Mathematics 9709 · AS & A Level · Newton's laws of motion

Newton's laws of motion — practice question

A railway engine with mass $120000\text{ kg}$ is hauling a coach with mass $60000\text{ kg}$ along a straight track that rises at an angle $\alpha$ to the horizontal, where $\sin \alpha = 0.02$. The engine and coach are linked by a light rigid coupling, parallel to the track. The engine supplies a driving force of $125000\text{ N}$, and the constant resistances to motion are $22000\text{ N}$ on the engine and $13000\text{ N}$ on the coach.
(a)[5]

Find the acceleration of the engine and the tension in the coupling.

(b)[4]

If the resistance forces are taken to be unchanged, determine the value of $\beta$.

Worked solution & mark scheme

This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: Newton’s second law attempted for the engine or coach, with the correct relevant terms

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