Mathematics 9709 · AS & A Level · Energy, work and power

Energy, work and power — practice question

A van with mass $3000\text{ kg}$ is towing a trailer of mass $500\text{ kg}$ on a straight, level road at a steady speed of $25\text{ m s}^{-1}$. The van-and-trailer arrangement is represented by two particles joined by a light inextensible cable. The van experiences a constant resistive force of $300\text{ N}$ and the trailer a constant resistive force of $100\text{ N}$.
(i)[2]

Calculate the power developed by the van’s engine.

(ii)[1]

State the tension in the cable.

(iii)[5]

The van reaches the bottom of a hill inclined at $4^\circ$ to the horizontal with speed $25\text{ m s}^{-1}$. The engine power is then increased to $25\,000\text{ W}$. If the resistance forces are unchanged, determine the new tension in the cable at the moment when the van is moving up the hill at $20\text{ m s}^{-1}$.

Worked solution & mark scheme

This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: Apply $P = Fv$, for example $P = 400 \times 25$

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