| Exam Board | CAIE |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2021 |
| Session | June |
| Marks | 5 |
| 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 straightforward two-part mechanics question requiring standard application of P=Fv and F=ma on horizontal ground, then resolving forces on an incline at constant speed. All steps are routine M1 techniques with no novel problem-solving required, making it slightly easier than average. |
| Spec | 6.02l Power and velocity: P = Fv6.02m Variable force power: using scalar product |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Forward force exerted by cyclist \(= \frac{150}{4}\ \text{N}\ [= 37.5\ \text{N}]\) | B1 | OE. \(P = Fv\) used correctly |
| \(\frac{150}{4} - 20 = m \times 0.25\) | M1 | Use of Newton's second law |
| \(m = 70\ \text{kg}\) | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(150/3 - 20 - 70g\sin\theta = 0\) | M1 | For resolving up the plane |
| \(\theta = 2.5°\) to 1 d.p. | A1 FT | From \(2.456\ldots\); FT \(\theta = \sin^{-1}\!\left(\dfrac{3}{m}\right)\) from (a) |
**Question 2(a):**
| Answer | Marks | Guidance |
|--------|-------|----------|
| Forward force exerted by cyclist $= \frac{150}{4}\ \text{N}\ [= 37.5\ \text{N}]$ | B1 | OE. $P = Fv$ used correctly |
| $\frac{150}{4} - 20 = m \times 0.25$ | M1 | Use of Newton's second law |
| $m = 70\ \text{kg}$ | A1 | |
---
**Question 2(b):**
| Answer | Marks | Guidance |
|--------|-------|----------|
| $150/3 - 20 - 70g\sin\theta = 0$ | M1 | For resolving up the plane |
| $\theta = 2.5°$ to 1 d.p. | A1 FT | From $2.456\ldots$; FT $\theta = \sin^{-1}\!\left(\dfrac{3}{m}\right)$ from **(a)** |2 A cyclist is travelling along a straight horizontal road. She is working at a constant rate of 150 W . At an instant when her speed is $4 \mathrm {~m} \mathrm {~s} ^ { - 1 }$, her acceleration is $0.25 \mathrm {~m} \mathrm {~s} ^ { - 2 }$. The resistance to motion is 20 N .
\begin{enumerate}[label=(\alph*)]
\item Find the total mass of the cyclist and her bicycle.\\
The cyclist comes to a straight hill inclined at an angle $\theta$ above the horizontal. She ascends the hill at constant speed $3 \mathrm {~m} \mathrm {~s} ^ { - 1 }$. She continues to work at the same rate as before and the resistance force is unchanged.
\item Find the value of $\theta$.
\end{enumerate}
\hfill \mbox{\textit{CAIE M1 2021 Q2 [5]}}