A2 Daily A Level Physics question
On a low-friction air track, cart A of mass m moves to the right at 1.2 m/s and collides head-on with cart B of mass 2m moving to the left at speed u. The carts stick together, and immediately after impact the pair moves at 0.20 m/s to the left. Which statement must be true?
Answer
The correct answer is A.
Correct: A — u = 0.90 m/s; and in the limit of a very large B, the joined carts would move left at almost B’s speed. A: Using sign-aware momentum balance m(1.2) + 2m(−u) = 3m(−0.20) gives u = 0.90 m/s, and as m_B ≫ m_A the post-collision speed tends to v_B to the left. B: u = 0.60 m/s would make the momenta equal and opposite (2m×0.60 = m×1.20), implying zero final speed, contradicting the stated 0.20 m/s left; its limiting claim also contradicts the dominance of a very massive B. C: Taking u = 1.20 m/s ignores the mass ratio and signs (it would overbalance leftwards), and its limiting claim wrongly predicts motion to the right when B is very massive. D: The value u = 0.90 m/s is correct, but the limiting claim is wrong—if B becomes very large, the combined motion follows B to the left, not to the right.