Revisiting the Least Force Required to Keep a Block from Sliding

Abstract

This article pertains to a problem on static friction that concerns a block of mass M resting on a rough inclined plane. The coefficient of static friction is μs and the inclination angle θ is greater than tan−1 μs. This means that some force F must be applied (see Fig. 1)1 to keep the block from sliding down the incline. Familiar textbook versions of this problem ask for the minimum value of F when it is applied in a certain specified direction, for example, parallel to the incline (φ= 0 in Fig. 1) or perpendicular to the incline (φ= 90°). Here, we generalize the problem by allowing the direction of the force to be adjustable and asking what the absolute minimum value of F is in order to keep the block from sliding.