| Exam Board | Edexcel |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2010 |
| Session | January |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Power and driving force |
| Type | Cyclist or runner: find resistance or speed |
| Difficulty | Standard +0.3 This is a standard M2 power-force-velocity question requiring the formula P=Fv and resolving forces parallel to motion. Part (a) is direct substitution (490=F×3.5), while part (b) involves resolving forces on an incline with variable resistance, leading to a quadratic equation. The steps are routine for M2 students who have practiced this topic, making it slightly easier than average overall. |
| Spec | 3.03f Weight: W=mg3.03m Equilibrium: sum of resolved forces = 06.02l Power and velocity: P = Fv |
| Answer | Marks |
|---|---|
| \(\frac{490}{3.5} - R = 0\) | B1 M1 A1 |
| \(R = 140\) N | A1 (4) |
| Answer | Marks |
|---|---|
| \(\frac{24}{u} + 70g \cdot \frac{1}{14} - 40u = 0\) | B1 |
| \(40u^2 - 49u - 24 = 0\) | M1 A2, 1, 0 |
| \((5u - 8)(8u + 3) = 0\) | DM1 |
| \(u = 1.6\) | DM1 A1 (7) |
## (a)
$\frac{490}{3.5} - R = 0$ | B1 M1 A1 |
$R = 140$ N | A1 (4) |
## (b)
$\frac{24}{u} + 70g \cdot \frac{1}{14} - 40u = 0$ | B1 |
$40u^2 - 49u - 24 = 0$ | M1 A2, 1, 0 |
$(5u - 8)(8u + 3) = 0$ | DM1 |
$u = 1.6$ | DM1 A1 (7) |
**Total: [11]**
---A cyclist and her bicycle have a total mass of $70$ kg. She cycles along a straight horizontal road with constant speed $3.5 \text{ ms}^{-1}$. She is working at a constant rate of $490$ W.
\begin{enumerate}[label=(\alph*)]
\item Find the magnitude of the resistance to motion.
[4]
\end{enumerate}
The cyclist now cycles down a straight road which is inclined at an angle $\theta$ to the horizontal, where $\sin \theta = \frac{1}{14}$, at a constant speed $U \text{ ms}^{-1}$. The magnitude of the non-gravitational resistance to motion is modelled as $40U$ newtons. She is now working at a constant rate of $24$ W.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Find the value of $U$.
[7]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M2 2010 Q5 [11]}}