| Exam Board | AQA |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2005 |
| Session | January |
| Marks | 7 |
| 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 perpendicular directions. With T₁ given, students simply resolve horizontally to find T₂, then vertically to find the spring force. It's a standard M1 exercise with clear setup and routine application of equilibrium conditions, making it easier than average. |
| Spec | 3.03m Equilibrium: sum of resolved forces = 03.03n Equilibrium in 2D: particle under forces |
| Answer | Marks | Guidance |
|---|---|---|
| \(200\sin30° = T\sin45°\) | M1, A1 | Resolving horizontally; Correct equation |
| \(T = \frac{200\sin30°}{\sin45°} = 141 \text{ N}\) | A1 (3) | AG; correct \(T\) from correct working |
| Answer | Marks | Guidance |
|---|---|---|
| \(200\cos30° + 141\cos45° + R = 500\times9.8\) | M1, A1, A1 | Resolving vertically with four terms; Correct values; Correct signs |
| \(R = 4630 \text{ N}\) | A1 (4) | Correct \(R\) |
## Question 5:
### Part (a)
$200\sin30° = T\sin45°$ | M1, A1 | Resolving horizontally; Correct equation
$T = \frac{200\sin30°}{\sin45°} = 141 \text{ N}$ | A1 (3) | AG; correct $T$ from correct working
### Part (b)
$200\cos30° + 141\cos45° + R = 500\times9.8$ | M1, A1, A1 | Resolving vertically with four terms; Correct values; Correct signs
$R = 4630 \text{ N}$ | A1 (4) | Correct $R$
---5 Two ropes are attached to a load of mass 500 kg . The ropes make angles of $30 ^ { \circ }$ and $45 ^ { \circ }$ to the vertical, as shown in the diagram. The tensions in these ropes are $T _ { 1 }$ and $T _ { 2 }$ newtons. The load is also supported by a vertical spring.\\
\includegraphics[max width=\textwidth, alt={}, center]{eb1f2470-aeeb-4b1d-a6c0-bdeb7048edd5-4_533_565_507_744}
The system is in equilibrium and $T _ { 1 } = 200$.
\begin{enumerate}[label=(\alph*)]
\item Show that $T _ { 2 } = 141$, correct to three significant figures.
\item Find the force that the spring exerts on the load.
\end{enumerate}
\hfill \mbox{\textit{AQA M1 2005 Q5 [7]}}