Gravitational Potential Energy of the earth

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SUMMARY

The discussion centers on calculating the height above Earth's surface where the gravitational potential energy (PEg) is 17.00% of its value at the surface. The relevant equations include PEg = (-GMm)/r and PElocal = mgy. The correct approach involves using the Earth's radius in the calculations, leading to the conclusion that the height must be significantly greater than 5 meters to achieve the desired potential energy ratio.

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  • Understanding of gravitational potential energy equations
  • Familiarity with the concepts of mass (m), gravitational constant (G), and radius (r)
  • Basic knowledge of physics principles related to energy
  • Ability to manipulate algebraic equations
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kt102188
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Homework Statement



How high above the surface of the Earth must a mass be located so its gravitational potential energy is only 17.00% of its value on the surface?


Homework Equations



PEg=(-GMm)/r, PElocal= mgy where y is height the object can fall

The Attempt at a Solution



I've tried a couple of different things but all my variables cancel out.

(-GMm)/r1=0.17((-GMm)/r2

r1/0.17=r2 If I randomly set r1 to be 1 r2= 5.88235 but that doesn't make sense because if you raise an object by 5m it would have a greater PEg

Any suggestions on where to go?
Thanks!
 
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Welcome to PF!

Hi kt102188! Welcome to PF! :smile:
kt102188 said:
r1/0.17=r2 If I randomly set r1 to be 1 r2= 5.88235 but that doesn't make sense because if you raise an object by 5m it would have a greater PEg

But the radius of the Earth is a lot larger than 1m. :confused:

(and remember, the question assumes that the PE at ∞ is zero :wink:)
 
Thank you! I was totally thinking of this wrong. Actually using the radius of Earth got the right answer.
 

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