| Exam Board | Edexcel |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2018 |
| Session | June |
| Marks | 8 |
| 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 work-energy-power question requiring the power equation P=Fv and Newton's second law. Part (a) involves finding resistance using F=ma and P=Fv with straightforward substitution. Part (b) adds an incline component but remains routine application of resolving forces and the power equation. Slightly above average due to two-part structure and combining multiple mechanics concepts, but follows standard M2 patterns with no novel insight required. |
| Spec | 6.02l Power and velocity: P = Fv |
| Answer | Marks |
|---|---|
| Use of \(P = Fv: F = \frac{180}{4}\) | B1 |
| Equation of motion: \(F - R = 75 \times 0.2\) | M1 |
| Equation in \(R\): \(\frac{180}{4} - R = 75 \times 0.2(45 - R = 15)\) | DM1 |
| \(R = 30\) | A1 |
| (4) |
| Answer | Marks |
|---|---|
| Equation of motion: \(D - 75g\sin\theta - R = 0\) | M1 |
| \(\frac{180}{v} - 75 \times g \times \frac{1}{21}\) – their \(R = 0\) | A2 ft |
| \(v = 2.77\) or \(2.8\) | A1 |
| (4) | |
| [8] |
## 3a.
Use of $P = Fv: F = \frac{180}{4}$ | B1 |
Equation of motion: $F - R = 75 \times 0.2$ | M1 |
Equation in $R$: $\frac{180}{4} - R = 75 \times 0.2(45 - R = 15)$ | DM1 |
$R = 30$ | A1 |
(4) | |
## 3b.
Equation of motion: $D - 75g\sin\theta - R = 0$ | M1 |
$\frac{180}{v} - 75 \times g \times \frac{1}{21}$ – their $R = 0$ | A2 ft |
$v = 2.77$ or $2.8$ | A1 |
(4) | |
[8] | |
**Notes for Q3:**
3(a)
- B1 for $F = \frac{180}{4}$ seen
- First M1 for equation of motion with usual rules, $F$ does not need to be substituted
- Second M1, dependent on first M1, for an equation in $R$ only with usual rules
- A1 for $R = 30$
3(b)
- M1 for equation of motion with usual rules but none of $D$, $\sin\theta$ nor $R$ need to be substituted
- A2 ft for a correct equation, in $v$ only, ft on their $R$
- A1 A0 if one error
- Third A1 for $2.77$ or $2.8$ (**Only answers**)
---3. A cyclist and his bicycle, with a combined mass of 75 kg , move along a straight horizontal road. The cyclist is working at a constant rate of 180 W . There is a constant resistance to the motion of the cyclist and his bicycle of magnitude $R$ newtons. At the instant when the speed of the cyclist is $4 \mathrm {~m} \mathrm {~s} ^ { - 1 }$, his acceleration is $0.2 \mathrm {~m} \mathrm {~s} ^ { - 2 }$.
\begin{enumerate}[label=(\alph*)]
\item Find the value of $R$.
Later, the cyclist moves up a straight road with a constant speed $v \mathrm {~m} \mathrm {~s} ^ { - 1 }$. The road is inclined at an angle $\theta$ to the horizontal, where $\sin \theta = \frac { 1 } { 21 }$. The cyclist is working at a rate of 180 W and the resistance to the motion of the cyclist and his bicycle from non-gravitational forces is again the same constant force of magnitude $R$ newtons.
\item Find the value of $v$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel M2 2018 Q3 [8]}}