Mathematics 9709 · AS & A Level · Energy, work and power
Energy, work and power — practice question
A car with mass $1800\,\text{kg}$ is pulling a trailer with mass $300\,\text{kg}$ along a straight road that slopes at an angle $\alpha$ to the horizontal, with $\sin \alpha = 0.05$. A tow-bar, which is light, rigid and parallel to the road, links the car and trailer. A resistance force of $800\,\text{N}$ acts on the car, while the trailer experiences a resistance force of $F\,\text{N}$. The car's engine provides a driving force of $3000\,\text{N}$.
(a)[5]
Given that $F = 100$, determine the acceleration of the car and the tension in the tow-bar.
(b)[5]
Instead, the total work done against $F$ over a distance of $50\,\text{m}$ up the road is $6000\,\text{J}$. At the beginning of the $50\,\text{m}$, the car is travelling at $20\,\text{m s}^{-1}$. Use an energy method to determine the speed of the car after the $50\,\text{m}$.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Newton’s second law used for the car, trailer or system” …