Mathematics 9709 · AS & A Level · Energy, work and power
Energy, work and power — practice question
A car with mass $1400\,\text{kg}$ is pulling a trailer with mass $500\,\text{kg}$ down a straight hill that is inclined at an angle of $5^\circ$ to the horizontal. The car and trailer are joined by a light rigid tow-bar. At the top of the hill the speed of the car and trailer is $20\,\text{m s}^{-1}$ and at the bottom of the hill their speed is $30\,\text{m s}^{-1}$.
(a)[5]
It is stated instead that, while the car and trailer travel downhill, the car’s engine does $150\,000\,\text{J}$ of work, and that resistance forces are absent. Determine the length of the hill.
(b)[4]
It is now stated that the trailer experiences a resistance force of $100\,\text{N}$, the hill has length $200\,\text{m}$, and the car and trailer move with constant acceleration. Determine the tension in the tow-bar between the car and trailer.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Increase in kinetic energy can be written as $= \tfrac12 \times 1900 \times 30^2 - \tfrac12 \times 1900 \times 20^2$” …