Question

Is potential energy the same thing as work?

Answer 1

No. Work is a change in potential energy. It's the difference between a check and your bank balance. A check represents a change in your bank balance.

Answer 2

The potential energy of a mass m raised to a height h above the ground is mgh, the reason being that mgh is the work that would be done if the mass fell to the ground.

Answer 3

I ask this question because I'm solving a physics GRE question and they had a solution for it, but they use PE as Work and I didn't know if it was correct. I used a different method and got the same answer. So I'm just wanting an explanation.

Answer 4

\[W=- \Delta U\] Put simply

Answer 5

If you know calculus:\[W=\int\limits_{1}^{2}F \cdot dr\]\[U=-\int\limits_{1}^{2}F \cdot dr\]

Or, most usefully:\[\frac{\partial U}{\partial r}=-F\]

Answer 6

I assume you're fine with the concept of potential energy. It's the thing where kinetic energy disapears to (a force is required to to that), so that KE+PE=constant. It's impossible to measure this constant directly, but we can see that the thing is conserved (as always the change in (KE+PE) is *always* 0).
When there is a change in PE (of course there will be an opposite and equal change in KE simultaneously), by definition work has been performed (by who and on who doesn't matter that much, as PE is stored by both the force field and the object, PE energy cannot exist without both).
When something's got a lot of potential energy, you know that a lot of work can be performed on it if it begins rolling down the potential hill.

Note that when I talk about higher and lower potential energies, there is no actual value that can be agreed on, as long as you're consistent in your problem it shouldn't matter. By convention PE=0 infinitely far away from a gravitational mass (that is, 0 is as high as it gets: this has the benefit that if you begin at infinity with 0 KE, KE will always =-PE, as KE+PE=0.