- #1
modulus
- 127
- 3
I'm getting really confused about a specific application of the work-energy theorem, and I'm hoping you guys at PF could help out.
I'll start out by stating three concepts I've learnt, and I'll develop the apparent contradiction I run into.
Number one. the negative of the work done by the conservative internal forces on a system equals the change in potential energy of the system. Fine. It sounds good. It feels good. It makes sense. And I don't have problems applying it.
Number two. The work done by the external forces on a system equals the change in total (mechanical) energy. It makes perfect sense. Sounds perfectly natural. And it's easy to apply. But, this is exactly where my problems start. From what I know, and how I've been using this concept, I understand that the change can be in the kinetic or the potential energy of the system.
And number three. This is what I'm not getting. The work done by all forces (external and internal) equals the change in kinetic energy of the system. From the first concept, we get that the work done by the internal forces is indeed the change in kinetic energy (it's like the work-energy theorem). But the second part says the external forces change the kinetic energy too (or I should say 'only'). But that doesn't make sense, the external forces can cause changes in the kinetic or potential energy. So the sum of the internal and external forces' work cannot account for only the change in kinetic energy.
And before ending the post, I need to give you one example where the external forces cause a change in potential energy. This example really confirmed my doubts. There was a spring of spring constant k. It had two equal masses attached on each side, and was pulled by a distance x/2 on each side. as I evaluated, the total work done by the external forces equaled the negative of the work done by the spring, and, most importantly, the increase in potential energy of the spring. So, external forces do change potential energy.
Please help...
I'll start out by stating three concepts I've learnt, and I'll develop the apparent contradiction I run into.
Number one. the negative of the work done by the conservative internal forces on a system equals the change in potential energy of the system. Fine. It sounds good. It feels good. It makes sense. And I don't have problems applying it.
Number two. The work done by the external forces on a system equals the change in total (mechanical) energy. It makes perfect sense. Sounds perfectly natural. And it's easy to apply. But, this is exactly where my problems start. From what I know, and how I've been using this concept, I understand that the change can be in the kinetic or the potential energy of the system.
And number three. This is what I'm not getting. The work done by all forces (external and internal) equals the change in kinetic energy of the system. From the first concept, we get that the work done by the internal forces is indeed the change in kinetic energy (it's like the work-energy theorem). But the second part says the external forces change the kinetic energy too (or I should say 'only'). But that doesn't make sense, the external forces can cause changes in the kinetic or potential energy. So the sum of the internal and external forces' work cannot account for only the change in kinetic energy.
And before ending the post, I need to give you one example where the external forces cause a change in potential energy. This example really confirmed my doubts. There was a spring of spring constant k. It had two equal masses attached on each side, and was pulled by a distance x/2 on each side. as I evaluated, the total work done by the external forces equaled the negative of the work done by the spring, and, most importantly, the increase in potential energy of the spring. So, external forces do change potential energy.
Please help...