| Exam Board | CAIE |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2022 |
| Session | March |
| Marks | 6 |
| 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 mechanics problem requiring application of Newton's second law and the power equation P=Fv. Part (a) involves resolving forces on an incline with given acceleration, and part (b) requires setting acceleration to zero for steady speed. Both parts use standard techniques with no novel insight required, making it slightly easier than average. |
| Spec | 3.03d Newton's second law: 2D vectors6.02l Power and velocity: P = Fv |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Forward force exerted by cyclist driving force \(= \frac{180}{6}\) \([= 30\text{ N}]\) | B1 | |
| \(DF - F - 70g\sin\alpha = 70 \times -0.2\) | M1 | Attempt Newton's second law, 4 terms required. A value must be used for \(\sin\alpha\) |
| \(30 - F - 70g \times 0.05 = 70 \times -0.2\) | A1 | Correct equation |
| \(F = 9\) | A1 | From exact working only |
| 4 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(\frac{180}{v} - F - 70g \times \sin\alpha = 0\) | M1 | Apply Newton's second law up the hill with \(a=0\). Must have 3 relevant terms using their \(F\) from 4(a). A value for \(\sin\alpha\) must be used |
| \(v = 4.09\text{ ms}^{-1}\) | A1 | Allow \(\frac{45}{11}\) |
| 2 |
## Question 4:
### Part 4(a):
| Answer | Mark | Guidance |
|--------|------|----------|
| Forward force exerted by cyclist driving force $= \frac{180}{6}$ $[= 30\text{ N}]$ | B1 | |
| $DF - F - 70g\sin\alpha = 70 \times -0.2$ | M1 | Attempt Newton's second law, 4 terms required. A value must be used for $\sin\alpha$ |
| $30 - F - 70g \times 0.05 = 70 \times -0.2$ | A1 | Correct equation |
| $F = 9$ | A1 | From exact working only |
| | **4** | |
### Part 4(b):
| Answer | Mark | Guidance |
|--------|------|----------|
| $\frac{180}{v} - F - 70g \times \sin\alpha = 0$ | M1 | Apply Newton's second law up the hill with $a=0$. Must have 3 relevant terms using their $F$ from **4(a)**. A value for $\sin\alpha$ must be used |
| $v = 4.09\text{ ms}^{-1}$ | A1 | Allow $\frac{45}{11}$ |
| | **2** | |
---4 The total mass of a cyclist and her bicycle is 70 kg . The cyclist is riding with constant power of 180 W up a straight hill inclined at an angle $\alpha$ to the horizontal, where $\sin \alpha = 0.05$. At an instant when the cyclist's speed is $6 \mathrm {~m} \mathrm {~s} ^ { - 1 }$, her acceleration is $- 0.2 \mathrm {~m} \mathrm {~s} ^ { - 2 }$. There is a constant resistance to motion of magnitude $F \mathrm {~N}$.
\begin{enumerate}[label=(\alph*)]
\item Find the value of $F$.
\item Find the steady speed that the cyclist could maintain up the hill when working at this power. [2]
\end{enumerate}
\hfill \mbox{\textit{CAIE M1 2022 Q4 [6]}}