6 A block of mass 5 kg is placed on a plane inclined at \(30 ^ { \circ }\) to the horizontal. The coefficient of friction between the block and the plane is \(\mu\).
- \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{fcc3d739-5c36-48ad-9c34-f69b28a06dba-10_424_709_392_760}
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\caption{Fig. 6.1}
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When a force of magnitude 40 N is applied to the block, acting up the plane parallel to a line of greatest slope, the block begins to slide up the plane (see Fig. 6.1).
Show that \(\mu < \frac { 1 } { 5 } \sqrt { 3 }\). - \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{fcc3d739-5c36-48ad-9c34-f69b28a06dba-11_422_727_264_749}
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\caption{Fig. 6.2}
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When a force of magnitude 40 N is applied horizontally, in a vertical plane containing a line of greatest slope, the block does not move (see Fig. 6.2).
Show that, correct to 3 decimal places, the least possible value of \(\mu\) is 0.152 .