# Question about PE and KE?

Why is it the difference in gravitational potential energy is given by U grav 1 - U grav 2 whereas for the same system, delta KE is given by k2 - k1???

Kindly Clarify! Thanks a LOT!

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Doc Al
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You're probably thinking of a situation where the total mechanical energy is conserved, thus:
ΔE = ΔKE + ΔU = 0

Therefore: ΔU = - ΔKE

I know that.. I meant about the intuition ... WHy is it U 1 - U2 and not the opposite

Doc Al
Mentor
I know that.. I meant about the intuition ... WHy is it U 1 - U2 and not the opposite
I'm not sure I understand the issue. One goes up while the other goes down.

Just a note about what Δ means: When going from 1 to 2, ΔU = U2-U1 and ΔKE = KE2 - KE1

I still don't get the point!

Doc Al
Mentor
I still don't get the point!

I think the simplest case is to look at work due to gravity:
When, let's say you throw in a rock upwards, we know conceptually that the work done is negative since the weight is directed downwards and the displacement is upwards, also, the gravitational potential energy is given by U = mgh (m = mass, g = acceleration due to gravity, h=height (relative to some reference)). The equation W=U1-U2 is consistent with this, when we throw a rock upwards, U2>U1 and hence W<0 (negative), in the other case when we drop a rock, U2<U1 and hence W>0 (positive). Thus the equation is consistent with our idea of work.

I think, this would help if you want a more intuitive approach on this.

jtbell
Mentor
Why is it the difference in gravitational potential energy is given by U grav 1 - U grav 2
This is incorrect. By definition, ΔU = U2 - U1. "Δ" means "final minus initial".

For an object falling freely under the influence of gravity, U2 < U1 because h2 < h1, therefore ΔU is negative. On the other hand, KE2 > KE1 because v increases as the object falls, therefore ΔKE is positive.