| Exam Board | OCR |
|---|---|
| Module | M2 (Mechanics 2) |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Work done and energy |
| Type | Energy method - driving force up incline, find work done by engine/force |
| Difficulty | Standard +0.3 This is a standard M2 mechanics question involving work-energy principles and power calculations on an incline. Part (i) is straightforward application of work-energy theorem; part (ii) uses F=ma with power formula (routine 'show that'); part (iii) requires working backwards from power to find force then acceleration. All techniques are standard M2 fare with no novel problem-solving required, making it slightly easier than average. |
| Spec | 6.02a Work done: concept and definition6.02e Calculate KE and PE: using formulae6.02j Conservation with elastics: springs and strings6.02k Power: rate of doing work6.02l Power and velocity: P = Fv |
A car of mass 700 kg is travelling up a hill which is inclined at a constant angle of $5°$ to the horizontal. At a certain point $P$ on the hill the car's speed is 20 m s$^{-1}$. The point $Q$ is 400 m further up the hill from $P$, and at $Q$ the car's speed is 15 m s$^{-1}$.
\begin{enumerate}[label=(\roman*)]
\item Calculate the work done by the car's engine as the car moves from $P$ to $Q$, assuming that any resistances to the car's motion may be neglected. [4]
\end{enumerate}
Assume instead that the resistance to the car's motion between $P$ and $Q$ is a constant force of magnitude 200 N.
\begin{enumerate}[label=(\roman*)]
\setcounter{enumi}{1}
\item Given that the acceleration of the car at $Q$ is zero, show that the power of the engine as the car passes through $Q$ is 12.0 kW, correct to 3 significant figures. [3]
\item Given that the power of the car's engine at $P$ is the same as at $Q$, calculate the car's retardation at $P$. [3]
\end{enumerate}
\hfill \mbox{\textit{OCR M2 Q6 [10]}}