OCR M1 2010 June — Question 7

Exam BoardOCR
ModuleM1 (Mechanics 1)
Year2010
SessionJune
TopicFriction

7 \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{4b703cf9-b3d3-4210-b57b-89136595f8a5-04_305_748_260_699} \captionsetup{labelformat=empty} \caption{Fig. 1}
\end{figure} A rectangular block \(B\) of weight 12 N lies in limiting equilibrium on a horizontal surface. A horizontal force of 4 N and a coplanar force of 5 N inclined at \(60 ^ { \circ }\) to the vertical act on \(B\) (see Fig. 1).
  1. Find the coefficient of friction between \(B\) and the surface. \begin{figure}[h]
    \includegraphics[alt={},max width=\textwidth]{4b703cf9-b3d3-4210-b57b-89136595f8a5-04_307_751_1000_696} \captionsetup{labelformat=empty} \caption{Fig. 2}
    \end{figure} \(B\) is now cut horizontally into two smaller blocks. The upper block has weight 9 N and the lower block has weight 3 N . The 5 N force now acts on the upper block and the 4 N force now acts on the lower block (see Fig. 2). The coefficient of friction between the two blocks is \(\mu\).
  2. Given that the upper block is in limiting equilibrium, find \(\mu\).
  3. Given instead that \(\mu = 0.1\), find the accelerations of the two blocks.