| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Forces, equilibrium and resultants |
| Type | Particle suspended by strings |
| Difficulty | Standard +0.3 This is a standard M1 equilibrium problem requiring resolution of forces in two directions and basic trigonometry. While it involves two unknowns (angle and tension) and requires systematic application of equilibrium conditions, the method is routine for this topic with no novel insight needed. The given relationship between tensions simplifies the algebra considerably. |
| Spec | 1.05j Trigonometric identities: tan=sin/cos and sin^2+cos^2=11.05l Double angle formulae: and compound angle formulae3.03e Resolve forces: two dimensions3.03n Equilibrium in 2D: particle under forces |
\includegraphics{figure_1}
A particle has mass $2$ kg. It is attached at $B$ to the ends of two light inextensible strings $AB$ and $BC$. When the particle hangs in equilibrium, $AB$ makes an angle of $30°$ with the vertical, as shown in Fig. 1. The magnitude of the tension in $BC$ is twice the magnitude of the tension in $AB$.
\begin{enumerate}[label=(\alph*)]
\item Find, in degrees to one decimal place, the size of the angle that $BC$ makes with the vertical. [4]
\item Hence find, to 3 significant figures, the magnitude of the tension in $AB$. [4]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 Q2 [8]}}