| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2013 |
| Session | January |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Forces, equilibrium and resultants |
| Type | Particle with string at angle to wall |
| Difficulty | Moderate -0.3 This is a standard two-force equilibrium problem requiring resolution of forces in two perpendicular directions and solving simultaneous equations. While it involves multiple steps (resolving horizontally and vertically, handling the geometry of angles), it follows a completely routine method taught in M1 with no conceptual surprises—slightly easier than average due to its textbook nature. |
| Spec | 3.03e Resolve forces: two dimensions3.03m Equilibrium: sum of resolved forces = 0 |
| Answer | Marks | Guidance |
|---|---|---|
| \((\uparrow)\), \(T \cos 30 + F \cos 60 = 2g\) | M1 A1 | |
| \((\rightarrow)\), \(T \cos 60 - F \cos 30 = 0\) | M1 A1 | |
| \(F = g = 9.8\) | M1 A1 | |
| \(T = \sqrt{3}g = 17\) or \(17.0\) | M1 A1 | (8) |
| Answer | Marks | Guidance |
|---|---|---|
| \((\uparrow)\), \(F = 2g \cos 60\) | M1 A1 | |
| \((\rightarrow)\), \(T = 2g \cos 30\) | M1 A1 | |
| \(F = g = 9.8\) | M1 A1 | |
| \(T = \sqrt{3}g = 17\) or \(17.0\) | M1 A1 | (8) |
$(\uparrow)$, $T \cos 30 + F \cos 60 = 2g$ | M1 A1 |
$(\rightarrow)$, $T \cos 60 - F \cos 30 = 0$ | M1 A1 |
$F = g = 9.8$ | M1 A1 |
$T = \sqrt{3}g = 17$ or $17.0$ | M1 A1 | (8)
**OR:**
$(\uparrow)$, $F = 2g \cos 60$ | M1 A1 |
$(\rightarrow)$, $T = 2g \cos 30$ | M1 A1 |
$F = g = 9.8$ | M1 A1 |
$T = \sqrt{3}g = 17$ or $17.0$ | M1 A1 | (8)
**Total for Question 3: 8**
---A particle $P$ of mass 2 kg is attached to one end of a light string, the other end of which is attached to a fixed point $O$. The particle is held in equilibrium, with $OP$ at $30°$ to the downward vertical, by a force of magnitude $F$ newtons. The force acts in the same vertical plane as the string and acts at an angle of $30°$ to the horizontal, as shown in Figure 3.
\includegraphics{figure_3}
Find
\begin{enumerate}[label=(\roman*)]
\item the value of $F$,
\item the tension in the string. [8]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 2013 Q3 [8]}}