Question

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

Answer 1

maximum force F such that block does not move is 20N

see figure, A force F is applied on object at an angle 60°. surface is rough, so friction will oppose relative motion between object and surface.

now, Fx = Fcos60° , Fy = Fsin60°

at vertical equilibrium,

N = Fsin60° + mg

now friction, fr = μN

= μ(Fsin60° + mg)

at horizontal equilibrium,

Fcos60° = μ(Fsin60° + mg)

⇒F = μmg/(cos60° - μsin60°)

putting values of all terms we get,

F ={ (1/2√3) × √3 × 10}/(1/2 - 1/2√3 × √3/2)

= 5/(1/2 - 1/4)

= 5/(1/4)

= 20 N