This is from an old AP test, and it's a multiple choice question, so I don't know why it's giving me so much hell, but here it goes:(adsbygoogle = window.adsbygoogle || []).push({});

1. The problem statement, all variables and given/known data

Suppose that a hole is drilled through the center of the Earth to the other side along its axis. A small object of mass m is dropped from rest into the hole at the surface of Earth, as shown [strike]above[/strike]below. If Earth is assumed to be a solid sphere of mass M and radius R and friction is assumed to be negligible, correct expressions for the kinetic energy of the mass as it passes Earth's center include which of the following?

[PLAIN]http://dl.dropbox.com/u/4439149/physucks_mc_hole_through_earth.jpg [Broken]

The two correct expressions are

[tex]\frac {1}{2}mgR[/tex]

and

[tex]\frac {GmM}{2R}[/tex]

2. Relevant equations

Ug=GmM/R

PS sorry the image is sideways.

3. The attempt at a solution

My first through was just the typical: initial potential equals final kinetic. That means that

GmM/R would be a proper expression of the kinetic energy, but that is not a correct answer.

I got to thinking, I bet the object still has some of its potential energy at the center. So I basically just considered all of the mass to be a distance of 1/2R away, the direction didn't matter since energy is scalar. That yields 2GmM/R, which is more than the original potential.

Then I started thinking, why does the specific Ug at the surface increase as h increases, in mgh, but Ug decreases as R increases when looking at the universal law. Then I realized I had severely confused myself over a multiple choice problem that is probably very simple.

Please help.

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# Homework Help: Energy of an Object Falling Through the Earth (yes, all the way through)

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