Exam-Style Problem
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Nov 2017 p42 q6
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Two particles P and Q, each of mass m kg, are attached to the ends of a light inextensible string. The string passes over a fixed smooth pulley which is attached to the edge of a rough plane. The plane is inclined at an angle α to the horizontal, where \(\tan \alpha = \frac{7}{24}\). Particle P rests on the plane and particle Q hangs vertically, as shown in the diagram. The string between P and the pulley is parallel to a line of greatest slope of the plane. The system is in limiting equilibrium.
- Show that the coefficient of friction between P and the plane is \(\frac{4}{3}\).
- A force of magnitude 10N is applied to P, acting up a line of greatest slope of the plane, and P accelerates at \(2.5 \, \text{m/s}^2\). Find the value of m.
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