| Exam Board | Edexcel |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2007 |
| Session | June |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Power and driving force |
| Type | Cyclist or runner: find resistance or speed |
| Difficulty | Moderate -0.3 This is a straightforward application of the power equation P = Fv at constant speed, requiring students to resolve forces on an incline and use P = (R + mg sin α)v. The calculation is direct with clean numbers (444 = (R + 90×10×1/21)×6), making it slightly easier than average for M2. |
| Spec | 3.03f Weight: W=mg3.03g Gravitational acceleration6.02l Power and velocity: P = Fv6.02m Variable force power: using scalar product |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| Force exerted \(= \frac{444}{6} = 74\) N | B1 | 444/6 seen or implied |
| \(R + 90g\sin\alpha = \frac{444}{6}\) | M1 A1 | Resolve parallel to slope for a 3 term equation; condone sign errors and sin/cos confusion |
| \(\Rightarrow R = 32\) N | A1 | 32(N) only |
## Question 1:
| Answer/Working | Marks | Guidance |
|---|---|---|
| Force exerted $= \frac{444}{6} = 74$ N | B1 | 444/6 seen or implied |
| $R + 90g\sin\alpha = \frac{444}{6}$ | M1 A1 | Resolve parallel to slope for a 3 term equation; condone sign errors and sin/cos confusion |
| $\Rightarrow R = 32$ N | A1 | 32(N) only |
---\begin{enumerate}
\item A cyclist and his bicycle have a combined mass of 90 kg . He rides on a straight road up a hill inclined at an angle $\alpha$ to the horizontal, where $\sin \alpha = \frac { 1 } { 21 }$. He works at a constant rate of 444 W and cycles up the hill at a constant speed of $6 \mathrm {~m} \mathrm {~s} ^ { - 1 }$.
\end{enumerate}
Find the magnitude of the resistance to motion from non-gravitational forces as he cycles up the hill.\\
\hfill \mbox{\textit{Edexcel M2 2007 Q1 [4]}}