A cart of mass m1 = 15 kg slides down a frictionless ramp and is made to collide with a second cart of mass m2 = 23 kg which then heads into a vertical loop of radius 0.21 m.

Question

(a) Determine the height h at which cart #1 would need to start from to make sure that cart #2 completes the loop without leaving the track. Assume an elastic collision.

**I understand that the carts would need to travel a total of the circumference (C=2 pi r = 1.32) but how do I work the distance into the conservation of momentum formula?

(b) Find the height needed if instead the more massive cart is allowed to slide down the ramp into the smaller cart.

Answer 1

Use conservation of momentum only to find M2 velocity from M2 ; ie V2=V1 (M2/(Mtotal)

Now, at the loop top, you must have g=V^2/2 to keep it on the track, so figure the KE of that motion, add it to PE of 2radius. Figure the velocity for that sum of energies. That is waht V2 has to be. Then V1 has to be V2(totalmass/M2) Now, you can figure h to drop M1 to get that V1.