OCR MEI M1 2011 January — Question 2 6 marks

Exam BoardOCR MEI
ModuleM1 (Mechanics 1)
Year2011
SessionJanuary
Marks6
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicVectors Introduction & 2D
TypeResultant of three coplanar forces
DifficultyModerate -0.8 This is a straightforward M1 mechanics question requiring basic resolution of forces into components using trigonometry, then finding magnitude and direction of the resultant. It's routine application of standard techniques with no problem-solving insight needed, making it easier than average but not trivial since it requires careful trigonometric work.
Spec3.03e Resolve forces: two dimensions3.03p Resultant forces: using vectors

2 Fig. 2 shows two forces acting at A. The figure also shows the perpendicular unit vectors \(\mathbf { i }\) and \(\mathbf { j }\) which are respectively horizontal and vertically upwards. The resultant of the two forces is \(\mathbf { F } \mathbf { N }\). \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{e36ef805-beff-4125-b332-439ccb0d91c4-3_264_922_479_609} \captionsetup{labelformat=empty} \caption{Fig. 2}
\end{figure}
  1. Find \(\mathbf { F }\) in terms of \(\mathbf { i }\) and \(\mathbf { j }\), giving your answer correct to three significant figures.
  2. Calculate the magnitude of \(\mathbf { F }\) and the angle that \(\mathbf { F }\) makes with the upward vertical.

2 Fig. 2 shows two forces acting at A. The figure also shows the perpendicular unit vectors $\mathbf { i }$ and $\mathbf { j }$ which are respectively horizontal and vertically upwards.

The resultant of the two forces is $\mathbf { F } \mathbf { N }$.

\begin{figure}[h]
\begin{center}
  \includegraphics[alt={},max width=\textwidth]{e36ef805-beff-4125-b332-439ccb0d91c4-3_264_922_479_609}
\captionsetup{labelformat=empty}
\caption{Fig. 2}
\end{center}
\end{figure}

(i) Find $\mathbf { F }$ in terms of $\mathbf { i }$ and $\mathbf { j }$, giving your answer correct to three significant figures.\\
(ii) Calculate the magnitude of $\mathbf { F }$ and the angle that $\mathbf { F }$ makes with the upward vertical.

\hfill \mbox{\textit{OCR MEI M1 2011 Q2 [6]}}