Determine the magnitude and direction of smallest force P required to start the wheel over the block.

1 Answers

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

**Consider triangle OMP **

**OM = 60 cm **

** OP = 60–15 = 45 cm **

**MP = {(OM)²– (OP) 2}½ = {3600 – 2025}½**

** = 39.68cm **

**tan β = MP/OP = 39.68/45**

**β = 41.400 **

**Using lamis theorem at point O P/sin 108.6° = 10/sin 90° = R/sin 161.4° **

**P = (10 × sin 108.6°)/sin 90° =9.4KN **

**Hence smallest force P = 9.4KN**

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