Exam-Style Problem
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June 2012 p43 q6
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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.
(i) When the force acts up the plane (see Fig. 1) the block remains at rest. Show that \(\mu \geq \frac{4}{5}\).
(ii) When the force acts down the plane (see Fig. 2) the block slides downwards. Show that \(\mu < \frac{7}{6}\).
(iii) Given that the acceleration of the block is 1.7 m s\(^{-2}\) when the force acts down the plane, find the value of \(\mu\).
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