CAIE M1 2012 June — Question 6

Exam BoardCAIE
ModuleM1 (Mechanics 1)
Year2012
SessionJune
TopicMotion on a slope

6 \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{918b65cc-617d-4942-8d96-b02eef21e417-3_156_558_1592_450} \captionsetup{labelformat=empty} \caption{Fig. 1}
\end{figure} \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{918b65cc-617d-4942-8d96-b02eef21e417-3_138_559_1612_1137} \captionsetup{labelformat=empty} \caption{Fig. 2}
\end{figure} A block of weight 6.1 N is at rest on a plane inclined at angle \(\alpha\) to the horizontal, where \(\tan \alpha = \frac { 11 } { 60 }\). The coefficient of friction between the block and the plane is \(\mu\). A force of magnitude 5.9 N acting parallel to a line of greatest slope is applied to the block.
  1. When the force acts up the plane (see Fig. 1) the block remains at rest. Show that \(\mu \geqslant \frac { 4 } { 5 }\).
  2. When the force acts down the plane (see Fig. 2) the block slides downwards. Show that \(\mu < \frac { 7 } { 6 }\).
  3. Given that the acceleration of the block is \(1.7 \mathrm {~m} \mathrm {~s} ^ { - 2 }\) when the force acts down the plane, find the value of \(\mu\).