| Exam Board | CAIE |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2009 |
| Session | November |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Motion on a slope |
| Type | Equilibrium on slope with horizontal force |
| Difficulty | Moderate -0.3 This is a standard M1 equilibrium problem requiring resolution of forces in two straightforward scenarios. Part (i) involves simple component resolution parallel to the slope (P = 12sin40°), while part (ii) requires resolving horizontally and perpendicular to the slope to find P. Both are textbook exercises with clear diagrams and well-practiced techniques, making this slightly easier than average for A-level. |
| Spec | 3.03e Resolve forces: two dimensions3.03m Equilibrium: sum of resolved forces = 03.03n Equilibrium in 2D: particle under forces |
| Answer | Marks | Guidance |
|---|---|---|
| Part (i) | ||
| \([P = W\sin40°]\) | M1 | For resolving forces parallel to the plane or for a correct triangle of forces or for resolving horizontally and vertically |
| \(P = 7.71\) | A1 | 2 |
| Part (ii) | ||
| \([\cos40° = \frac{S}{\sin40°}]\) | M1 | |
| \(P = 10.1\) | A1 | 2 |
| **Part (i)** | | |
|---|---|---|
| $[P = W\sin40°]$ | M1 | For resolving forces parallel to the plane or for a correct triangle of forces or for resolving horizontally and vertically |
| $P = 7.71$ | A1 | 2 |
| **Part (ii)** | | |
|---|---|---|
| $[\cos40° = \frac{S}{\sin40°}]$ | M1 | |
| $P = 10.1$ | A1 | 2 |1
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{efa7175f-832b-4cd3-82ab-52e402115081-2_458_472_267_493}
\captionsetup{labelformat=empty}
\caption{Fig. 1}
\end{center}
\end{figure}
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{efa7175f-832b-4cd3-82ab-52e402115081-2_351_435_365_1217}
\captionsetup{labelformat=empty}
\caption{Fig. 2}
\end{center}
\end{figure}
A small block of weight 12 N is at rest on a smooth plane inclined at $40 ^ { \circ }$ to the horizontal. The block is held in equilibrium by a force of magnitude $P \mathrm {~N}$. Find the value of $P$ when\\
(i) the force is parallel to the plane as in Fig. 1,\\
(ii) the force is horizontal as in Fig. 2.
\hfill \mbox{\textit{CAIE M1 2009 Q1 [4]}}