Repose

Repose, Angle of. If a mass be placed upon a board and the latter be tilted up until the mass is just on the point of sliding, the angle which the board makes with the horizontal is called the angle of repose. In this case there is equilibrium between the weight, w, of the mass acting vertically downward, F, the friction, acting along the board, and R, the resistance of the board, acting normally. By resolving these forces along the plane and perpendicular to it we get (1) F - w sin d

(2) R=: W cos 6. Hence - = tan 8. The ratio r is the coefficient of friction; hence the angle of repose may be denned as that angle whose tangent is the coefficient of friction. It is sometimes known as the angle of friction.