- #1
Xyius
- 508
- 4
Homework Statement
I basically need to find the resulting motion of an object that is falling through the Earth. I also need to find how long it takes. I am ignoring friction and assuming the density of the Earth is constant.
2. The attempt at a solution
Here is an image of my work. (I used MathType program, its easier for me than using the LaTex code)
[PLAIN]http://img825.imageshack.us/img825/2844/earthc.gif
This seems to have been the hard part, I am getting stumped on the easier part, knowing how to solve the differential equation! I know that this is of the same form for Hookes Law, but what is throwing me off is the fact that the formula is with respect to "r." I know that when solving the differential equation for simple harmonic motion, you use Newtons second law which is is only in the x direction, but since this is "r" does that mean I have to do it for both x and y components and use trigonometry? Or can I simply write Newtons second law as..
[itex]F=m\frac{d^2r}{dt^2}[/itex]
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