Physics Problem Involving Gravitational Force on an object based on R

AI Thread Summary
To determine the distance r inside the Earth where the gravitational force equals that at r = 4RE, the assumption of uniform density is crucial. The initial approach using conservation of energy to equate gravitational potential energies was deemed ineffective. Instead, applying Gauss's Law is suggested, despite the user not being familiar with it. The discussion highlights the need to consider gravitational force and potential rather than electric force concepts. A resource link was provided to assist in understanding the application of these principles.
taylorkrauss
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Homework Statement



At what distance r inside the Earth is the gravitational force due to Earth the same as at
the distance r = 4RE (where the latter distance is clearly outside Earth)? Assume uniform
density of Earth.


Homework Equations



conservation of energy? TME = GPE + KE



The Attempt at a Solution



At first I thought I could do conservation of energy and set both GPE's equal to each other and solve for a new Radius, but this is not working out well. Is there something I need to do involving the density of Earth and the mass? I really have no idea. Thanks for any help!
 
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Energy conservation doesn't appear relevant to me... I'd go with Gauss.
 
Hmm...I haven't learned Gauss's Law though. This wants Gravitational Force and Gravitational Potential not Electric Force and EPE, so I'm not sure how I'd apply Gauss (after googling, I saw it was a theroem for electric potential). How would you go about using Gauss's Law?
 
That was perfect! Thank you!
 

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