| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2007 |
| 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 two-force equilibrium problem requiring resolution of forces in two perpendicular directions. Students apply standard methods (resolve horizontally and vertically) with a simple angle (30°) and given weight. The calculations involve basic trigonometry and simultaneous equations that are immediately solvable. This is easier than average as it's a textbook application of equilibrium with no problem-solving insight required. |
| Spec | 3.03a Force: vector nature and diagrams3.03b Newton's first law: equilibrium3.03m Equilibrium: sum of resolved forces = 03.03n Equilibrium in 2D: particle under forces |
| Answer | Marks | Guidance |
|---|---|---|
| (a) \(P \sin 30° = 24\) → \(P = 48\) | M1 A1 | 3 marks |
| (b) \(Q = P \cos 30°\) → \(≈ 41.6\) | M1 A1 | 3 marks |
**(a)** $P \sin 30° = 24$ → $P = 48$ | M1 A1 | 3 marks
**(b)** $Q = P \cos 30°$ → $≈ 41.6$ | M1 A1 | 3 marks | accept $24\sqrt{3}$, awrt 42 | 6 marks total
---\includegraphics{figure_1}
A particle of weight 24 N is held in equilibrium by two light inextensible strings. One string is horizontal. The other string is inclined at an angle of 30° to the horizontal, as shown in Figure 1. The tension in the horizontal string is $Q$ newtons and the tension in the other string is $P$ newtons. Find
\begin{enumerate}[label=(\alph*)]
\item the value of $P$, [3]
\item the value of $Q$. [3]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 2007 Q1 [6]}}