Solving Momentum Problem: Max Height of m1 After Elastic Collision

[Elmon]

Two blocks are free to slide along a frictionless wooden track ABC as shown in Figure P9.20. The block of mass m1 = 4.93 kg is released from A. Protruding from its front end is the north pole of a strong magnet, repelling the north pole of an identical magnet embedded in the back end of the block of mass m2 = 9.60 kg, initially at rest. The two blocks never touch. Calculate the maximum height to which m1 rises after the elastic collision.

The figure shows m1 on a curved ramp at a height of 5 m.

Since it is elastic, I know energy and momentum are conserved. So I have:

(1/2)m1*v1o^2+(1/2)m2*v2o^2 = (1/2)m1*v1f^2+(1/2)m2*v2f^2
and
m1*v1o+m2*v2o = m1*v1f+m2*v2f

m2 is initially at rest, so v2o=0. Now I am not sure how I am supposed to use these to find height, or anything at all for that matter. Can anyone give me a point in the right direction?

 

[Doc Al]

Two equations, two unknowns. One of those unknowns will give you the energy of m1 immediately following the collision. Mechanical energy is conserved.

 

[Elmon]

Well, mechanical energy is KE+PE, so

(1/2)m1*v1f+m1*g*hf = (1/2)m1*v1o+m1*g*ho

But I am not sure how to connect that to the other equations I have.

I am having a hard time getting my head around this one.

 

[Doc Al]

Since you didn't include the figure, I'm just guessing as to what it shows.

Well, mechanical energy is KE+PE, so

(1/2)m1*v1f+m1*g*hf = (1/2)m1*v1o+m1*g*ho

Make sure you square those speeds in the KE terms. I assume v1o is the initial speed of m1 immediately after the collision. (That speed is called v1f in your collision equations.)

But I am not sure how to connect that to the other equations I have.

The collision equations will give you the speed of m1 after the collision.

There are three steps to this problem:

(1) The fall of m1 from point A to where it collides with m2
(2) The collision
(3) The rise of m1​

In each step, energy is conserved. In step 2, momentum is also conserved.

 

[Elmon]

Okay, I got it, thanks a lot. When you put it into three steps, something clicked and everything came out. Thanks again.