An example to illustrate the angle of friction

Leaving Certificate 1999 Higher Level. Question 7 (a)
A particle of weight W rests on a rough plane inclined at 26 to the horizontal.
P is the least force, acting up along the plane needed to move the particle up the plane. Prove that if P is less than W then the angle of friction is less than 32 .

Suggested solution

On the point of motion P = Wsin26 + m Wcos26 < W

sin26 + m cos26 < 1

m cos26 < 1- sin26

m <

tan l <

l <

l < 32