| Exam Board | Edexcel |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2016 |
| Session | June |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Advanced work-energy problems |
| Type | Engine power on road constant/variable speed |
| Difficulty | Standard +0.3 This is a standard M2 power-resistance problem requiring systematic application of P=Fv in two scenarios to find two unknowns, followed by routine work-energy principle application. The setup is clear, the mathematics is straightforward (solving simultaneous equations, then basic energy conservation), and it follows a well-practiced template with no novel insight required. Slightly easier than average due to its predictable structure. |
| Spec | 6.02a Work done: concept and definition6.02i Conservation of energy: mechanical energy principle6.02l Power and velocity: P = Fv6.02m Variable force power: using scalar product |
2. A car of mass 800 kg is moving on a straight road which is inclined at an angle $\theta$ to the horizontal, where $\sin \theta = \frac { 1 } { 20 }$. The resistance to the motion of the car from non-gravitational forces is modelled as a constant force of magnitude $R$ newtons. When the car is moving up the road at a constant speed of $12.5 \mathrm {~ms} ^ { - 1 }$, the engine of the car is working at a constant rate of $3 P$ watts. When the car is moving down the road at a constant speed of $12.5 \mathrm {~ms} ^ { - 1 }$, the engine of the car is working at a constant rate of $P$ watts.
\begin{enumerate}[label=(\alph*)]
\item Find
\begin{enumerate}[label=(\roman*)]
\item the value of $P$,
\item the value of $R$.\\
(6)
When the car is moving up the road at $12.5 \mathrm {~ms} ^ { - 1 }$ the engine is switched off and the car comes to rest, without braking, in a distance $d$ metres. The resistance to the motion of the car from non-gravitational forces is still modelled as a constant force of magnitude $R$ newtons.
\end{enumerate}\item Use the work-energy principle to find the value of $d$.
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\hfill \mbox{\textit{Edexcel M2 2016 Q2 [10]}}