AS Daily A Level Physics question
On a smooth horizontal air track, cart A (mass m) moves to the right at speed u towards cart B (mass 10m) moving to the left at speed u/5. The carts collide head-on and stick together. Based only on momentum considerations, which statement must be true about the velocity of the joined carts immediately after the collision?
Answer
The correct answer is C.
Correct: C — Moves to the left with a small speed, about one-tenth of u. The heavier cart’s leftward momentum (10m × u/5 = 2mu) outweighs A’s rightward momentum (mu), giving a net leftward momentum of magnitude mu; sharing this across the combined mass (11m) leads to a small leftward speed (~u/11, i.e. about u/10). A The net momentum is leftward (2mu vs mu), so the joined carts cannot move right, let alone faster than u. B Wrong direction: because leftward momentum is larger, the final velocity cannot be to the right. C Consistent with momentum direction (left) and with the magnitude being reduced by the large total mass (u/11 ≈ u/10). D Coming to rest would require exactly equal and opposite initial momenta; here they are unequal (2mu vs mu), so the final momentum is not zero.