Homework Help: Simple mass ratio problem

It's a bit more complicated than that.

Do a balance of momentum at the start to get a ratio of the two separation speeds.

Then apply the eqns of motion to the movement of each skater and solve for the unknown ratio.

 

The center of mass of the couple can't move, because the total momentum will still be zero. Thats the key point here.. so you'll need to find masses such that if one was twice as far away from the starting point at the other, that the total CoM would still be in the starting point.

 

0 = M1v-M2v (because they are going in opposite directions..so..
M1v = M2v ?

 

Of course there is initial momentum if the two skaters are both moving.
p = mv
And we know that both skaters do have velocity and mass.

There are no numerical masses so you are solving for the variables M1 and M2, using equations. It will most likely turn out that the ratio will be expressed without varibles, and as a number.

 

They arent moving at the beginning.

 

Sorry, I misread the question.

 

They are moving at different velocities, so it's more a case of,

M1.V1 = M2.V2
M1/M2 = V2/V1

Let M1/M2 = λ, say

then,

V2 = λ.V1
========

Now do the eqns of motion bit, where both masses have the same deceleration, you know the start and end velocities of each mass, and M1 travels twice the distance that M2 does.
Solve for λ.