Mathematics 9709 · AS & A Level · Energy, work and power
Energy, work and power — practice question
A railway engine with mass $75\,000\,\text{kg}$ is ascending a straight hill that makes an angle $\alpha$ with the horizontal, where $\sin\alpha = 0.01$. The engine moves at a steady speed of $30\,\text{m s}^{-1}$. Its power output is $960\,\text{kW}$. A constant force opposes the motion of the engine.
(a)[3]
Determine the resistance force.
(b)[4]
The engine reaches a stretch of track that is horizontal. At the beginning of this stretch the engine is moving at $30\,\text{m s}^{-1}$ and the engine power is now lowered to $900\,\text{kW}$. The resistance to motion is no longer fixed, but during the next $60\,\text{s}$ the work done against the resistance force is $46\,500\,\text{kJ}$. Determine the speed of the engine at the end of the $60\,\text{s}$.
Worked solution & mark scheme
This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Driving force is $DF=\frac{960000}{30}$” …