A block of mass ` 4 kg` is pushed against a rough vertical wall with a force `80 N` is applied on the block in a direction parallel to the wall . Will the block move? If yes , what is acceleration of the block ?

Explanation

`N_(0) =80 N`
`(f_(s))_(max) = mu_(s) N = 0.5 xx 80 = 40 N`
`F : resultant force = sqrt((30)^(2) + (40)^(2)) = 50 N`
`tan theta = (30)/(40) = (3)/(4) rArr theta = 37^(@)`
The block will move when the resultant external force on it exceeds `(f_(s))_(max)`. When it moves , the direction of the force of friction will be opposite to the block's direction of motion
`a = (F - (f_(s))_(max))/(m) = ( 50 - 40)/(4) = 2.5 m//s^(2)`