How Far Does m1 Travel Before Colliding with m2?

[postfan]

Homework Statement

Two small particles of mass m1 and mass m2 attract each other with a force that varies with the inverse cube of their separation. At time t0, m1 has velocity v directed towards m2, which is at rest a distance d away. At time t1, the particles collide.
How far does m1 travel in the time interval (t0 and t1)? Note: you may use t1 and t0 in your answer. Enter m1, m2, t1 and t0 for masses and times.

Homework Equations

The Attempt at a Solution

I used the center of mass as the collision point, so I calculated (taking x=0 at m1) it to be m2*d/(m1+m2). What did I do wrong?

 

[SteamKing]

Why did you assume that the C.O.M. would be the collision point? If you jumped off the Brooklyn Bridge, is it reasonable to assume that you would travel to almost the center of the earth?

 

[postfan]

The title of the question literally was 'Center of Mass', in that case what should I do?

 

[haruspex]

I used the center of mass as the collision point, so I calculated (taking x=0 at m1) it to be m2*d/(m1+m2). What did I do wrong?

You are overlooking that in the reference frame you are given m1 has an initial velocity but m2 does not. The COM of the system is therefore moving. This increases the distance m1 moves to the collision point.
Even without that complication, I don't believe your formula is right. What is the ratio of the two accelerations? If both started at rest, what would that mean about the ratio of the distances moved?

Why did you assume that the C.O.M. would be the collision point?

Because it tells you they are small particles, not bothering to give the actual sizes.

 

[ehild]

The particles will collide at the CM, but the CM moves with a constant velocity, and you need to figure out the time when they collide. It depends on the force of interaction between them, so you need to consider how the particles move, either solving the the dynamical equations F=m1a1 and -F=m2a2, or using conservation of energy. The force of interaction is conservative.

ehild