Mathematics 9709 · AS & A Level · Energy, work and power
Energy, work and power — practice question
A car with mass $1500\,\text{kg}$ is towing a trailer of mass $750\,\text{kg}$ up a straight hill that is $800\,\text{m}$ long and inclined at an angle of $\sin^{-1} 0.08$ to the horizontal. The resistive forces acting on the car and trailer are $400\,\text{N}$ and $200\,\text{N}$ respectively. A light rigid tow-bar connects the car to the trailer. At the foot of the hill, the car and trailer move at $30\,\text{m s}^{-1}$, and at the top they move at $20\,\text{m s}^{-1}$.
(a)[5]
Use an energy method to determine the constant driving force as the car and trailer move up the hill.
(b)[4]
After the car and trailer reach the top of the hill, the system of car and trailer travels along a straight level road. The car’s engine provides a driving force of $2400\,\text{N}$ and the resistances to motion stay unchanged. Determine the acceleration of the system and the tension in the tow-bar.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Apply kinetic energy $\tfrac12 mv^2$ to any two parts” …