| Exam Board | CAIE |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2004 |
| Session | November |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Motion on a slope |
| Type | Equilibrium on slope with horizontal force |
| Difficulty | Moderate -0.8 This is a straightforward M1 equilibrium problem requiring resolution of forces in two standard configurations. Students apply basic trigonometry and force resolution (parallel/perpendicular to plane) with no friction complications due to the smooth surface. The two-part structure and standard setup make it easier than average, though it requires careful component resolution in part (ii). |
| Spec | 3.03e Resolve forces: two dimensions3.03n Equilibrium in 2D: particle under forces |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(P = 18\cos60°\) or \(\sin30° = \frac{P}{18}\) | M1 | For resolving forces parallel to the plane or for trigonometry in the correct triangle of forces |
| \(P = 9\) | A1 | Total: 2 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| M1 | For resolving forces parallel to the plane or trigonometry in correct triangle of forces, or resolving both vertically and horizontally | |
| \(P\cos30° = 18\cos60°\) | A1 | |
| \(\tan30° = \frac{P}{18}\) | A1 | |
| \(18 = R\cos30°\) and \(P = R\sin30°\) | A1 | |
| \(P = 10.4\) (accept \(6\sqrt{3}\)) | A1 | Total: 3 |
## Question 2:
### Part (i):
| Answer/Working | Mark | Guidance |
|---|---|---|
| $P = 18\cos60°$ or $\sin30° = \frac{P}{18}$ | M1 | For resolving forces parallel to the plane or for trigonometry in the correct triangle of forces |
| $P = 9$ | A1 | **Total: 2** |
### Part (ii):
| Answer/Working | Mark | Guidance |
|---|---|---|
| | M1 | For resolving forces parallel to the plane or trigonometry in correct triangle of forces, or resolving both vertically and horizontally |
| $P\cos30° = 18\cos60°$ | A1 | |
| $\tan30° = \frac{P}{18}$ | A1 | |
| $18 = R\cos30°$ and $P = R\sin30°$ | A1 | |
| $P = 10.4$ (accept $6\sqrt{3}$) | A1 | **Total: 3** |
**SR** for candidates who mix sin/cos or have tan upside down: max 3/5
M marks as scheme M1 M1; Both $P = 15.6$ in **(i)** and $P = 31.2$ in **(ii)** — A1
**SR** for candidates who use $W = 18g$: max 3/5
Allow M marks with $g$ present — M1 M1; Both $P = 90$ in **(i)** and $P = 104$ in **(ii)** — A12
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{38ece0f6-1c29-4e7a-9d66-16c3e2b695f9-2_229_382_852_589}
\captionsetup{labelformat=empty}
\caption{Fig. 1}
\end{center}
\end{figure}
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{38ece0f6-1c29-4e7a-9d66-16c3e2b695f9-2_222_383_854_1178}
\captionsetup{labelformat=empty}
\caption{Fig. 2}
\end{center}
\end{figure}
A small block of weight 18 N is held at rest on a smooth plane inclined at $30 ^ { \circ }$ to the horizontal, by a force of magnitude $P$ N. Find\\
(i) the value of $P$ when the force is parallel to the plane, as in Fig. 1,\\
(ii) the value of $P$ when the force is horizontal, as in Fig. 2.
\hfill \mbox{\textit{CAIE M1 2004 Q2 [5]}}