A block of mass `m` is supported on a rough wall by applying a force in figure Coefficient of static friction between block and wall is `mu`
For what range of value of `p` , the block remain in static equilibrium ?

Explanation

(a) If the block has tendency to move down , friction will act upwards
`rarr : N = F cos alpha`
`f = mu N = mu F cos alpha`
`uarr : F sin alpha + f = mg`
`F sin alpha + mu F cos alpha = mg`
`F_(min) = (mg)/(sin alpha + mu cos alpha)`
(b) If the block has tendency to move up , friction will act downwards
`uarr : F sin alpha = mg + f = mg + mu F cos alpha`
`F sin alpha - mu F cos alpha = mg`
`F_(max) = (mg)/(sin alpha - mu cos alpha)`
`F_(min) le F le F_(max)`