You are NOT a lecturer who teaches dynamics. Do not tell such obvious lies. Please Register or Log in to view the hidden image!
I study Mechanical Engineering, Dynamics is a compulsory subject. If I push a wall with force and the wall does not move, I did NO WORK, because F(0) = 0. But I feel exhausted, where did my energy go?
It's because of the way muscles exert force. They do this by a biochemical process that continuously consumes chemical energy (appearing finally as heat) while the muscle fibres are in tension. The process is complicated: look up sliding element theory, for example, if you want to read about how it works. I am not an expert on this. But you are now hijacking your own thread onto a totally different subject.
They didn't cover this in your compulsory subject? That's unfortunate. You did no external work on the wall because the wall didn't move. However, some internal transformations of energy occurred within your body. Some chemical energy in your muscles was transformed into internal kinetic energy of the muscle fibres and into waste heat. There are many other internal energy transfers that occurred as you pushed against the wall. When you talk about work, you need to be clear about what system you're considering. Here, it seems that you were considering the system that consists of your entire body, and its potential to do work on the outside environment (which includes the wall). If you were to define a different system, you might be able to reclassify some of the internal energy transfers as work, because those energy transfers would no longer necessarily be internal processes.
Faculty of Engineering, Mechanical Division. I teach Dynamics, Statics, Mechanics of Solid, Engineering Statistics.
Saint: Okay. I'm surprised you were unaware of the answer to the question of why no work is done when you push against a wall, given your job. Anyway, at least now you know.
It depends how we draw the boundary of our control volume. It we draw it around the wall only, and the wall does not move, the force exerted on it will do zero work.
I feel very sorry for you students; just kidding, you obviously have no students or even any education in engineering.
Actually, it's not quite true. When you push against a wall, the atoms in your hand try to push into the atoms in the wall. The usual result is that the solid structure of the wall deforms slightly - electron clouds butt up against one another and there's a little give. In effect, the electromagnetic repulsive force from the wall increase until it balances the pushing force from your hand. In bulk, the wall doesn't move, but near the point of contract there is a small amount of buckling. If you take this into account, there might be a tiny amount of mechanical work done by your hand on the wall. That work is "converted" into electrical potential energy. That has nothing to do with why your muscles get tired if you keep pushing against the wall, though.
I think there could also be a bit of influence from the Pauli Exclusion Principle, beside simple electrostatic repulsion.
And, when you push and the wall doesn’t move it pushes back at you with the same force. You use a balance of pushing and pulling muscles in your body to counter the forces but still apply forward pressure on the wall. So you are using groups of muscles for weight balance against each other in your own body too. If your body wasn’t countering the push back from the wall, all that would happen is you would push yourself away from the wall… ?