Gravitational potential energy

[Tokspor]

What would happen to the change in potential energy of a satellite if it escaped earth's gravitational pull?

Let's say a satellite escaped earth's gravitational pull. What would happen to its potential energy and why? Based on the gravitational potential energy U = -GmM/r, that as r increased, U gets less negative. Therefore, I said it would increase continuously, answer choice A.

A) It increases continuously
B) It increases then stops entirely
C) It increases then decreases slightly
D) It increases then decreases towards zero

But the correct answer is D. I thought the wording was strange for this. If this was correct, shouldn't it be worded "it increases towards zero" at least?

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[G1SG2]

What would happen to the change in potential energy of a satellite if it escaped earth's gravitational pull?

Let's say a satellite escaped earth's gravitational pull. What would happen to its potential energy and why? Based on the gravitational potential energy U = -GmM/r, that as r increased, U gets less negative. Therefore, I said it would increase continuously, answer choice A.

A) It increases continuously
B) It increases then stops entirely
C) It increases then decreases slightly
D) It increases then decreases towards zero

But the correct answer is D. I thought the wording was strange for this. If this was correct, shouldn't it be worded "it increases towards zero" at least?

Yeah, that's a bit weird. Makes it sound like U becomes >0 and then decreases back to 0. It WOULD eventually become zero though because I think we have to assume that r increases to infinity, and any number divided by infinity would be 0. Only D mentions zero, which makes it the best answer.

 

[Chuck's Right Foot]

What would happen to the change in potential energy of a satellite if it escaped earth's gravitational pull?

Let's say a satellite escaped earth's gravitational pull. What would happen to its potential energy and why? Based on the gravitational potential energy U = -GmM/r, that as r increased, U gets less negative. Therefore, I said it would increase continuously, answer choice A.

A) It increases continuously
B) It increases then stops entirely
C) It increases then decreases slightly
D) It increases then decreases towards zero

But the correct answer is D. I thought the wording was strange for this. If this was correct, shouldn't it be worded "it increases towards zero" at least?

Look at your formula again.

The negative sign is why the answer is D. As R increases, the value is increasing!!! normally with a fraction, the larger the denominator, the smaller the value. The exception is with negative numbers. -1/4 > -1/2

Eventually the distance is so great there is no attractive force.

 

[G1SG2]

Look at your formula again.

The negative sign is why the answer is D. As R increases, the value is increasing!!! normally with a fraction, the larger the denominator, the smaller the value. The exception is with negative numbers. -1/4 > -1/2

Eventually the distance is so great there is no attractive force.

I think the OP is just confused about the wording..."It increases then decreases towards zero"

 

[Chuck's Right Foot]

I think the OP is just confused about the wording..."It increases then decreases towards zero"

ahhhh. I didn't read closely enough.

 

[Seraph 84]

I think the question is combining both local and general forms of gravitational potential energy. Near the Earth, you would use mgh, so its gravitational potential energy increases initially; however once it's gotten to an appreciable height you'd have to use the general form U = -GmM/r. The part that I can't justify is why the potential energy decreases, because as you get further away, it actually increases and eventually becomes zero. Maybe they're thinking of the magnitude of potential energy?

 

[G1SG2]

Where is this question from?

 

[Tokspor]

It's from Kaplan's MCAT Qbank. I began using this because it was one of the few places, or actually the only, aside from AAMC where I could find online (by "online," I mean something more in-line with the computed-based format) practice without enrolling in a course. Have you used this in any way or heard any feedback about it?

 

[G1SG2]

It's from Kaplan's MCAT Qbank. I began using this because it was one of the few places, or actually the only, aside from AAMC where I could find online practice without enrolling in a course. Have you used this in any way or heard any feedback about it?

Kaplan really sucks sometimes. I've heard that the Qbank has some hard questions, but that one doesn't make sense (the wording is weird).

 

[matth87]

Potential Energy is due to position in the gravitation field. If you don't have the gravitation field then you have no potential energy due to it.

