Solving a Puzzling Momentum Problem

[Canuck156]

I was looking through the revision section of my textbook in preperation for my test tomorrow, when I came across an interesting problem, which I can't manage to solve.

The problem is:

A body of mass 2kg collides elastically with another body that is stationary. The moving mass continues on in it's initial direction, at 1/4 of its initial velocity. What is the mass of the stationary object?

I realize that the conservation of momentum, and the conservation of kinetic energy must be used to solve this problem. I can solve it for any specific case (ie. substitute in a value for the velocity of the first object) but not generally, although it should be the same answer. I always end up with 2 equations and 3 unknowns that I cannot cancel out.

Thanks for any help.

 

[Tide]

I don't see what the three unknowns would be. You have only the mass of the second object and its final speed and you find both of those with momentum and energy conservation.

P.S. It's strictly a one dimensional problem since the original mass continues in its original direction so neither object has a transverse component of velocity by momentum conservation,.

 

[Canuck156]

Well, theoretically there are 3 unknowns - the initial speed of object 1, the final speed of object 2, and the mass of object 2. However, since we are given a ratio of the initial and final velocities of object 1, I think I should be able to cancel these out somehow. I just can't figure out how.

Yes, I recognized that it was a one-dimensional problem, but was still unable to solve it. It's only the mathematics that mean I can't do it.

 

[teclo]

well the final velocity of the moving object would be (1/4) v(init) leaving only two unknowns, right? I'm only working through the problem in my head, but i think you should be able to represent the two unknowns in terms of the first objects initial velocity.

 

[Canuck156]

Yes, telco, I thought that too, when I was working through it in my head. But when I tried to do it on paper, I couldn't simplify the other unknowns in terms of the initial velocity. I still can't figure out how to do it.

 

[teknodude]

Not sure if this is right, but i calculated the mass to be 1.2 kg

I used the equation v1f = ((m1+m2)/ (m1+m2))v1i
v1f= final velocity v1i= initial velocity

v1f= 1/4 v1i

Then i just did some algebra to solve for m2