| Exam Board | AQA |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2008 |
| Session | January |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Forces, equilibrium and resultants |
| Type | Particle suspended by strings |
| Difficulty | Moderate -0.8 This is a straightforward equilibrium problem requiring resolution of forces in two directions with a simple geometry (30° angle). The question guides students through drawing a force diagram and provides the answer to verify in part (b), making it easier than average. Standard M1 content with routine application of Newton's first law and basic trigonometry. |
| Spec | 3.03e Resolve forces: two dimensions3.03m Equilibrium: sum of resolved forces = 0 |
| Answer | Marks | Guidance |
|---|---|---|
| Diagram with three forces, labels and arrow heads. Different variables must be used for each tension. | B1 (Total: 1) | Diagram with three forces, labels and arrow heads. Different variables must be used for each tension. |
| Answer | Marks | Guidance |
|---|---|---|
| \(T_1 \sin 30° = 4 \times 9.8\) → \(T_1 = \frac{4 \times 9.8}{\sin 30°} = 78.4 \text{ N}\) | M1, A1, A1 (Total: 3) | Two term equation from resolving vertically. Must see a \(\sin\) or \(\cos\) term for M1. Correct equation. Correct tension form correct working. |
| Answer | Marks | Guidance |
|---|---|---|
| \(T_2 = 78.4 \cos 30° = 67.9 \text{ N}\) | M1, A1 (Total: 2) | Two term equation from resolving horizontally. Correct tension. |
### Part (a)
Diagram with three forces, labels and arrow heads. Different variables must be used for each tension. | B1 (Total: 1) | Diagram with three forces, labels and arrow heads. Different variables must be used for each tension.
### Part (b)
$T_1 \sin 30° = 4 \times 9.8$ → $T_1 = \frac{4 \times 9.8}{\sin 30°} = 78.4 \text{ N}$ | M1, A1, A1 (Total: 3) | Two term equation from resolving vertically. Must see a $\sin$ or $\cos$ term for M1. Correct equation. Correct tension form correct working.
### Part (c)
$T_2 = 78.4 \cos 30° = 67.9 \text{ N}$ | M1, A1 (Total: 2) | Two term equation from resolving horizontally. Correct tension.
---3 A particle, of mass 4 kg , is suspended in equilibrium by two light strings, $A P$ and $B P$. The string $A P$ makes an angle of $30 ^ { \circ }$ to the horizontal and the other string, $B P$, is horizontal, as shown in the diagram.\\
\includegraphics[max width=\textwidth, alt={}, center]{217f0e3e-9d1b-41f1-8299-f56d073fbbeb-2_231_757_1841_639}
\begin{enumerate}[label=(\alph*)]
\item Draw and label a diagram to show the forces acting on the particle.
\item Show that the tension in the string $A P$ is 78.4 N .
\item Find the tension in the horizontal string $B P$.
\end{enumerate}
\hfill \mbox{\textit{AQA M1 2008 Q3 [6]}}