 

[Podalarius]

I think the question is combining both local and general forms of gravitational potential energy. Near the Earth, you would use mgh, so its gravitational potential energy increases initially; however once it's gotten to an appreciable height you'd have to use the general form U = -GmM/r. The part that I can't justify is why the potential energy decreases, because as you get further away, it actually increases and eventually becomes zero. Maybe they're thinking of the magnitude of potential energy?

There shouldn't be a difference between the "local" and "general" forms of gravitational potential energy - the first is just an approximation of the second. Potential energies are necessarily given relative to a reference point. In the local form, that's usually given by the ground, or the lowest point an object will reach, so that one of the terms will go to zero. In the more general form of the equation, that reference point is given at a point an infinite distance from the gravitational source. You absolutely cannot compare the two. If the reference for the potential energy in the more general form of the equation were the ground of the planet, the further away you get, the higher the potential energy will be. There is never zero gravitational interaction between two masses - the field might get small, but as you integrate over it, it must get larger the further you get from the reference if it is a positive force - the reference for gravity on a general scale is at infinity, so you are always approaching it, hence why it is negative. "Increases then decreases" is just terrible science, but in the absence of better choices, the general form of gravity, using the common definition, eventually reaches zero, so that's what you'll have to go with.

 

[boaz]

Well said. Good science!

 

[joshinjosh]

I rememeber answering that same exact question in another book, may have been ek. Nonetheless, the answer should be A.

The graviational potential continually increases.
Like Podalarius pointed out, there is always gravitational potential energy (GP) no matter how far you are appart. So as you travel further you are increasing GP. Sure there is a zero limit, but the GP never reverses direction, which choice D implies. You can't argue about magnitude because the GP is constantly decreasing in magnitude, but increasing relatively.

Also, you can look at it in terms of kinetic energy (KE). To put it simply, as you get further and further out, you are converting KE in to PE. PE is increasing.

hope this helps,

Josh

 

[Podalarius]

Oops, yeah - increases then decreases should never be right. Increases always is far more sensible.

 

[wanderer]

What would happen to the change in potential energy of a satellite if it escaped earth's gravitational pull?

Let's say a satellite escaped earth's gravitational pull. What would happen to its potential energy and why? Based on the gravitational potential energy U = -GmM/r, that as r increased, U gets less negative. Therefore, I said it would increase continuously, answer choice A.

A) It increases continuously
B) It increases then stops entirely
C) It increases then decreases slightly
D) It increases then decreases towards zero

But the correct answer is D. I thought the wording was strange for this. If this was correct, shouldn't it be worded "it increases towards zero" at least?

The most correct answer would be "It increases until it (almost) reaches zero.": (i.e. the limit as r approaches infinity is zero.) It never decreases.
It has to be choice A or B, and choice A is the more logical of the two although it is poorly worded.

 

[matth87]

g = gravitational field
m = mass of earth
r = radius
G = newtons gravitational constant

g = (G x m)/(r^2)

Potential Energy = mgh

Yes your height from the surface of the earth is increasing, but your g is also decreasing. There is some proportionality between g and h. Eventually though when you leave the gravitation field g will = 0. This means that PE will be non existant due to the gravitation field by earth.

 

[boaz]

Podalarius is 100% correct. The gravitational potential energy should not be confused with gravitational force. Although the algebra-based courses don't deal with this basic idea, the technical definition of potential energy is the integral of the force function.

For example, if you shoot a rocket into space, the gravitational force gets weaker and weaker as it gets further from Earth (1/r^2). And, the amount of work that needs to be done over a given distance decreases accordingly. However, the TOTAL amount of work done ultimately depends on how far the rocket went. More work is done if it gets to pluto than if it gets just to the moon. The total amount of work done is equal to the change in potential energy.

This is one of the problems with so called "algebra-based physics".

 

[boaz]

Disclaimer: My physics course was algebra-based. So I am not holier-than-thou.