Gravitational Potential Energy

[IgE]

Homework Statement

The gravitational self potential energy of a solid energy of a solid ball of mass density p and radius R is E. What is the gravitational self potential energy of a ball of mass density p and radius 2R?

Homework Equations

The Attempt at a Solution

The gravitational potential energy is given by the equation "mgh=U" where the mass relevant is the center of mass. Since it is a sphere with uniform density, the CM is in the center. This puts the CM of the first ball R above the ground and the second ball 2R above the ground. As for mass the second ball is heavier. Mass2/mass1= ((4/3 pi (r) cubed) p)/((4/3 pi (2 R) cubed) p) which tells me that ball 2 is 8 times heavier. Since g does not change the U of the second ball should be 8 times 2 which is 16 E. However the answer is 32 E. This question is hard. ahah Thanks! =)

 

[SammyS]

Homework Statement

The gravitational self potential energy of a solid energy of a solid ball of mass density p and radius R is E. What is the gravitational self potential energy of a ball of mass density p and radius 2R?

The Attempt at a Solution

The gravitational potential energy is given by the equation "mgh=U" where the mass relevant is the center of mass. Since it is a sphere with uniform density, the CM is in the center. This puts the CM of the first ball R above the ground and the second ball 2R above the ground. As for mass the second ball is heavier. Mass2/mass1= ((4/3 pi (r) cubed) p)/((4/3 pi (2 R) cubed) p) which tells me that ball 2 is 8 times heavier. Since g does not change the U of the second ball should be 8 times 2 which is 16 E. However the answer is 32 E. This question is hard. ahah Thanks! =)

Hello IgE. Welcome to PF.

I'm quite sure that you have totally misinterpreted the question.

It is asking for the gravitational self potential energy. This is not a ball on the earth. You are not being asked the potential energy of a ball, in the vicinity of earth, whose center of mass is a distance of R from the ground.

This is a ball of density ρ which is being held together by its own self gravity. Since gravity is an attractive force, I suspect that the self potential energy is negative.

How much energy will it take to disassemble this ball, moving each bit of its mass infinitely far away from all the rest of its mass?

 

[IgE]

That gives me the right answer now! Yayy!Oh man, I spent two hours on this problem solving it in so many different ways only realize i had the problem misinterpreted. This is hard medicine to digest ahhahah. Thank you so much!