Help with a Gravitational Attraction problem

[jessicak]

Homework Statement

Two asteroids of 1.0x10⁷kg and 6.0x10⁷kg respectively, are initially at rest in interstellar space separated by a large distance. Thier mutual gravitational attraction then causes then to fall toward each other on a straight line. Assume the asteroids are spheres of radius 130m and 420m respectively.

A) what is the velocity of each asteroid before they hit?
130m, v=? 420m asteroid, v=
What is the kinetic energy of each?
What is the total kinetic energy?
B) The collision is totally inelastic. What is the velocity of the joined asteroids after they hit?

Homework Equations

K=1/2mv²
v^f = (m¹v₁ + m²v²)/(m¹ + m²)

The Attempt at a Solution

I have absolutely no idea about how to get the initial velocities, but I know where to go from there.

 

[zhermes]

two asteroids ... Are initially at rest in interstellar space

... ... ...

i have absolutely no idea about how to get the initial velocities, but i know where to go from there.

 

[jessicak]

They are at rest initially. The problem asks to find the velocity of the asteroids right before their collision. They are attracted to each other, and therefore have some velocity before they hit.

 

[zhermes]

Part A) is one process----coming together from far apart.
part B) is another---the collision.

For part A, the initial velocities are zero; you can use conservation of energy/momentum to find the final velocities.

For part B, the initial velocities will be the 'final velocities' of part A, right? Then you can plug into the equations you gave to find the final quantities.

 

[Filip Larsen]

It may help to describe the difference between the total potential energy of the two asteroids when their centers are a large distance d from each other and when their surfaces are just touching. What happens to this energy difference when d is very much larger than the sum of the two radii, and can you use this to calculate a good approximation to its value?

 

[jessicak]

ok, so i have all the questions of part a answered

130m asteroid: -0.00354m/s
420m asteroid: 0.000588m/s

However, when I try to use the formula for the final velocity (vf= (m1v1 +m2v2)/(m1 +m2) I get -1.88x10^-6 which my online homework rejects. Thoughts?

 

[Filip Larsen]

If they start at rest, what can you say about their velocity after they stuck together? (hint: think about total momentum, before and after collision)

 

[Filip Larsen]

130m asteroid: -0.00354m/s
420m asteroid: 0.000588m/s

By the way, did those values get accept by your online homework? Using the numbers in your first post I get speeds that are slightly different.

 

[jessicak]

Yes, they were. I was a little surprised by the values, though.