Magnitude and direction of force:

Determine magnitude and direction of smallest force P which is required to start the wheel over the block. As shown in the figure.

Sol.: Let the reaction of block be R. The least force P is always perpendicular in reaction R. When the wheel is just on point of movement up, then it loose contact with the inclined plane and reaction at this point becomes zero.

Consider ?OMP

OM = 60cm

OP = 60-15 = 45cm

MP = {(OM)2 - (OP)2}1/2

= {3600 - 2025}1/2

= 39.68cm

tan     = MP/OP = 39.68/45,           = 41.400

Using lamis theorem at O

P/sin108.6° = 10/sin90° = R/sin161.4°

P = (10 × sin108.6°)/sin90° =9.4KN Thus smallest force P = 9.4KN