Why Do We Calculate ΔU as U2 - U1 and ΔKE as KE2 - KE1 in Physics?

[ehabmozart]

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!

 

[Doc Al]

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

Therefore: ΔU = - ΔKE

 

[ehabmozart]

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

 

[mathsciguy]

Are you talking about this in the context of mechanics relating to work?

 

[Doc Al]

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

 

[ehabmozart]

I still don't get the point!

 

[Doc Al]

I still don't get the point!

How about giving a specific example that illustrates your question.

 

[mathsciguy]

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]

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.