Edexcel M1 2003 January — Question 2 6 marks

Exam BoardEdexcel
ModuleM1 (Mechanics 1)
Year2003
SessionJanuary
Marks6
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicForces, equilibrium and resultants
TypeEquilibrium of particle under coplanar forces
DifficultyModerate -0.3 This is a standard M1 equilibrium problem requiring resolution of forces in two perpendicular directions and basic trigonometry. While it involves multiple steps (resolving horizontally and vertically, then solving simultaneous equations), the method is routine and well-practiced. It's slightly easier than average because the setup is straightforward with clear perpendicular axes and standard force magnitudes.
Spec3.03e Resolve forces: two dimensions3.03m Equilibrium: sum of resolved forces = 0

\includegraphics{figure_1} In Fig. 1, \(\angle AOC = 90°\) and \(\angle BOC = \theta°\). A particle at \(O\) is in equilibrium under the action of three coplanar forces. The three forces have magnitude 8 N, 12 N and \(X\) N and act along \(OA\), \(OB\) and \(OC\) respectively. Calculate
  1. the value, to one decimal place, of \(\theta\), [3]
  2. the value, to 2 decimal places, of \(X\). [3]

\includegraphics{figure_1}

In Fig. 1, $\angle AOC = 90°$ and $\angle BOC = \theta°$. A particle at $O$ is in equilibrium under the action of three coplanar forces. The three forces have magnitude 8 N, 12 N and $X$ N and act along $OA$, $OB$ and $OC$ respectively. Calculate

\begin{enumerate}[label=(\alph*)]
\item the value, to one decimal place, of $\theta$, [3]
\item the value, to 2 decimal places, of $X$. [3]
\end{enumerate}

\hfill \mbox{\textit{Edexcel M1 2003 Q2 [6]}}