A railway locomotive of mass 240000 kg is towing a coach of mass 36000 kg down a hill inclined at an angle of sin⁻¹ 0.04 to the horizontal. The driving force produced by the locomotive is 450000 N and there are resistances to motion of 120000 N on the locomotive and 15000 N on the coach. The coupling between the locomotive and the coach is light, rigid and parallel to the hill. Find the acceleration of the locomotive and the tension in the coupling.

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2025). The mark or mark type is shown in brackets.

1. [*M1] Attempt at Newton's second law at least once; Correct number of terms, allow sign errors, allow sin/cos mix, allow g missing.
2. [A2] A1 for any equation correct. A2 for any 2 equations correct. Allow sin 2.3 or better for 0.04. A candidate may be using their a in the either of the first 2 equations if they have used the 3rd equation to find a.
3. [DM1] Solving for a or T, from equation(s) with the correct number of relevant terms; Allow g missing, terms should be components where necessary. Must get to a =... or T=...
4. [A1] Acceleration = 1.54ms⁻² and Tension = 56100 N; Allow a = 709/460, a=1.54130..., T=56086.9... Allow with use of sin 2.3. If using a=1.54, then T=56400 from locomotive equation or T=56040 from coach equation. If using a=1.541, then T=56160 from locomotive equation or T=56076 from coach equation.