A heavy uniform cylindrical drum is placed, with its axis horizontal, on a slope inclined at an angle α
to the horizontal. It is prevented from sliding or rolling down the slope by a triangular wedge. The weight of the wedge is negligible compared with the weight of the drum. The angle at the point of wedge is β, and the coefficient of friction between the wedge and the slope is μ, where μ>tan(α). Show that, however smooth the surface of the drum, the wedge will keep it in equilibrium provided that β is between α and arctan(μ).
2. Relevant equation.
Force of friction <= coefficient of friction * magnitude of normal contact force
Moment of a force=force * perpendicular distance to pivot
The Attempt at a Solution
Resolving along and perpendicular to the plane of the slope and taking moments about the center of mass of the drum gives equations involving: the weight of the drum; the contact forces between the wedge and the drum and between the wedge and the slope; and the angles α and β. However I cannot find a way to manipulate them in order to derive the required inequality.