Force required to start the roller:

A roller shown in the figure given below is of mass 150Kg. What force T is required to start the roller over block A?

Sol.: Let R be reaction given by block to the roller, and is to act at point A subtends an angle of ? as shown in the figure given below,

For finding angle θ  ,

Sin θ  = 75/175 = 0.428

= 25.37°

Apply lami's theorem at 'A', as the body is in equilibrium

T/sin(90° + 25.37°) = 150 × g/ sin(64.63° + 65°)

T = [150 × g × sin(90° + 25.37°)]/ sin(64.63° + 65°)

T = 1726.33N