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.

1.
Halliday
,
Resnick
, and
Walker
,
Fundamentals of Physics
, 8th ed. (
Wiley
,
2008
), p.
132
, Prob. 20(a).
2.
Serway
and
Vuille
,
College Physics
, 9th ed. (
Brooks/Cole
,
2011
), p.
119
, Prob. 47.
3.
See, for example,
Herbert Bristol
White
,
Tables of Integrals and Other Mathematical Data
, 4th ed. (
MacMillan Co.
,
1961
), p.
79
.
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