Gravitation deep hole physics problem

AI Thread Summary
The discussion revolves around calculating the work done to lift a 1-kg mass from a deep hole that reaches half of Earth's radius. The initial approach incorrectly used the gravitational force formula, prompting clarification that the correct formula is F = m * (GM/r^2). It was emphasized that only the mass of Earth interior to the lifted mass should be considered, with a uniform mass density assumption for calculations. Participants discussed how to compute the volume of the interior section, leading to a better understanding of the problem. Ultimately, the original poster expressed gratitude for the guidance received, indicating they can now complete the problem.
brad sue
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Hi I am stuck with this problem:
A deep hole in Earth reaches a depth of one half of Earth's radius. How much work is done when a 1-kg mass is slowly lifted from the bottom of the hole to Earth's surface?
I use the expression of the gravitation force, F=GMm/R3
so the work would be:
integral (F*(R/2)) from R=R/2 to R=R
I am not sure I am right so I need your input please.
Thank you
Brad
 
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Make sure you include the dependence that M has on r (the integration variable).
 
Your Force function is incorrect.

The Gravitational Force has an INVERSE SQUARE form F = m \frac{GM}{r^2} .
The Force by Gravity will only be due to the mass of Earth that is
INTERIOR to the mass being lifted - presume uniform mass density, that is M = M_E \frac{V_{inside}}{V_E} .
 
Last edited:
lightgrav said:
Your Force function is incorrect.

The Gravitational Force has an INVERSE SQUARE form F = m \frac{GM}{r^2} .
The Force by Gravity will only be due to the mass of Earth that is
INTERIOR to the mass being lifted - presume uniform mass density, that is M = M_E \frac{V_{inside}}{V_E} .

Thank you.
But How can I compute the Vinside? we only have the length nothing else?
B
 
Volume? LxWxH !
Yeah, rxrxr = r^3 , the variable r ,
compared with R_E^3 , the maximum R .
 
lightgrav said:
Volume? LxWxH !
Yeah, rxrxr = r^3 , the variable r ,
compared with R_E^3 , the maximum R .

OK! I am sorry . sometimes I am a little bit way off!

thank you so much
I can finish this problem now.

B
 

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