Theoretical Question: Is W = PE?

[Goldenwind]

This isn't a homework question, just something I was pondering one day.

W = Fd = mad
PE = mgh

m = m, obviously
g and a are both measurements of acceleration
h and d are both measurements of distance

If g = a, and h = d, is it fair to say that W = PE?

Therefore, W = a change in KE, so PE = Change in KE?

 

[Andrew Mason]

This isn't a homework question, just something I was pondering one day.

W = Fd = mad
PE = mgh

m = m, obviously
g and a are both measurements of acceleration
h and d are both measurements of distance

If g = a, and h = d, is it fair to say that W = PE?

Therefore, W = a change in KE, so PE = Change in KE?

Not quite. The work done on an object can result in a change in kinetic and/or potential energy. In order for W to be equal to KE, the accelerating force would have to be at right angles to the direction of the gravitational force.

The correct equations are:

PE = mgh
$$W = \vec F \cdot\vec d = m\vec a \cdot\vec d = mad\cos\theta$$

ie. h would be 0 and $\cos\theta$ would be 1.

AM

 

[dynamicsolo]

This isn't a homework question, just something I was pondering one day.

W = Fd = mad
PE = mgh

m = m, obviously
g and a are both measurements of acceleration
h and d are both measurements of distance

If g = a, and h = d, is it fair to say that W = PE?

Therefore, W = a change in KE, so PE = Change in KE?

All you can really show by this argument is that work and energy have the same units; this does not let us conclude anything at a deeper conceptual level by itself. You'll run into a more extreme case of this when you study torque: you'll learn that torque and energy have the same units but are not much related at all.