What Determines the Collision Speed of Two Unequal Mass Asteroids?

[oreostar90]

Homework Statement

Two spherical asteroids have the same radius R. Asteroid 1 has mass M and asteroid 2 has mass 2.58·M. The two asteroids are released from rest with distance 12.35·R between their centers. What is the speed of second asteroid just before they collide? Give answer in units of (G·M/R)1/2.

Homework Equations

Ki + Ui = Kf + Uf

U= -GMm/r

K= 1/2 m v^2

The Attempt at a Solution

My Ki is 0. So I get

0 -GMm/r1 = 1/2 m vf^2 + -GMm/r2

r1= 12.35R
r2= 2R

so i solved for Vf = sqrt( 2GM (-1/ r1 + 1/r2) )

and then I get Vf = .915 (GM/R)^(1/2)

What am I doing wrong, as that is the wrong anwser.

 

[G01]

EDIT: ERROR IN THIS POST, see post 6.

 

[oreostar90]

Consider this: Both asteroids will be accelerated to the point halfway between them. Now, where do you think the asteroids collide? How far does the asteroid we care about move before it reaches the other asteroid?

hmm are you recommending me to work with kinematic equations?

I do not see where you would go with knowing that information.

i) o ----------------- o
f) oo

I got a hint: You will need to use two conservation laws.

So I was thinking now I would use momentum and what I had earlier...but not sure if I should. I might need this one spelled out to me...

 

[G01]

EDIT: ERROR IN THIS POST, see post 6.

 

[oreostar90]

umm, 2 times the radius of the mass?

Which I had as 2R for r2...

 

[G01]

umm, 2 times the radius of the mass?

Which I had as 2R for r2...

SORRY! I was tired and thought you were making a mistake that you weren't! Your values of R are correct! Very sorry!

I think your problem is in the following fact:

Remember that the kinetic energy on the right hand side of the equation will be split evenly between BOTH asteroids. What does this tell you?

Again, very sorry for misleading you. I must have really been out of it then!