| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Forces, equilibrium and resultants |
| Type | Particle suspended by strings |
| Difficulty | Moderate -0.3 This is a standard M1 equilibrium problem with straightforward resolution of forces. Part (a) requires basic trigonometry and symmetry to find tension from vertical equilibrium. Part (b) involves recognizing that one string becomes slack when its tension reaches zero, then resolving horizontally and vertically—a common textbook exercise requiring no novel insight, making it slightly easier than average. |
| Spec | 3.03m Equilibrium: sum of resolved forces = 03.03n Equilibrium in 2D: particle under forces |
| Answer | Marks | Guidance |
|---|---|---|
| (a) \(0.8g = 27 \sin 30°\) | \(T = 0.8g = 7.84 \text{ N}\) | B1 M1 A1 |
| (b) \(F = T \cos 30°\), \(0.8g = T \sin 30°\) | \(F = 0.8g\sqrt{3} = 13.6 \text{ N}\) | B1 B1 M1 A1 |
(a) $0.8g = 27 \sin 30°$ | $T = 0.8g = 7.84 \text{ N}$ | B1 M1 A1
(b) $F = T \cos 30°$, $0.8g = T \sin 30°$ | $F = 0.8g\sqrt{3} = 13.6 \text{ N}$ | B1 B1 M1 A1 | **7 marks**A small ball $B$, of mass 0.8 kg, is suspended from a horizontal ceiling by two light inextensible strings. $B$ is in equilibrium under gravity with both strings inclined at 30° to the horizontal, as shown.
\includegraphics{figure_2}
\begin{enumerate}[label=(\alph*)]
\item Find the tension, in N, in either string. [3 marks]
\item Calculate the magnitude of the least horizontal force that must be applied to $B$ in this position to cause one string to become slack. [4 marks]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 Q2 [7]}}