Mathematics 9709 · AS & A Level · Energy, work and power
Energy, work and power — practice question
A lorry with mass $14\,000\,\text{kg}$ travels along a road, beginning at rest at point $O$. It gets to point $A$, and then continues to point $B$, where it has a speed of $24\,\text{m s}^{-1}$. The stretch $OA$ is straight, horizontal and $400\,\text{m}$ long. The stretch $AB$ is straight, slopes downwards at an angle of $\theta^\circ$ to the horizontal, and has length $300\,\text{m}$.
(i)[3]
For the journey from $O$ to $B$, determine the lorry’s gain in kinetic energy and write its loss in potential energy in terms of $\theta$.
The resistive force on the lorry is $4800\,\text{N}$ and the work done by the driving force from $O$ to $B$ is $5000\,\text{kJ}$.
(ii)[3]
Determine the value of $\theta$.
Worked solution & mark scheme
This 6-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Use $KE = \tfrac12 mv_B^2$ together with $PE = mg(AB)\sin\theta$” …