| Exam Board | Edexcel |
|---|---|
| Module | M2 (Mechanics 2) |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Power and driving force |
| Type | Variable resistance: find k or constants |
| Difficulty | Standard +0.3 This is a standard M2 work-energy question requiring force equilibrium at constant speed (resolving forces parallel to slope) and power calculation. The steps are routine: equate component of weight to resistance to find k, then apply P=Fv with resistance plus weight component. Slightly easier than average due to straightforward setup and clear numerical values. |
| Spec | 6.02k Power: rate of doing work6.02l Power and velocity: P = Fv6.06a Variable force: dv/dt or v*dv/dx methods |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(R(\checkmark),\ 100g \times \frac{1}{20} = k \times \left(\frac{7}{2}\right)^2\) | M1 A1 | Resolving along slope with correct terms |
| \(\Rightarrow k = 4\) | A1 | (3) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(R(\nearrow),\ F - 100g \times \frac{1}{40} - 16 = 0\) | M1 A2 | |
| \(\Rightarrow F = 40.5\ \text{N}\) | A1 | |
| \(P = 40.5 \times 2\) | M1 | |
| \(= 81\ \text{W}\) | A1 | (6) (9) |
# Question 4:
## Part (a)
| Answer/Working | Marks | Guidance |
|---|---|---|
| $R(\checkmark),\ 100g \times \frac{1}{20} = k \times \left(\frac{7}{2}\right)^2$ | M1 A1 | Resolving along slope with correct terms |
| $\Rightarrow k = 4$ | A1 | (3) |
## Part (b)
| Answer/Working | Marks | Guidance |
|---|---|---|
| $R(\nearrow),\ F - 100g \times \frac{1}{40} - 16 = 0$ | M1 A2 | |
| $\Rightarrow F = 40.5\ \text{N}$ | A1 | |
| $P = 40.5 \times 2$ | M1 | |
| $= 81\ \text{W}$ | A1 | (6) **(9)** |
---4. The resistance to the motion of a cyclist is modelled as $k v ^ { 2 } \mathrm {~N}$, where $k$ is a constant and $v \mathrm {~m} \mathrm {~s} ^ { - 1 }$ is the speed of the cyclist. The total mass of the cyclist and his bicycle is 100 kg . The cyclist freewheels down a slope inclined at an angle $\alpha$ to the horizontal, where $\sin \alpha = \frac { 1 } { 20 }$, at a constant speed of $3.5 \mathrm {~m} \mathrm {~s} ^ { - 1 }$.
\begin{enumerate}[label=(\alph*)]
\item Show that $k = 4$.
The cyclist ascends a slope inclined at an angle $\beta$ to the horizontal, where $\sin \beta = \frac { 1 } { 40 }$, at a constant speed of $2 \mathrm {~m} \mathrm {~s} ^ { - 1 }$.
\item Find the rate at which the cyclist is working.\\
(6 marks)
\end{enumerate}
\hfill \mbox{\textit{Edexcel M2 Q4 [9]}}