Momentum and Newton's Laws 的問題

The questions are just simple application of momentum.
1. speed of X = (24/100)/3 m/s = 0.08 m/s
hence, momentum = (2x95/1000) x 0.08 Ns = 0.0152 Ns
2. Use conservation of momentum
0.0152 = (3x95/1000).v
where v is the speed of Y after colision
solve for v
3. The centre of mass of the 2 carriages is just the centre of mass of the whole system. So just find the momentum of the system, which is the answer obtained in (1).
4. acceleration = change of velocity/time
= 0.063/0.5 m/s2 = 0.13 m/s2
5. force = mass x acceleration = (95/1000) x 0.13 N
6. Same as answer in (5) because of action and reaction relationship.
7. The 2 carraiges form an isolated system. Since no external force is acting on the system, momentum is conserved. The velocity of the centre of mass of the whole system is therefore unaffected by the collision.
8. Alternatively, you can find it out from momentum exchange,
gain in momentum by Y = (95/1000) x 0.063 Ns
Loss of momentum by X = (2x95/1000)(u-0.063) Ns
where u is the initial velocity of X
hence, (95/1000) x 0.063 = (2x95/1000)(u-0.063)
u = 0.0945 m/s