Suppose two carts, one twice as massive as the other, fly apart when the compressed spring that joins them is released.

Suppose two carts, one twice as massive as the other, fly apart when the compressed spring that joins them is released. How fast does the heavier cart roll com- pared with the lighter cart?

 

Answer

initially there is zero momentum, so since there are no external forces acting on the system, the total momentum of the system remains zero throughout call m, v the mass and velocity of the smaller car, M, V of the larger car we have m v + MV =0 or mv = - MV we can express the velocity of the larger car as V = -(m/M) v we are told that M=2m, so that V=-v/2 so that option 5 is correct the minus sign arises because velocity is a vector and we must include signs to be accurate. However, the question asks for speed so we are only concerned with the magnitude, so it is completely correct to say the heavier cart has half the speed of the lighter cart.