Gravity in a uniform density sphere and a shel

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SUMMARY

The discussion centers on the gravitational force experienced by a point mass located inside a uniform density shell and a solid sphere. It is established that the net gravitational force acting on a point mass inside a uniform density shell is zero, regardless of its position within the shell. This conclusion is derived from the principle that the gravitational field inside a spherical shell vanishes, which can be proven using calculus by integrating the contributions of all mass elements within the shell.

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  • Understanding of Newton's Law of Universal Gravitation
  • Basic knowledge of calculus for proving gravitational principles
  • Familiarity with concepts of mass distribution and symmetry
  • Knowledge of gravitational fields and forces
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musicfairy
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Today the teacher went over the force of gravity in a uniform density sphere and a shell. I got lost somewhere in the lecture. Can someone please explain this stuff to me?

Let's say there's a uniform density shell with a point mass inside it that's not at the center. What would the net force acting on it be? I'm guessing it's not 0 because it's some distance away from the center of mass.

shellwithpoint.jpg


In my bad drawing above which side would exert a greater force on the particle? One side is closer but the other side has more mass...



If there's a shell and a solid sphere with the same mass and each has a point mass a distance r from its center, would the force acted on the point mass be the same for both cases?


Someone please help. This doesn't make much sense to me. =(
 
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musicfairy said:
One side is closer but the other side has more mass...
Exactly. And so, just based on those two considerations, the conclusion is ambiguous. It turns out that the net field vanishes inside the shell. You can prove this if you know calculus.
 


So how do you prove it?
 


Think "adding up all the forces in a continuous way".
 

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