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

Question-AnswerCategory: Engineering MechanicsDetermine the magnitude and direction of smallest force P required to start the wheel over the block. 
Mazurek Gravity Staff asked 1 year ago

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

 

1 Answers
Mazurek Gravity Staff answered 1 year ago


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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