| Exam Board | CAIE |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2022 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Work done and energy |
| Type | Power from force and speed |
| Difficulty | Moderate -0.3 This is a standard mechanics question testing routine application of Newton's second law (part a), kinetic energy formula (part b), and work-energy principle (part c). All parts follow textbook methods with straightforward calculations requiring no novel insight, making it slightly easier than average for A-level mechanics. |
| Spec | 6.02d Mechanical energy: KE and PE concepts6.02i Conservation of energy: mechanical energy principle6.02l Power and velocity: P = Fv |
| Answer | Marks | Guidance |
|---|---|---|
| \(F - 30 = 70 \times 0.3\) | M1 | Use of Newton's Second Law |
| \(P = 4F\) | B1 | Using \(P = Fv\) |
| \([= 51 \times 4] = 204 \text{ W}\) | A1 |
| Answer | Marks |
|---|---|
| \(\text{Change in KE} = \dfrac{1}{2} \times 70 \times 12^2 - \dfrac{1}{2} \times 70 \times 6^2\) | M1 |
| \(3780 \text{ J}\) | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| For work energy equation | M1 | |
| \(70g \times d\sin 5 - 30d = 3780\) | A1 FT | FT change in kinetic energy from (b) |
| \(d = 122\) | A1 |
## Question 5:
### Part (a):
$F - 30 = 70 \times 0.3$ | M1 | Use of Newton's Second Law
$P = 4F$ | B1 | Using $P = Fv$
$[= 51 \times 4] = 204 \text{ W}$ | A1 |
### Part (b):
$\text{Change in KE} = \dfrac{1}{2} \times 70 \times 12^2 - \dfrac{1}{2} \times 70 \times 6^2$ | M1 |
$3780 \text{ J}$ | A1 |
### Part (c):
For work energy equation | M1 |
$70g \times d\sin 5 - 30d = 3780$ | A1 FT | FT change in kinetic energy from (b)
$d = 122$ | A1 |
---5 A cyclist is riding along a straight horizontal road. The total mass of the cyclist and her bicycle is 70 kg . At an instant when the cyclist's speed is $4 \mathrm {~m} \mathrm {~s} ^ { - 1 }$, her acceleration is $0.3 \mathrm {~m} \mathrm {~s} ^ { - 2 }$. There is a constant resistance to motion of magnitude 30 N .
\begin{enumerate}[label=(\alph*)]
\item Find the power developed by the cyclist.\\
The cyclist comes to the top of a hill inclined at $5 ^ { \circ }$ to the horizontal. The cyclist stops pedalling and freewheels down the hill (so that the cyclist is no longer supplying any power). The magnitude of the resistance force remains at 30 N . Over a distance of $d \mathrm {~m}$, the speed of the cyclist increases from $6 \mathrm {~ms} ^ { - 1 }$ to $12 \mathrm {~ms} ^ { - 1 }$.
\item Find the change in kinetic energy.
\item Use an energy method to find $d$.\\
\includegraphics[max width=\textwidth, alt={}, center]{4e555003-16f1-4453-ab25-c50929d4b5b3-10_725_785_260_680}
Two particles $P$ and $Q$, of masses 0.3 kg and 0.2 kg respectively, are attached to the ends of a light inextensible string. The string passes over a fixed smooth pulley at $B$ which is attached to two inclined planes. $P$ lies on a smooth plane $A B$ which is inclined at $60 ^ { \circ }$ to the horizontal. $Q$ lies on a plane $B C$ which is inclined at $30 ^ { \circ }$ to the horizontal. The string is taut and the particles can move on lines of greatest slope of the two planes (see diagram).
\end{enumerate}
\hfill \mbox{\textit{CAIE M1 2022 Q5 [8]}}