(a)[5]
Show that it follows that $\mu = \frac{5\tan\theta - 1}{5 + \tan\theta}$.
(b)[2]
Hence find the values that $\theta$ may take.
Mathematics 9709 · AS & A Level · Forces and equilibrium
Forces and equilibrium — practice question
A particle $P$ has mass $6$ kg and is resting on a rough plane that makes an acute angle $\theta$ with the horizontal. A horizontal force of magnitude $12$ N acts on $P$ as shown in the diagram. The line of action of this horizontal force is in a vertical plane containing the line of greatest slope of the plane through $P$. The coefficient of friction between $P$ and the plane is $\mu$. $P$ is in equilibrium and is just about to slide down the plane.