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: 
Time to jump into the fray. This equation here

$$W=\int\mathbf F\cdot\text d\mathbf x$$

is just the definition of the work $W$ done by a force $\mathbf F$ along some path that you are performing the integral over. It is always applicable, as it is a definition. However this equation $$W=\Delta K$$ is *only* valid when $W$ is the *total* work being performed on your object. If there are multiple forces acting on your object then, you would need to first add up all of the work done by each force, and then this total work will be the change in kinetic energy.

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> 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?
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Your force is doing positive work on the rock. Gravity is doing negative work on the rock. The net work in this case is $0$, so the change in kinetic energy is $0$. The definition of work is all you need. Is $\int\mathbf F\cdot\text d\mathbf x\neq0$? Then your force is doing work. You can try to follow where all of the energy is going, but that is just bookkeeping (which is essentially the purpose of energy in introductory Newtonian mechanics). All you need to do to determine if a force is doing work is look at the integral.

The problem with your qualitative definition of work is that it is hard to apply generally, as similar scenarios will need to be explained very differently. For example, in your case with lifting the rock, one could argue that the work you are doing is increasing the potential energy of the rock-Earth system. Ok, that is fine. But now let's say you, the rock, and myself are in space far away from any substantial gravitational influences. Let's say you also start pulling up on the rock (that already has some upward velocity) with a force equal to what its weight would be on Earth, but I pull down on the rock with that same amount of force. You are doing the exact same thing here, and you are doing the same amount of work as before. But now we cannot say that you are changing the potential energy of the rock, as it is not being acted upon by some gravitational force. Instead now you have to consider the rope / me / energy I am expending, etc. It becomes complicated and unnecessary if all you wanted to know is if you are doing work or not. Just look at the integral and you are good to go.

Work is always associated with some form of energy exchange, but I would highly recommend against trying to use energy exchange as a definition of work, as the application of this definition is usually much less practical than just doing the integral found in the definition of work.
The problem with work is the word we use for it. Since we work everyday, we're used to associate "physical work" and "effort", and that's confusing.

Physical work is a well defined quantity, but it needs 3 surnames, and this is usually omitted. You must specify these three parameters:

Work done [by some force] [on some system] [along this path]
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Note how deep is this sentence. Work is done by forces, not by people. You don't do work, a force does work, not you.

Plus, work must be considered on a system. If you lift a rock, you are doing possitive work on the rock. However, gravity is doing negative work on the rock.

$W\_{you}=mg\cdot h\cdot 1$; because $cos(0º)=1$

$W\_{gravity}=mg\cdot h\cdot -1$; because $cos(180º)=-1$

So the total work on the rock is $0$ and that's why you are not increasing its kinetic energy. If you perform extra forces, then you will accelerate teh rock ($F=ma$, you know). So you'll accelerate the rock and hence the KE changes. It makes sense.

But you have to realize that you are considering the rock as a well delimited system. If you include the chemical energy stored in your arms, then your system under consideration is not the rock alone anymore. Your new system under study will be the rock-person system, and then you have to consider ALL forces involved in that system, not just your arm.

In conclusion: work needs 3 specifications. You seem to be needing to focus on the "on what system" part.

Hope this helped