OCR M1 2005 January — Question 3 9 marks

Exam BoardOCR
ModuleM1 (Mechanics 1)
Year2005
SessionJanuary
Marks9
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicForces, equilibrium and resultants
TypeResultant of coplanar forces
DifficultyModerate -0.8 This is a straightforward mechanics question requiring resolution of forces into components using basic trigonometry, followed by finding magnitude and direction of the resultant. It's a standard textbook exercise with clear diagram and routine method, making it easier than average for A-level, though not trivial since it requires careful angle work and Pythagoras/tan calculations.
Spec3.03p Resultant forces: using vectors

3 \includegraphics[max width=\textwidth, alt={}, center]{5b10afa1-1c45-4370-a0e6-ad8fd626df9a-3_638_839_269_653} Three coplanar forces of magnitudes \(5 \mathrm {~N} , 8 \mathrm {~N}\) and 8 N act at the origin \(O\) of rectangular coordinate axes. The directions of the forces are as shown in the diagram.
  1. Find the component of the resultant of the three forces in
    1. the \(x\)-direction,
    2. the \(y\)-direction.
    3. Find the magnitude and direction of the resultant.

3\\
\includegraphics[max width=\textwidth, alt={}, center]{5b10afa1-1c45-4370-a0e6-ad8fd626df9a-3_638_839_269_653}

Three coplanar forces of magnitudes $5 \mathrm {~N} , 8 \mathrm {~N}$ and 8 N act at the origin $O$ of rectangular coordinate axes. The directions of the forces are as shown in the diagram.\\
(i) Find the component of the resultant of the three forces in
\begin{enumerate}[label=(\alph*)]
\item the $x$-direction,
\item the $y$-direction.\\
(ii) Find the magnitude and direction of the resultant.
\end{enumerate}

\hfill \mbox{\textit{OCR M1 2005 Q3 [9]}}