Gravitational potential energy dot points? (2 Viewers)

[loong21]

I'm trying to write my notes, but I can't grasp the idea of gravitational potential energy!
I don't know if I am looking at it the wrong way or if I've made it too complicated or even if i'm simply wrong.
The two dot points regarding GPE are completely fucking me over..

Can somebody please explain to me what I need to know for this dot point? All I wrote for this is that due to the law of conservation of energy when work is done, gravitational potential energy is created??
- Explain that a change in gravitational potential energy is related to work done.

Also this dot point, I find much harder, I can't even begin to write a note for this one? So many textbooks and sites are saying so many different things about this point! is the main idea of this point to do with a change in gpe or something? i have no idea??
- Define gravitational potential energy as the work done to move an object from a very large distance away to a point in a gravitational
field.

Thankyou! help would be much appreciated!

 

[CptSpauld1ng]

For the first dot point, GPE isn't necessarily 'created' when work is done. Work done is equal dPE + dKE, so if the KE stays the same, work done is equal to the change in GPE. As for the second, Imagine you have an object an infinite distance away, its GPE is 0. If that object moves to a position in the field, the GPE in its new position is equal to the work done to bring it there because Work = dPE.

 

[hit patel]

- Define gravitational potential energy as the work done to move an object from a very large distance away to a point in a gravitational
field.
: The movement of an object in a field requires work to be done which requires energy. In a gravitational field, -Gm1m2/r^2 which is actually also equal to mgh for distances of movement of 0-200 km altitude. But gravity itself is a force which does work in the opposite direction to the work done to move an object against a gravitational field. Since work is vector, the gravitational acceleration is always negative since the work is done in opposite direction and work is done on the object whereas when the object opposes gravitational acceleration and obtains altitude, work is done by the object meaning it is positive and as object goes up a gravitation field the work is done by object and therefore the Ep increases but still is always negative since the gravitation acceleration is always negative until it reaches an infinite distance away where gravitational acceleration is 0.

 

[treebrains]

It's probably better to do past paper questions that are relevant to changes in GPE. Maybe it might help to understand that everything possesses mechanical energy, which is the sum of KE and GPE. This is how energy is conserved -> GPE is just energy that will turn into KE at some other point in time, given the chance, hence it is potential. You should also know that Work is equal to Fs and also change in KE. Hence because energy is conserved (mechanical energy) then as GPE increases, KE decreases, et cetera, and because KE is changing Work is being done -> GPE is also changing, so (the same) Work is being done. The same work is done to decrease GPE as it is to increase KE.

 

[QZP]

I will derive GPE = -Gm1m2/r for you:

We first defined GPE as the work done required to move an object from, say, Earth's surface where GPE is taken to be 0. Hence GPE = mgh (GPE = W = Fs = (mg)s = mgh)

Can you see the limitation in this?

We now must redefine GPE such that it will account for the extremities in altitude. The limitation in GPE = mgh is that we take g to be a constant and hence as h approaches infinite, GPE approaches infinite - but this is logically wrong since we know that g varies according to the position within the gravitational field (the further we are away from a massive body, the weaker its gravitational field).

Now, instead of taking GPE = W = Fs = (mg)s, we take F = Gm1m2/r^2 (Universal Law of Gravitation). The formula now becomes GPE = Gm1m2/r (after you do the algebra) - but wait. We don't have the negative like the mentioned formula of GPE = -Gm1m2/r.

Consider the extremities of r:
As r approaches zero, GPE approaches infinite
As r approaches infinite, GPE approaches zero

Hence GPE increases as we are closer to the surface - but this doesn't make sense logically. Therefore formula is now GPE = -Gm1m2/r. This accounts for both extremities of r (GPE decreases with extreme far distances via the universal gravitational law, and GPE decreases with extreme close due to the negative that makes it so GPE is MORE negative i.e. less at surface than anywhere else.)

We can interpret this final formula as gravitational potential energy is the work done to move an object from very large distances away (infinite) to a point within the gravitational field.

If you aren't strong in math just accept the formula :S

Disclaimer: This is how I learnt it due to the lack of ability for teachers to explain the derivation to me and it may not be absolutely correct.