Trying to really understand work

[U.Renko]

I was looking at some sliding doors and thinking/reviewing about the concept of work.
So I have a few questions

In order to close or open it, gravity does no work since the door moves on horizontal and not vertically. So far I understand it.

1)If I move it back and forth and return to the same place, again no work is involved. Except if we consider loss of energy due to friction. But that energy is converted in heat...
So in the end is there a net work or not?

2)If I open it and close it, it's stopped then moves and stops again, so the initial kinetic energy is zero and final kinetic energy is zero, therefore total work should be zero. But what if we take heat into consideration?

3)What about those little wheels? Do they store some kind of potential energy?

4)If I pick an object, like some dumbell and keep holding it, the total work on it due to gravity is zero. Eventually I'll start to get tired, lose some calories, and sweat a little bit so my arms muscles are turning energy into heat, rising body temperature and so on.
So, are they doing work?

 

[elegysix]

there are two types of forces which do work here. conservative and non-conservative.

when you move something and then return it back to its initial position, any work done by gravity is zero. this is because it is a conservative force, and work done by it only depends on initial and final positions.

however, work was done by the non-conservative forces, such as air drag and friction, which constantly work against you by creating heat and drag and so forth. this type of work is path dependent, and so different paths mean different amounts of work, regardless of the initial and final positions.

 

[Lsos]

In moving a door, whatever work you put into it is a result the door's inertia and ultimately fricition. The little wheels have kinetic energy when they are moving. However, that will also inevitably get turned into heat.

When holding a dumbbell you get tired due to inefficiencies of the human body/ your muscles. It has more to do with biology than physics, but ultimately, at a cellular level, there is motion due to a force going on, even though you might not see it. If this inefficiency bothers you, you can simply rest the dummbell on a table where it will remain supported forever.

 

[U.Renko]

I see...

If I understood correctly, the amount of heat generated in my first example is path-dependent.
I remember hearing from my teacher that "work done by friction" is not a rigorously correct term, altough I can't remember exactly why...

And for the arms muscles example, surely the human body is a complicated system, but in the end there is work done at cellular level.

Is that right?

 

[Ken G]

I remember hearing from my teacher that "work done by friction" is not a rigorously correct term, altough I can't remember exactly why...

I don't think there's any issue with work being done by friction. I suspect the problem here is that there is a general meaning for work, but there's also a specific context where it is of greatest convenience, and the two get confused. The general meaning of work is simply a force applied over a distance, and you multiply the two together (in general there is a vector dot product there, but let's just talk about one dimension to keep it simple). That applies just as much to friction as to conservative forces. But in the case of conservative forces, there is a particularly easy bookkeeping-- the work done will not be path dependent, but will only depend on the initial and final locations. Then you can define a "potential energy function", which depends on location only, to keep track of work done, and it's all very much easier. But that great convenience doesn't mean conservative forces are the only ones that do work-- it just means they are the ones whose work is easier to track. When you lift weights, you are doing lots of work, but you are not doing any net work on the weights. Instead, the work being done is happening in the muscles, and is creating heat.

Perhaps a good example to imagine is a block sliding on sandpaper. The block might start out with lots of kinetic energy, but as it slides, it comes to a halt. This means friction did negative work on the block, as the force was in the opposite direction from the distance over which it was applied. But since energy is conserved, that negative work on the block has to show up as positive energy somewhere else, and that's generally heat. Now if you push the block the other way, the force reverses sign and is again opposite the motion-- the friction is always doing negative work on the block, regardless of the direction of the motion. That's like a barbell going up and down-- there is always negative work being done by some type of friction. In addition, there is work being done against gravity, and by gravity, alternatively, but that part of the work balances out-- it is only the work done against friction that keeps being negative on the barbell, and generates positive heat all the time.

 

[chrisbaird]

When you lift a barbell, you do work on it to raise to a higher gravitational potential. When you let it fall back to its original position, you could get that energy back; for instance, the barbell does work on a crank which turns a generator and produces electricity, or the barbell does work on a cheap brittle tabletop and accelerates wood-chips so that they go flying everywhere. Unfortunately, our arms do not have a mechanism for recovering energy mechanically, so letting the barbell fall back to its original position in your hand just means that the original work you put into the system has turned into waste heat.