Gravitational potential energy (GPE) (2 Viewers)

[eyeseeyou]

Why is there more GPE when an object is higher?

 

[InteGrand]

Why is there more GPE when an object is higher?

 

[eyeseeyou]

So it's by definition that "there is more GPE when an object is higher"?

 

[InteGrand]

So it's by definition that "there is more GPE when an object is higher"?

Pretty much. Note also that intuitively if we lift an object higher and higher, we've done more work against gravity to get it up there, so more (gravitational) potential energy is being stored in it.

 

[eyeseeyou]

Pretty much. Note also that intuitively if we lift an object higher and higher, we've done more work against gravity to get it up there, so more (gravitational) potential energy is being stored in it.

So if we lift something up, forces of gravity act upon it hence there is more GPE when it is higher. The higher it is lifted, the more forces act on it hence it has more GPE. Right?

 

[InteGrand]

So if we lift something up, forces of gravity act upon it hence there is more GPE when it is higher. The higher it is lifted, the more forces act on it hence it has more GPE. Right?

Not really, no. When we lift it up, we do work against gravity in order to move it up. Remembering that work done = change in energy, this work we do to it to move it up is transferred to the object as (gravitational) potential energy. It is clear that the higher we move it up, the more work against gravity we have to do (given by W = mgh for relatively low altitudes), so the more GPE that gets transferred to it.

 

[kashkow]

I need some help with a GPE question that I got wrong in my MCQ for trials.

Basically the gist of it was two identical satellites, P and Q, orbit a planet mass M at heights R and 2R respectively.

Which statement about GPE is correct:

A) Q has greater Ep than P
B) Q has twice Ep than P
C) Q has three times Ep as P
D) Q has less Ep than P

I don't really understand the answer; what would be your answers to this question?

(I could provide my answer + thought process but I first want to see what you think the answer should be)

Not sure if this is the right thread to put it in or if I should've started my own thread but this seemed appropriate.

Cheers!

 

[InteGrand]

I need some help with a GPE question that I got wrong in my MCQ for trials.

Basically the gist of it was two identical satellites, P and Q, orbit a planet mass M at heights R and 2R respectively.

Which statement about GPE is correct:

A) Q has greater Ep than P
B) Q has twice Ep than P
C) Q has three times Ep as P
D) Q has less Ep than P

I don't really understand the answer; what would be your answers to this question?

(I could provide my answer + thought process but I first want to see what you think the answer should be)

Not sure if this is the right thread to put it in or if I should've started my own thread but this seemed appropriate.

Cheers!

Q is higher up, so has a greater GPE than P. So the answer should be (A).

 

[kashkow]

Q is higher up, so has a greater GPE than P. So the answer should be (A).

Cheers, Integrand; that is the correct answer. So that sorta indicates that it must be me thats wrong and not the answers/question.

However I did B so I'm just wondering if/where my thought process must be wrong. (I knew this was a correct answer, just didn't think it was the "Best answer" since I thought B was more accurate)

So my thought process:

Basically with E=mgh (for smaller scale altitudes) I got 2mgR for Q compared to mgR for P.
Thus Q has twice potential energy.
Similarly I also calculated the GPE for large scale planetary objects and obtained a similar result...
So for Q:

-1/2 *Gmm/R

Compared to P:

-Gmm/R

I deduced that -1/2 is only half as much negative energy as -1 so it is effectively got more GPE but by twice as much... I know that might be seen as flawed logic since -1/2 is not "twice as much" mathematically, so is this where my logic was wrong?

That is basically why I chose B, because of those two answers, and even though I knew A was right, I thought B was more precise...

So could you please tell me is that where my logic went wrong with this question? or if I am totally missing the point or something?
Thanks

 

[InteGrand]

Cheers, Integrand; that is the correct answer. So that sorta indicates that it must be me thats wrong and not the answers/question.

However I did B so I'm just wondering if/where my thought process must be wrong. (I knew this was a correct answer, just didn't think it was the "Best answer" since I thought B was more accurate)

So my thought process:

Basically with E=mgh (for smaller scale altitudes) I got 2mgR for Q compared to mgR for P.
Thus Q has twice potential energy.
Similarly I also calculated the GPE for large scale planetary objects and obtained a similar result...
So for Q:

-1/2 *Gmm/R

Compared to P:

-Gmm/R

I deduced that -1/2 is only half as much negative energy as -1 so it is effectively got more GPE but by twice as much... I know that might be seen as flawed logic since -1/2 is not "twice as much" mathematically, so is this where my logic was wrong?

