A particle of mass m m\,m kg rests on a rough plane inclined at an angle of 30° 30°\,30° to the horizontal. The particle is on the point of sliding down the plane.
Show that the coefficient of friction between the particle and the plane is 33\displaystyle \frac{\sqrt{3}}{3}33.
A force of magnitude P P\,P newtons is now applied to the particle up a line of greatest slope. Find, in terms of m m\,m and ggg, the set of values of P P\,P for which the particle remains at rest.