| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Forces, equilibrium and resultants |
| Type | Particle with string at angle to wall |
| Difficulty | Easy -1.2 This is a straightforward statics problem requiring resolution of forces in two directions with a simple geometry (30° angle). Part (a) involves basic trigonometry and equilibrium equations, while part (b) is essentially given once (a) is solved. Significantly easier than average A-level questions as it's a standard M1 exercise with no problem-solving insight required. |
| Spec | 1.05g Exact trigonometric values: for standard angles3.03e Resolve forces: two dimensions3.03m Equilibrium: sum of resolved forces = 03.03n Equilibrium in 2D: particle under forces |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| Resolve \(\uparrow\): \(T\cos30 - W = 0\) | M1 | |
| \(\frac{\sqrt{3}}{2}T = 10 \therefore T = \frac{20\sqrt{3}}{3} = 11.5\) N (3sf) | M1 A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| Resolve \(\rightarrow\): \(H - T\sin30 = 0\) | M1 | |
| \(H = \frac{1}{2}T\) so \(T:H = 1:\frac{1}{2} = 2:1\) | M1 A1 | (6) |
## Question 1:
### Part (a)
| Answer/Working | Marks | Guidance |
|---|---|---|
| Resolve $\uparrow$: $T\cos30 - W = 0$ | M1 | |
| $\frac{\sqrt{3}}{2}T = 10 \therefore T = \frac{20\sqrt{3}}{3} = 11.5$ N (3sf) | M1 A1 | |
### Part (b)
| Answer/Working | Marks | Guidance |
|---|---|---|
| Resolve $\rightarrow$: $H - T\sin30 = 0$ | M1 | |
| $H = \frac{1}{2}T$ so $T:H = 1:\frac{1}{2} = 2:1$ | M1 A1 | **(6)** |
---1.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{6fb27fe5-055a-4701-bd80-e66ebd57292a-2_403_550_214_609}
\captionsetup{labelformat=empty}
\caption{Fig. 1}
\end{center}
\end{figure}
Figure 1 shows a light, inextensible string fixed at one end to a point $P$. The other end is attached to a small object of weight 10 N . The object is subjected to a horizontal force $H$ so that the string makes an angle of $30 ^ { \circ }$ with the vertical.
\begin{enumerate}[label=(\alph*)]
\item Find the magnitude of the tension in the string.
\item Show that the ratio of the magnitude of the tension to the magnitude of $H$ is $2 : 1$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 Q1 [6]}}