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March 29, 2024, 08:21:29 am

Author Topic: Gravitational Potential Energy  (Read 1056 times)  Share 

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Jefferson

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Gravitational Potential Energy
« on: May 20, 2019, 06:09:46 pm »
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QUESTION: Would the gravitational potential energy of a satellite be greater or less if its mass is doubled?
SOLUTION: "Yes - double since gravitational potential energy depends on the mass of the satellite"
(not sure what they mean by "yes")

For the equation
U = - GMm/r
increasing the radius will increase U (from negative to zero).

However, if you were to increase the mass, would this not mean that U would decrease (more negative)?
e.g. from U = -5 to U = -10.

Below are two sources (attachments) which state that increasing the mass would instead increase U. Please clarify.
Thank you.
« Last Edit: May 20, 2019, 06:16:33 pm by Jefferson »

stella_atarnotes

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Re: Gravitational Potential Energy
« Reply #1 on: May 20, 2019, 06:22:19 pm »
+2
QUESTION: Would the gravitational potential energy of a satellite be greater or less if its mass is doubled?
SOLUTION: "Yes - double since gravitational potential energy depends on the mass of the satellite"
(not sure what they mean by "yes")

For the equation
U = - GMm/r
increasing the radius will increase U (from negative to zero).

However, if you were to increase the mass, would this not mean that U would decrease (more negative)?
e.g. from U = -5 to U = -10.

Below are two sources (attachments) which state that increasing the mass would instead increase U. Please clarify.
Thank you.

Hey, you've got to remember that GPE will always be negative. Infinity is defined as zero gravitational potential energy and as an object is moved to infinity (e.g. away from the Earth), it gains kinetic energy and thus must lose GPE, therefore the GPE at a given point will always be less than zero. This means that the more negative the GPE, the more potential energy an object has. Its a really tricky concept to get your head around.

Jefferson

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Re: Gravitational Potential Energy
« Reply #2 on: May 20, 2019, 06:38:34 pm »
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Hey, you've got to remember that GPE will always be negative. Infinity is defined as zero gravitational potential energy and as an object is moved to infinity (e.g. away from the Earth), it gains kinetic energy and thus must lose GPE, therefore the GPE at a given point will always be less than zero. This means that the more negative the GPE, the more potential energy an object has. Its a really tricky concept to get your head around.

Hi, thanks for replying.
I was taught that as an object is moved further away from the central body, it gains GPE (KE decreases). GPE will continue to increase to 0, at an infinite distance away.
Likewise, as the object falls to Earth, its GPE decreases and KE increases (goes faster).

stella_atarnotes

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Re: Gravitational Potential Energy
« Reply #3 on: May 20, 2019, 07:02:14 pm »
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Hi, thanks for replying.
I was taught that as an object is moved further away from the central body, it gains GPE (KE decreases). GPE will continue to increase to 0, at an infinite distance away.
Likewise, as the object falls to Earth, its GPE decreases and KE increases (goes faster).

Hi,

Sorry I meant to say "as an object is moved from infinity to a point". You are correct that as an object moves further from the central body it will gain GPE (less negative number) and decrease in KE. There are really 2 forms of the GPE equation, one is U = - GMm/r and the other is Ep = mgh which is used when an object is near the earths surface. Using the second equation, the textbook will be correct since it doesn't factor in the negative sign of the U = - GMm/r. Ep is sort of like a simplification of the U equation since we usually consider GPE on a smaller scale rather than the scale of the entire universe.

If the planet's surface is chosen at a zero level, Ep at x is positive.
If infinity is chosen at the zero level, Ep is negative.

This may be why the textbook says GPE increases. 

DrDusk

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Re: Gravitational Potential Energy
« Reply #4 on: May 25, 2019, 12:58:01 am »
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Just some trivial derivations here for your understanding just in case :)