I How Does Gravity Affect Potential Energy in Physics?

[SwanseaStephen]

Hey guys, my name's Stephen, and this is my first post (hopefully of many). I never studied above algebra based physics and am not in a physics-related field, but now as an adult I'm trying to really learn physics, so bare with me and don't assume I know anything. I'm happy to find a forum where I can post questions to help further my understanding. SO, here goes...

The equation potential energy = mass x gravity x height brought me to a thought experiment.

Let's say you have a 1kg mass at 1m height, with a gravity of 10 m/s^2. Now imagine I flipped a gravity switch and instantaneously the value of gravity was cut in half, to 5. Of course the mass is constant, and at that instantaneous moment the height should be unchanged as well. It follows that at this moment the potential energy of the ball should also decrease in half. That could be an incorrect assumption on my part, but if this is correct, then where would that energy GO? Would the ball, under half as much gravity, raise to a height of 2m using kinetic energy, and if so, as it comes closer to h = 2 meters is the kinetic energy going back into potential energy, where PE = m(1/2 g)(2h) and thus the total energy in the system remained constant?

Please let me know if my understanding is correct here or if I've messed up somewhere.

Also idk what the prefixes mean yet so sorry if I put the wrong prefix down

 

[jbriggs444]

then where would that energy GO?

You've imagined a situation where there is a switch that can turn gravity on or off. No such switch is possible using the known laws of physics.

As you've reasoned for yourself, if such a switch existed, you would run into problems with conservation of energy.

 

[Ibix]

where would that energy GO?

As jbriggs444 points out, you can't do that. In Newtonian gravity, the answer would depend on what magic you used to make gravity drop ny half. Einstein's theory of gravity won't even let you describe a gravitational field that changes instantly like that, magic or not.

If you think about how you could actually quickly lower gravity by half - say by using a very powerful rocket to move the Earth rapidly away from the 1kg mass - you'll find that the potential energy change is completely accounted for in the work done moving the Earth.

 

[russ_watters]

Now imagine I flipped a gravity switch and instantaneously the value of gravity was cut in half, to 5. Of course the mass is constant, and at that instantaneous moment the height should be unchanged as well. It follows that at this moment the potential energy of the ball should also decrease in half. That could be an incorrect assumption on my part, but if this is correct, then where would that energy GO?

Your magic switch magically got rid of it.

 

[DrStupid]

Einstein's theory of gravity won't even let you describe a gravitational field that changes instantly like that, magic or not.

According to Einstein gravity force is just another fictious force and fictius forces can be switched off instantly, e.g. by switching off an engine of an accelerating rocket. Let's say, we have a rocket which is accelerated with 10 m/s² by two equal engines. Inside this rocket there is a 1 kg mass placed at 1 m height above a level that has been definied to be zero. This situation is equivalent to the description of the OP above. The "gravity switch" just turns off one of the engines, reducing the acceleration of the rocket to 5 m/s. In the result, the potential energy of the mass will decrease in half.

 

[A.T.]

According to Einstein gravity force is just another fictious force and fictius forces can be switched off instantly, e.g. by switching off an engine of an accelerating rocket. Let's say, we have a rocket which is accelerated with 10 m/s² by two equal engines. Inside this rocket there is a 1 kg mass placed at 1 m height above a level that has been definied to be zero. This situation is equivalent to the description of the OP above. The "gravity switch" just turns off one of the engines, reducing the acceleration of the rocket to 5 m/s. In the result, the potential energy of the mass will decrease in half.

In a frame like that, potential energy cannot be defined in a way consistent with conservation of energy.

 

[DrStupid]

In a frame like that, potential energy cannot be defined in a way consistent with conservation of energy.

That depends on what you mean with "a frame like that". The force is conservative as long as the acceleration remains constant. Changing the field also changes the potential energy. That applies to both, the fictious forces in the accelerating rocket and the gravity field as described above. Thus a possible answer would be, that the question (where the energy goes) is pointless if energy is not conserved.

 

[A.T.]

That depends on what you mean with "a frame like that".

A frame with changing acceleration.

 

[Vanadium 50]

According to Einstein gravity force is just another fictious force and fictius forces can be switched off instantly

In GR gravity cannot be "switched off instantly".

Russ is right - the same magic that shuts off gravity gets rid of its potential energy.

 

[DrStupid]

In GR gravity cannot be "switched off instantly".

I wasn't talking about gravity, but about gravitational force.

 

[Vanadium 50]

I wasn't talking about gravity, but about gravitational force.

Tomato, tomahto.

 

[DrStupid]

Tomato, tomahto.

?

 

[jbriggs444]

?

Two words for the same concept. Fred and Ginger sang it as "You say tomato and I say tomahto". (https://en.wikipedia.org/wiki/Let's_Call_the_Whole_Thing_Off)

Shakespeare said it in Romeo and Juliet as "That which we call a rose by any other name would smell as sweet".

Also sometimes phrased as "a distinction without a difference".

 

[DrStupid]

Two words for the same concept.

But gravity and gravittational force are actually not the same concept in GR. Gravitational force is frame-dependent and dosn't exists in free falling frames. In contrast to gravity it can be switched off instantly just by switching to such a frame of reference (e.g. by cutting the cable of an elevator). And with the gravitational force the corresponding potential energy disappears as well. But I already explained that in #5. Therefore I still do not know what Vanadium 50 tries to tell me.

 

[Vanadium 50]

Therefore I still do not know what Vanadium 50 tries to tell me.

I'm trying to tell you that if you use magic to shut off gravity OR gravitational force the same magic fixes the potential energy problem. Magic is magic.

 

[DrStupid]

I'm trying to tell you that if you use magic to shut off gravity OR gravitational force the same magic fixes the potential energy problem. Magic is magic.

Changing the frame of reference is not magic.

 

[russ_watters]

Changing the frame of reference is not magic.

You arent just changing frame of reference. Reread your own example you just gave: cutting an elevator cable is not merely a frame change!

This isn't The Matrix!

Probably more to the point, the OP isn't even suggesting a frame change.

 

[DrStupid]

cutting an elevator cable is not merely a frame change!

But changing from the rest-frame of the cabin before cutting the cable into the rest frame of the cabin after cutting the cable is. Let me suggest another setup in order to limit the possibilities for this kind of hair-splitting:

Let's assume the setup is located outside a spherical mass distribution, moving downward with constant velocity. As soon as it crosses the surface, the gravitational force will be switched off (according to the shell theorem). With a sufficiently large sphere and sufficiently high velocity this could happen instantly within every accuracy of measurement. With two concentric spheres it would also be possibe to switch between different gravitational forces.

 

[russ_watters]

But changing from the rest-frame of the cabin before cutting the cable into the rest frame of the cabin after cutting the cable is.

You're adding something to the problem that doesn't change the key issue being discussed, while simultaneously including and ignoring the very thing being discussed. It doesn't matter how many times you say it...nor does your next new scenario accomplish it either (in that scenario, the only way to make the GPE disappear is to calculate it wrong in the first place).

I will now use my magical powers to end the thread.