10. Two titanium box approach each other head-on with the same speed and collide

Question

10. Two titanium box approach each other head-on with the same speed and collide elastically. After the collision, one of the boxes, who's mass is 1500 grams remains at rest. What is the mass of the other box? 11. A hollow sphere of mass m and radius r rolls without slipping along a loop-the-loop track, with a height of h and radius R = 10.0 m. The sphere is released from rest somewhere on the straight section of the track. From what minimum height h above the bottom of the track must the sphere be released in order that it not leave the track at the top of the loop? 2R

Explanation / Answer

10)  For two masses m and M,
initial momentum p = mv - Mv = (m - M)v
where m is presumed headed to the right (+ve) and M to the left (-ve).
final momentum p = MV = (m - M)v
where V is the velocity of the particle still moving post-collision.
So V = v(m - M)/M
For an elastic head-on collision, we know that the
relative velocity of approach = relative velocity of separation, or in this case,
2v = V
So 2v = v(m - M)/M
and 2M = m - M
and m = 3M
and, since M was moving after the collision, m = 1500g and
M = 500 g

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