| Exam Board | OCR MEI |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2008 |
| Session | January |
| Marks | 17 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Work done and energy |
| Type | Energy method - driving force on horizontal road |
| Difficulty | Moderate -0.3 This is a straightforward M2 mechanics question testing standard energy methods and power calculations. Part (i) uses basic KE and work-energy theorem, part (ii) applies energy conservation with friction (the most challenging part, requiring careful accounting of energy transfers), and part (iii) uses standard P=Fv and F=ma relationships. All techniques are routine for M2 with no novel problem-solving required, making it slightly easier than average. |
| Spec | 6.02a Work done: concept and definition6.02b Calculate work: constant force, resolved component6.02d Mechanical energy: KE and PE concepts6.02e Calculate KE and PE: using formulae6.02i Conservation of energy: mechanical energy principle6.02k Power: rate of doing work6.02l Power and velocity: P = Fv |
A cyclist and her bicycle have a combined mass of 80 kg.
\begin{enumerate}[label=(\roman*)]
\item Initially, the cyclist accelerates from rest to 3 m s$^{-1}$ against negligible resistances along a horizontal road.
\begin{enumerate}[label=(\Alph*)]
\item How much energy is gained by the cyclist and bicycle? [2]
\item The cyclist travels 12 m during this acceleration. What is the average driving force on the bicycle? [2]
\end{enumerate}
\item While exerting no driving force, the cyclist free-wheels down a hill. Her speed increases from 4 m s$^{-1}$ to 10 m s$^{-1}$. During this motion, the total work done against friction is 1600 J and the drop in vertical height is $h$ m.
Without assuming that the hill is uniform in either its angle or roughness, calculate $h$. [5]
\item The cyclist reaches another horizontal stretch of road and there is now a constant resistance to motion of 40 N.
\begin{enumerate}[label=(\Alph*)]
\item When the power of the driving force on the bicycle is a constant 200 W, what constant speed can the cyclist maintain? [3]
\item Find the power of the driving force on the bicycle when travelling at a speed of 0.5 m s$^{-1}$ with an acceleration of 2 m s$^{-2}$. [5]
\end{enumerate}
\end{enumerate}
\hfill \mbox{\textit{OCR MEI M2 2008 Q2 [17]}}