| Exam Board | CAIE |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2022 |
| Session | November |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Work done and energy |
| Type | Constant speed up/down incline |
| Difficulty | Moderate -0.3 This is a straightforward mechanics problem requiring standard formulas: distance = speed × time, change in PE = mgh (with h = d sin 20°), and work = force × distance. The constant speed simplifies the force calculation (pulling force = friction + component of weight down slope). All steps are routine applications of M1 content with no conceptual challenges. |
| Spec | 6.02a Work done: concept and definition6.02e Calculate KE and PE: using formulae |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(PE = 5g \times 15 \times 1.8\sin20\) | M1 | Attempt to find PE gain. |
| \(PE = 462\text{ J}\) | A1 | From \(461.727\ldots\) |
| Total: 2 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(WD = 5g \times 15 \times 1.8\sin20 + 40 \times 15 \times 1.8\) or \(WD = (5g\sin20 + 40) \times 15 \times 1.8\) | M1 | Uses WD by pulling force \(=\) PE gain \(+\) WD against friction or \(WD = Fs\). |
| \(WD = 1540\text{ J}\) | A1 FT | From \(1541.727\ldots\) FT '\(1080 +\) PE from (a)'. |
| Total: 2 |
## Question 2:
**Part (a)**
| Answer | Marks | Guidance |
|--------|-------|----------|
| $PE = 5g \times 15 \times 1.8\sin20$ | **M1** | Attempt to find PE gain. |
| $PE = 462\text{ J}$ | **A1** | From $461.727\ldots$ |
| | **Total: 2** | |
**Part (b)**
| Answer | Marks | Guidance |
|--------|-------|----------|
| $WD = 5g \times 15 \times 1.8\sin20 + 40 \times 15 \times 1.8$ **or** $WD = (5g\sin20 + 40) \times 15 \times 1.8$ | **M1** | Uses WD by pulling force $=$ PE gain $+$ WD against friction or $WD = Fs$. |
| $WD = 1540\text{ J}$ | **A1 FT** | From $1541.727\ldots$ FT '$1080 +$ PE from **(a)**'. |
| | **Total: 2** | |2 A box of mass 5 kg is pulled at a constant speed of $1.8 \mathrm {~ms} ^ { - 1 }$ for 15 s up a rough plane inclined at an angle of $20 ^ { \circ }$ to the horizontal. The box moves along a line of greatest slope against a frictional force of 40 N . The force pulling the box is parallel to the line of greatest slope.
\begin{enumerate}[label=(\alph*)]
\item Find the change in gravitational potential energy of the box.
\item Find the work done by the pulling force.
\end{enumerate}
\hfill \mbox{\textit{CAIE M1 2022 Q2 [4]}}