| Exam Board | Edexcel |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2013 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Work done and energy |
| Type | Maximum speed on horizontal road |
| Difficulty | Moderate -0.3 This is a straightforward M2 mechanics question requiring standard application of P=Fv and F=ma. Part (a) involves simple rearrangement with power at constant speed (3 marks). Part (b) requires resolving forces on an incline and applying Newton's second law (4 marks). Both parts use routine techniques with no novel problem-solving required, making it slightly easier than average. |
| Spec | 3.03d Newton's second law: 2D vectors6.02l Power and velocity: P = Fv |
| Answer | Marks |
|---|---|
| Use of \(\frac{P}{V} = F\) | M1 |
| \(\frac{32000}{V} = 800\) | A1 |
| \(V = 40\) | A1(3) |
| Answer | Marks | Guidance |
|---|---|---|
| \(F = \frac{32000}{20} = 1600\) | M1 | Find the driving force |
| \(1600 - 800 + 1200g \sin \theta = 1200a\) | M1 | Equation of motion for their F. Requires all 4 terms. Condone sign errors and trig confusion |
| \(800 + \frac{1200g}{40} = 1200a\) | A1 | Correct equation (allow with \(\sin \theta\)) |
| \(a = 0.91 \text{ (m s}^{-2}\text{)}\) | A1 | Accept 0.912 |
| (4) | ||
| [7] |
**(a)**
| Use of $\frac{P}{V} = F$ | M1 | |
| $\frac{32000}{V} = 800$ | A1 | |
| $V = 40$ | A1(3) | |
**(b)**
| $F = \frac{32000}{20} = 1600$ | M1 | Find the driving force |
| $1600 - 800 + 1200g \sin \theta = 1200a$ | M1 | Equation of motion for their F. Requires all 4 terms. Condone sign errors and trig confusion |
| $800 + \frac{1200g}{40} = 1200a$ | A1 | Correct equation (allow with $\sin \theta$) |
| $a = 0.91 \text{ (m s}^{-2}\text{)}$ | A1 | Accept 0.912 |
| | (4) | |
| | [7] | |A car has mass 1200 kg. The maximum power of the car's engine is 32 kW. The resistance to motion due to non-gravitational forces is modelled as a force of constant magnitude 800 N. When the car is travelling on a horizontal road at constant speed $V$ m s$^{-1}$, the engine of the car is working at maximum power.
\begin{enumerate}[label=(\alph*)]
\item Find the value of $V$. [3]
\end{enumerate}
The car now travels downhill on a straight road inclined at an angle $\theta$ to the horizontal, where $\sin \theta = \frac{1}{40}$. The resistance to motion due to non-gravitational forces is still modelled as a force of constant magnitude 800 N. Given that the engine of the car is again working at maximum power,
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item find the acceleration of the car when its speed is 20 m s$^{-1}$. [4]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M2 2013 Q2 [7]}}