Hell,
I'm confused now. So lets make things easier.
Guju is correct that KE is always the same formula.
But potential energy? Um, yeah, it's always the definite integral of the dot product of force and displacement, but that is a seriously flawed way for an average premed to think about it. You just learn the different formulas, and use them. If there's gravity, it's mgh, if there's a spring, yadda yadda. Just know them. I hate that the conceptual approach is not right, but it isn't.
Work-Energy Theorem? Vastly overrated in terms of difficulty. In all cases, change in energy is work done. That's all. If there's more energy at the end (potential plus kinetic) then work got done to raise it. If there's less, then negative work got done (or, another way to think about it, the system did work on something else). On the MCAT this can be applied to two types of questions:
- If the total energy (kinetic plus whatever type of potential is relevant to this problem) changes, then that change is the work done by some force you haven't accounted for (in other words, a force that wasn't dealt with in your potential energy term). Friction is the usual suspect, plus any outside force specified by the problem.
- If you are asked how much work is done by one of the conservative forces (for MCAT purposes, a complete list is gravity, electrostatic, and springs, I think), then work done is just the change in the relevant potential energy term. If there's less potential energy at the end, then it dropped because that force did work -- it must have, because the (potential) energy had to go somewhere. If more, the force did negative work (work was done to raise the PE).
The second problem type may account for grey's confusion about gravity: work done by gravity is not necessarily zero. In all cases (
all cases), work done by gravity is the change in gravitational potential energy. If something winds up lower than it started, gravity did work, regardless why or how it got lower. If it winds up higher, gravity did negative work (work got done to raise that PE). Use mgh.
Similarly -- for electric fields, if a charged something winds up at a spot with a different potential from that where it started, work got done by the electric field. Use the formula. If something attached to a spring winds up at a spot with different displacement from where it started, work got done by the spring. Use the formula.
In practice, use the work done, and thus the change in some form of energy (usually kinetic), whenever either:
(1a) the path (direction and/or speed) or mechanism (such as a collision, if you are asked for work done by the collision) is complicated or unknown; or
(1b) you don't care how, or how fast, whatever it is got wherever it is;
and
(2a) one of the three conservative forces is present; or
(2b) a non-conservative force (i.e., any force besides those three) is present, and you can see from the problem how to use the work formula (Fdcos(theta)) on it, and it's simple to do so. Usually, but not always, only one of 2a and 2b is present in a problem.
That's Work-Energy. I think it's confusing because they call it a theorem and give it capital letters; maybe the lesson is to avoid capitalizing it.
Great big breath. When I write the definitive MCAT physics book, y'all have to tell your friends to buy it, 'kay?
(This was longer than I thought it would be -- I think I'm doing some dead horse beating. I suppose that means Q is going to jump in here any time, because we know she's into that...)