I know the force of gravity inside a hollow sphere is 0, but

  • #1

Main Question or Discussion Point

We were never given an explanation in class. I remember in my high school physics class last year, our teacher told us this is true but never showed us why. All he said was that you had to integrate a function relating distance to mass, and the result would be a net force of 0 anywhere inside the hollow sphere

Can someone help me out with this? Maybe not tell me the answer, just inform me on what equation to work with, as i enjoy figuring things out on my own if possible.

Thanks, guys!
 

Answers and Replies

  • #2
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G dm1 m2 / r^2 to find net force. Or G dm / r^2 to find the field.
Doing the integral with dm is a little odd feeling so write dm in terms of some coordinate system that makes symmetrical sense.
 
  • #3
Doc Al
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Look up Newton's Shell Theorems.
 
  • #4
A.T.
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http://en.wikipedia.org/wiki/Shell_theorem

But there is a simpler way to show this directly form the superposition principle: You can treat the cavity as a sphere having negative gravity superimposed with a bigger massive uniform sphere. Trivially for all points inside the cavity the two effects cancel.
 
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  • #5
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Hi.

Tell us if You need help with integrals. While studying Shell Theorem, that is.

Cheers.
 
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  • #6
Doc Al
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But there is a simpler way to show this directly form the superposition principle: You can treat the cavity as a sphere having negative gravity superimposed with a bigger massive uniform sphere. Trivially for all points inside the cavity the two effects cancel.
I don't get your reasoning here. Certainly the negative mass sphere cancels that portion of the massive sphere which it overlaps. But that still leaves you with the shell to account for.
 
  • #7
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Hi.

Yes, I do understand what You had in mind when suggesting the use of superposition principle: Both big ball and smaller ball act as if all the mass was concentrated at the center. However, for this argument to work, one should already know that outer shell has no influence... Nice train of thought, though.

Cheers.
 
  • #8
A.T.
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Yes, you are both right. I remembered a simple proof that the G-field must be uniform in the more general case, inside a spherical cavity which is not concentric with the massive sphere. Given the symmetry of the special concentric case the zero field is the only one that fits this.

However, that simple poof at some point assumes a linearly growing field inside a uniform massive sphere, which is basically the shell theorem, and still requires integration in the proof.
 

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