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- Thread starter ohheytai
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cepheid

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Okay, let's just take this step by step.

Step 1 - Close Facebook and concentrate =p

Step 2 - for the first problem, examine each statement individually and determine whether it is true or false.

The first statement "as the object moves from r1 to r2, the potential energy of the system decreases." Is that true? Hint: the potential energy is given by the blue/purple curve. Is this curve increasing or decreasing as you move outward from the star?

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increasing so the first one is false right?

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cepheid

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increasing so the first one is false right?

Correct. Now for the second statement. The kinetic energy is just the difference between the total energy of the system, and the potential energy, agreed? So, if the total energy of the system is A, what is the difference between that and value of U (blue curve) at r2? Is this difference equal to A-B? (You can tell what the answer is just by looking at it).

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yes it is?

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cepheid

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As far as the third and fourth statements are concerned, only one of them can be true. If the total energy of the system is A (represented by that horizontal line), then as the planet moves outward, the potential energy of the system increases until its value eventually equals A (the green and blue curves cross). At that point, all of the energy has been converted to potential, and so the kinetic energy must be zero right? So, does the object escape?

Another way to look at it: to escape the "potential well", the total energy of the system must be greater than the maximum potential energy that is required to reach any radius (otherwise you can't go beyond that radius). Therefore, you can look at the boundary of the well (the shaded purple region) as a potential "barrier" that has to be overcome. You can't go "through" it, so to speak.

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cepheid

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yes it is?

Don't just guess. Tell me why. Hint: what is the potential energy equal to at r2?

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cepheid

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For the sixth and final statement: again, keep in mind that the difference between the total energy of the system ("A" in this case) and the potential energy of the system is the kinetic energy of the object. So, what does energy conservation require?

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it's equal to B at r2 and it does escape right?

- #10

cepheid

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it's equal to B at r2

Yes. So if the potential energy is B at r2, and the total energy is A, what is the difference between them?

and it does escape right?

Is "A" enough energy to get over the barrier? Re-read my post about the third and fourth statements.

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ohhh okayyy nooo it doesnt escape thanks!! can you help me with part 2 now?

would it just be The planet and star cannot get farther apart than r2?

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cepheid

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would it just be The planet and star cannot get farther apart than r2?

That's true, but consider also this (applicable to this situation as well):

If the total energy of the system is A (represented by that horizontal line), then as the planet moves outward, the potential energy of the system increases until its value eventually equals A (the green and blue curves cross). At that point, all of the energy has been converted to potential, and so the kinetic energy must be zero right?

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okay thank you very much! and could you help me with this too?

You stand on a spherical asteroid of uniform density whose mass is 1.0x10^16 kg and whose radius is 8 km (8103 m). These are typical values for small asteroids, although some asteroids have been found to have much lower average density and are thought to be loose agglomerations of shattered rocks. You want to figure out how fast you have to throw the rock so that it never comes back to the asteroid and ends up traveling at a speed of 4 m/s when it is very far away.

How fast do you have to throw the rock so that it never comes back to the asteroid and ends up traveling at a speed of 4 m/s when it is very far away?

launch speed (relative to you)

i got 16.9161 but it was wrong so now i dont think i know how to do this correctly

i tried K_initial + U_initial = K_final + U_final where U final = 0 and K=.5mv^2

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it ain't a bound system tbh, the r extends relentless which is enough proof the star is gonna escape. the potential energy keeps growing but with a decreasing rate of growth, hence the potential energy will eventually stop at a point and stay there eternally. kinetic energy will also stay at the same value when the star has totally escaped from the gravity of the planet, so the system's energy remains the same after the two energies both reached stable situations, as the graph illustrates.

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cepheid

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it ain't a bound system tbh, the r extends relentless

The 'r' is just the radial distance from the star, which is the independent variable here. Therefore, how r varies is irrelevant. The fact that you can CONSIDER what the energy is at any distance r from the star that you want, doesn't mean that the system is bound.

which is enough proof the star is gonna escape. the potential energy keeps growing but with a decreasing rate of growth, hence the potential energy will eventually stop at a point and stay there eternally.

No. The potential energy is always increasing (albeit at an ever smaller rate as you point out). Although it approaches 0 asymptotically, it NEVER flattens out. Therefore, for any value of the total energy of the system that is below zero (which includes A, B, and C), the system is bound. You need a total energy > 0 to escape.

Oh and by the way, I think you meant to say that the *planet* is going to escape the gravity of the star, right? (which is still wrong, but at least it labels the objects correctly) =p

kinetic energy will also stay at the same value when the star has totally escaped from the gravity of the planet, so the system's energy remains the same after the two energies both reached stable situations, as the graph illustrates.

I don't know what you're trying to say here. The kinetic energy of the system steadily decreases as r increases, just as energy conservation demands. It is the total energy of the system that remains constant.

I'm sorry to bash you on your first post, but you're saying things that are blatantly wrong.

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