Two Uniform Spheres in Deep Space

[isabellef]

An experiment is performed in deep space with two uniform spheres, one with mass 30.0 kg and the other with mass 109.0 kg. They have equal radii, r = 0.20 m. The spheres are released from rest with their centers a distance 42.0 m apart. They accelerate toward each other because of their mutual gravitational attraction. You can ignore all gravitational forces other than that between the two spheres.

A) When their centers are 27.0 m apart, find the speed of the 30.0 kg sphere.

B) Find the speed of the sphere with mass 109.0 kg.

C) Find the magnitude of the relative velocity with which one sphere is approaching the other.

D) How far from the initial position of the center of the 30.0 {\rm kg} sphere do the surfaces of the two spheres collide?


I know that m1*v1=m2*v2 and U=-(G*m1*m2)/r, but I'm not sure how to use these equations to find what the question is looking for. Any suggestions would be greatly appreciated!

 

[Delphi51]

Welcome to PF, Isabellef.
Looks like you can use either a force approach (force -> acceleration -> velocity) or an energy approach where the gravitational potential energy initially changes to kinetic + gravitational later. Try both and see if you get the same answer?

 

[isabellef]

Thanks for the welcome and for the help. But I'm not exactly sure what you mean by the two different approaches. Could you maybe clarify a little bit?

 

[Delphi51]

Well you could start with F = GM1*M2/d², then use F = ma to get the acceleration of each mass.

The other approach would be to start with
initial energy = final energy
U1 = U2 + KE

 

[isabellef]

Oh okay, I realized that I was just plugging in the wrong numbers, but now I have the right answers. Thank you!

Although, I'm still confused on part D. I'm not sure what equation to use. Any ideas?

 

[Delphi51]

Oh, I hope you did the acceleration method! If you have the acceleration, you can just use a motion formula to find the distance. You'll probably need to find the time first. Careful, you'll have to take the radius of the sphere into account in the final answer.

 

[isabellef]

Oh okay, that makes sense. Thanks for all the help!

 

[Delphi51]

Most welcome!