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# GP and GPE difference ~ A2 Physics watch

1. I just wanted to check that I'm not going insane without consulting a doctor:

Gravitational potential is to do with the change in height rather than mass, if a point in the Universe has something very small like a GP of 1x10^-13(J/Kg) weighing 2kg, its GPE would be 2x10^-13(J), can this be converted to find its initial velocity using 1/2mv^2 at t=0?

..But surely it is more than this? The GP doesn't seem to take into consideration the change in the value of gravity because it would accelerate exponentially as it moves towards a point mass like the earth, and infact the GPE would be alot more than expected than the initial very small value of 2x10^-13(J)?

Writing this I have a feeling that 2x10^-13(J) isn't actually GPE but something else, can't quite put my finger on what it is though.
2. (Original post by Stephens)
..But surely it is more than this? The GP doesn't seem to take into consideration the change in the value of gravity
outside the value of earth g is not a constant any more hence the very reason why you're using V=-GM/R(derived by integration), .you only use g inside the earth (mgh) as acceleration can be assumed constant
3. (Original post by rbnphlp)
outside the value of earth g is not a constant any more hence the very reason why you're using V=-GM/R(derived by integration), .you only use g inside the earth (mgh) as acceleration can be assumed constant
Gotcha. So does Vm=mgh?

If so, I can't quite get my head round it because of the example I've said in my original post.
4. (Original post by Stephens)
Gotcha. So does Vm=mgh?
mgh is only valid for small distances because the gravity which mgh relies on is fairly constant. So Vm=mgh is only valid for small distances.
5. (Original post by Stephens)
Gotcha. So does Vm=mgh?
both are the same , but used in different scenarios mgh is although gives GPE is only used when calculations on the surface of earth .eg : a book of 10kg being raised to 10 m height ..
Vm on the other hand is used for calculations involving outside the earth eg; A satellite taken from the earth 's surface to a distance r.If we require to find the gravitational potential energy we use V.m
6. (Original post by Sakujo)
mgh is only valid for small distances because the gravity which mgh relies on is fairly constant. So Vm=mgh is only valid for small distances.
Is there a equation therefore for working out the total amount of work done against gravity to reach (R-x)? < Including the change in gravity? (R being distance between both masses and x being radius of the earth or which ever radius of point mass is being used).

I have a feeling I'm going around in circles here.
7. (Original post by Stephens)
Is there a equation therefore for working out the total amount of work done against gravity to reach (R-x)? < Including the change in gravity? (R being distance between both masses and x being radius of the earth or which ever radius of point mass is being used).

I have a feeling I'm going around in circles here.
Difference in potential at two different points in space times the mass of the object. Potential is calculated independent of gravity, in other words gravity has no effect on potential. To find out what you want to know simply find GM/r at one point and GM/r at another, find the difference in potential and times by the mass to get potential energy or work done.
8. (Original post by Sakujo)
Difference in potential at two different points in space times the mass of the object. Potential is calculated independent of gravity, in other words gravity has no effect on potential. To find out what you want to know simply find GM/r at one point and GM/r at another, find the difference in potential and times by the mass to get potential energy or work done.
Ah ofcourse, came across this earlier, apologies.

I mean, is it better to think of (V.m) as a kinetic energy at a point in space? Or something else? I was reading earlier V had something to do with the amount of energy required to move it to a distance R=infinity making V=0?

~Repped you Sakujo, in a few hours I'll do the other guy
9. (Original post by Stephens)
Ah ofcourse, came across this earlier, apologies.

I mean, is it better to think of (V.m) as a kinetic energy at a point in space? Or something else? I was reading earlier V had something to do with the amount of energy required to move it to a distance R=infinity making V=0?
Well potential is defined as work done per unit mass to move a point mass from infinity to that point. So I guess Vm= work done per unit mass times mass= work done. I think of it simply as energy
10. (Original post by Stephens)
Ah ofcourse, came across this earlier, apologies.

I mean, is it better to think of (V.m) as a kinetic energy at a point in space? Or something else? I was reading earlier V had something to do with the amount of energy required to move it to a distance R=infinity making V=0?

~Repped you both, btw.
this one anology some one on tsr told me and its helped me remember it quite well.
Spoiler:
Show
(Original post by stonebridge)
The potential at that point is a property of the Earth's field.
Put another mass there and that mass has potential energy.
The amount of potential energy depends on the mass you put there, and the gravitational potential at that point.
11. (Original post by Stephens)
Ah ofcourse, came across this earlier, apologies.

I mean, is it better to think of (V.m) as a kinetic energy at a point in space? Or something else? I was reading earlier V had something to do with the amount of energy required to move it to a distance R=infinity making V=0?

~Repped you Sakujo, in a few hours I'll do the other guy
Gravitational potential energy is the work done in moving an object from infinity to the point under consideration. If you draw a graph of gravitational force against distance, then you get an exponential curve. The gravitational potential energy is the area under this curve. I found this graph to be a good way of imagining it.
12. (Original post by LearningMath)
Gravitational potential energy is the work done in moving an object from infinity to the point under consideration. If you draw a graph of gravitational force against distance, then you get an exponential curve. The gravitational potential energy is the area under this curve. I found this graph to be a good way of imagining it.

I think this is what I'm having trouble with, infinite is refering to infinity small or long?
13. (Original post by Stephens)
I think this is what I'm having trouble with, infinite is refering to infinity small or long?
Inifinitly far away.
14. (Original post by Stephens)
I think this is what I'm having trouble with, infinite is refering to infinity small or long?
Haha :P The curve never touches the x axis, you just have to imagine there is some point where it is no longer worth considering, and call this point infinity.
15. (Original post by LearningMath)
Haha :P The curve never touches the x axis, you just have to imagine there is some point where it is no longer worth considering, and call this point infinity.
(Original post by Sakujo)
Inifinitly far away.
Thought so, but then:

"Gravitational potential energy is the work done in moving an object from infinity to the point under consideration. "

GPE is the work done in moving an object from the end of the universe to the point M on earth? That doesn't make sense, as mgh is relative to the height between both points on earth and the small distance to another point mass, not relative to the end of the universe, or where ever infinity may be?

This is driving me crazy.
16. (Original post by Stephens)
Thought so, but then:

"Gravitational potential energy is the work done in moving an object from infinity to the point under consideration. "

GPE is the work done in moving an object from the end of the universe to the point M on earth? That doesn't make sense, as mgh is relative to the height between both points on earth and the small distance to another point mass, not relative to the end of the universe, or where ever infinity may be?

This is driving me crazy.
Just forget about mgh, it's useless at large distances.

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