Understanding Work with Conservative Forces | Physics

[pokemon123]

so the concept of work I've never really understood (even after a year and a half of physics classes rip). What mainly confuses me is when the work done is positive or negative. From what I understand the net work=deltaKE or net work=-PE assuming energy is conserved (so if an external force was in the system this thereom does NOT hold true). But I get confused by this in situations where you seemingly are able to gain kinetic energy and potential energy despite having conservative forces.

For example: I define the system as the Earth, my hand, and a rock. If I lift the rock up and accelerate it shouldn't it gain KE because vf>vi (my hand is accelerating too so it gains KE) but isn't my hand and the rock also gaining PE because we are higher than before. Someone tried to explain this to me by saying that the reason why we're accelerating is because the overall potential energy is less at the top than at the bottom (i.e other PE like spring, electric) but I can't think of another significant type of PE in this scenario.

So yeah I'm confused how you seemingly can gain both PE and KE with conservative forces despite the work energy theorem stating the contrary.

note: I have only taken algebra so i would not understand calculus.

 

[Dale]

If I lift the rock up and accelerate it shouldn't it gain KE because vf>vi (my hand is accelerating too so it gains KE) but isn't my hand and the rock also gaining PE because we are higher than before

Yes. Note that this is not an isolated system. There is an external force from your muscles acting on your hand. That external force adds energy to the system resulting in an increase of both PE and KE.

The easiest way to fix that is to include your whole body as part of the system instead of just your hand. When you do that you find that the PE of your body goes down. The gravitational PE goes up, but the chemical PE goes down more. In the end the system has the same energy, but some of the energy has changed from chemical PE to gravitational PE and KE.

 

[kuruman]

The work-energy theorem says Δ(KE) = W_Net and always holds true. In your example, when you accelerate your hand holding a rock up, the system gains both potential and kinetic energy. The sum of the two increases in time, which means that mechanical energy is not conserved. This increase in mechanical energy is accounted for by the expenditure of biochemical energy. The rest of you arm that is attached to your hand and is not part of the system exerts a non-conservative force that does work on the system. You burn calories in order to increase the mechanical energy of the rock and your hand so that the total energy change, biochemical plus mechanical, is zero. Total energy is always conserved so that if you see that the mechanical energy of a system increases and you have accounted for all the conservative forces that do work on the system, you have to conclude that there must be some non-conservative force at play. A rocket shot up in space gains mechanical energy at the expense of the chemical energy in the rocket fuel.

 

[pokemon123]

Yes. Note that this is not an isolated system. There is an external force from your muscles acting on your hand.

The easiest way to fix that is to include your whole body as part of the system instead of just your hand. When you do that you find that the PE of your body goes down. The gravitational PE goes up, but the chemical PE goes down more.

ah I see, Thanks! this definitely makes me understand the concept of work energy thereom better.

thank you too kuruman!