy is conserved.

You can in fact think the total Work done as the exchange house total money exchange

Hope this is useful. Regards