What is the maximum value of the force F such that the block shown in the arrangement, does not move?

Step-by-step solution

The forces acting on the block are shown. Since the block is not moving forward for the maximum force F applied, therefore F cos 60 ° = f = μ N …(i) (Horizontal Direction) and F sin 60 ° + m g = N …(ii) From (i) and (ii) F cos 60 ° = μ [ F sin 60 ° + m g ] ⇒         F = μ m g cos 60 ° − μ sin 60 ° = 1 2 3 × 3 × 10 1 2 − 1 2 3 × 3 2 = 5 1 4 = 20   N