Mathematics 9709 · AS & A Level · Energy, work and power
Energy, work and power — practice question
A lorry with mass $16000\text{ kg}$ moves at steady speed from the base, $O$, to the summit, $A$, of a straight hill. The length $OA$ is $1200\text{ m}$ and $A$ lies $18\text{ m}$ above the level of $O$. The lorry’s driving force is constant and equal to $4500\text{ N}$. When it reaches $A$ the lorry goes on along a straight horizontal road, working against a constant resistance of $2000\text{ N}$. The driving force is then no longer constant, and the speed rises from $9\text{ m s}^{-1}$ at $A$ to $21\text{ m s}^{-1}$ at point $B$ on the road. The distance $AB$ is $2400\text{ m}$.
(i)[3]
Find the amount of work done against the resistance opposing the lorry’s motion.
(ii)[3]
Find $F\text{ N}$ by any valid method, where $F\text{ N}$ is the mean value of the driving force of the lorry as it moves from $A$ to $B$.
(iii)[2]
Since the driving force at $A$ is $1280\text{ N}$ above $F\text{ N}$ and the driving force at $B$ is $1280\text{ N}$ below $F\text{ N}$, show that the power produced by the lorry’s engine at $B$ is the same as at $A$.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Use work-energy: work done by the driving force = gain in PE + work done against resistance” …