Elastic Collision on an Incline

[Soaring Crane]

A block of mass m = 2.20 kg slides down a 30 degree incline which is 3.6 m high. At the bottom it strikes a block of mass M = 7 kg which is at rest on the horizontal surface. If the collision is elastic and friction can be ignored, determine the:

speeds of the two blocks

and

how far back up the incline the smaller mass will go.

Does this involve collisions in two dimensions? Please respond with any help if you can.

Thanks.

 

[Sirus]

You can find the speed of the block that was on the incline when it hits the second block. Now you should have some 2D collision formulas that will allow you to find the velocities of the blocks after the collision. At that point, you can find the distance up the incline the smaller mass will travel (using energy concepts).

 

[kmcf]

Do this by taking the collision to happen on the horizontal surface (HS) -- the 7kg block must sit on the HS, the 2.2kg block slides down the incline on to the HS (not losing speed) collides with the 7kg block, then slides back up the incline. So do the problem in 3 steps: find the speed of the 2.2kg block at the bottom of the incline, do the 1-D collision (conserving momentum and energy), then find how high the 2.2kg block goes.
2D formulae won't work because they assume that no forces act during the collision, but here there will be forces exerted by the surfaces that will act (otherwise the particles would not move along the surfaces!).

 

[philosophking]

Would you mind posting your answers? I did it, but I'm not sure if I did it right :) thanks.

 

[Sirus]

Post yours first.

 

[philosophking]

haha, wasn't sure if I was allowed to... :/

v_m = -7.756086752 (opposite direction)
v_M = 3.774815111

Second one follows from this, so no answer needed.

 

[Sirus]

Oops! I thought you were the original poster. Oh well! Good fun. I would check those answers but I don't feel like digging up those formulas.

We'll see what Soaring Crane has to say.