Gravitational potential energy of two particles and work done by gravitational force

[brett812718]

[SOLVED] Need Help on Gravitation Potential Energy Problem

Homework Statement

(a) A 5.3 kg particle and a 3.0 kg particle have a gravitational attraction with a magnitude of 2.6 x10^-12 N. What is the gravitational potential energy of the two-particle system?


(b) If you triple the separation between the particles, how much work is done by the gravitational force between the particles?

(c) How much work is done by you?

Homework Equations

F=(GmM)/r^2
U=-(GmM)/r

The Attempt at a Solution

First I used the given information to solve for r using Newtons law of gravitation. Then I pluged r=1.96E1 into the potential energy equation to get -5.41E-11J but that was wrong.

 

[Hootenanny]

Homework Statement

(a) A 5.3 kg particle and a 3.0 kg particle have a gravitational attraction with a magnitude of 2.6 x10^-12 N. What is the gravitational potential energy of the two-particle system?


(b) If you triple the separation between the particles, how much work is done by the gravitational force between the particles?

(c) How much work is done by you?

Homework Equations

F=(GmM)/r^2
U=-(GmM)/r

The Attempt at a Solution

First I used the given information to solve for r using Newtons law of gravitation. Then I pluged r=1.96E1 into the potential energy equation to get -5.41E-11J but that was wrong.

Recheck your arithmetic, you separation value is incorrect.

 

[brett812718]

is R=2.012E1 and U=-5.25E-11 correct

 

[Hootenanny]

is R=2.012E1 and U=-5.25E-11 correct

Correct indeed

 

[brett812718]

Also would the solution to part b be U=-(GMm)/3r

 

[Hootenanny]

Also would the solution to part b be U=-(GMm)/3r

Not quite, the work done is change in gravitational potential energy.

 

[brett812718]

Work=((-GMm)/3r)-((-GMm)/r)

 

[Hootenanny]

Work=((-GMm)/3r)-((-GMm)/r)

Much better

 

[brett812718]

I got 3.5E-11J but that was also incorrect

 

[Hootenanny]

I got 3.5E-11J but that was also incorrect

I get something different. Furthermore, be careful with the sign.

 

[brett812718]

I got ((-GMm)/3r)=-1.75E-11J and ((-GMm)/r)=-5.25E-11J
is((-GMm)/3r)=-1.75E-11J correct?

 

[Hootenanny]

I got ((-GMm)/3r)=-1.75E-11J and ((-GMm)/r)=-5.25E-11J
is((-GMm)/3r)=-1.75E-11J correct?

Yes, your calculations are correct, just be aware of the sign of your final answer.

 

[brett812718]

work=-3.50E-11J

 

[brett812718]

because work is equal to the negative change in potential energy

 

[brett812718]

and part c is 3.50E-11J

 

[Hootenanny]

work=-3.50E-11J

Correct.

 

[brett812718]

thank you for your help

 

[Hootenanny]

thank you for your help

A pleasure