That is basically why I chose B, because of those two answers, and even though I knew A was right, I thought B was more precise...

So could you please tell me is that where my logic went wrong with this question? or if I am totally missing the point or something?
Thanks

Q has half the GPE of P, not twice. This is because the GPE function is inversely proportional to the distance r (since U = - GmM/r).

Q doesn't have negative half the GPE of P, just half. Despite having half the GPE of P, Q has a greater GPE than P, because GPE's here are negative (in other words, 0.5x is greater than x for negative quantities x).

Also, mgh is only a valid approximation for low altitudes. For orbital altitudes, it's no longer valid, and we need to use the -GmM/r.

 

[kashkow]

Q has half the GPE of P, not twice. This is because the GPE function is inversely proportional to the distance r (since U = - GmM/r).

Q doesn't have negative half the GPE of P, just half. Despite having half the GPE of P, Q has a greater GPE than P, because GPE's here are negative (in other words, 0.5x is greater than x for negative quantities x).

Also, mgh is only a valid approximation for low altitudes. For orbital altitudes, it's no longer valid, and we need to use the -GmM/r.

Ahhh I think I got it now! Yeah, I can see where I messed up; Basically all the answers given are a "mathematical" answer where it means:

A) Q > P
B) Q =2P
C) Q =3P
D) Q < P

In terms of GPE.

This means that B, C and D are wrong because if we applied mathematically above it would not be right. I just messed up somewhere in my logic and thought for some reason that having "half of a negative amount" = "twice as much of the original amount" (which is actually starting to use qualitative descriptions) and backed this up with "evidence" of mgh. Also I didn't realise that orbital altitudes like this one meant mgh was invalid. lol

Thanks anyway for clearing this up for me, really appreciate it!

 

[eyeseeyou]

Explain why the formula Ep=mgh cannot be used at significant distances away from the surface of the earth (1 mark)

 

[eyeseeyou]

Also

An object is stationary in space and located at a distance 6000 km from the centre of a certain planet. It is found that 1.5 MJ of work needs to be done to move the object to a stationary point 12,000 km from the centre of the planet

Calcuate how much more work needs to be done to move the object to a stationary point 56,000 km from the centre of the planet (4 marks)

 

[Tamama251]

Explain why the formula Ep=mgh cannot be used at significant distances away from the surface of the earth (1 mark)

Because once you leave the Earth to the corner of the universe (if there is one), it won't fall back to earth (hopefully).



1 mark for an explain? Da faque?

 

[ml125]

Explain why the formula Ep=mgh cannot be used at significant distances away from the surface of the earth (1 mark)

As altitude increases, g varies. Therefore Ep=mgh cannot be used for significant distances away from the surface of the earth.

Also

An object is stationary in space and located at a distance 6000 km from the centre of a certain planet. It is found that 1.5 MJ of work needs to be done to move the object to a stationary point 12,000 km from the centre of the planet

Calcuate how much more work needs to be done to move the object to a stationary point 56,000 km from the centre of the planet (4 marks)

 

[Fizzy_Cyst]

Alternatively in the last step above, could just do from 1.2x10^7 to 5.6x10^7, then no need to subtract

 

[ml125]

Alternatively in the last step above, could just do from 1.2x10^7 to 5.6x10^7, then no need to subtract

Ah yes, noticed that as well. Only did this because at first I had interpreted the question incorrectly - added in the last step after I'd realised a difference was required haha

 

[eyeseeyou]

Thanks ml125

 

[eyeseeyou]

In this question, what is the "R" value (not the answer to the question)
The mass of the earth (Me) is 6.0 times 10^24 kg and its average radius is 6380km. Calculate the gravitational potential energy of a 20,000 kg mass raised to a height of 650km above the earth's surface (2 marks)

 

[trecex1]

In this question, what is the "R" value (not the answer to the question)
The mass of the earth (Me) is 6.0 times 10^24 kg and its average radius is 6380km. Calculate the gravitational potential energy of a 20,000 kg mass raised to a height of 650km above the earth's surface (2 marks)

The radius + height above surface