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52_Problem CHAPTER 10 - PROBLEM 10.47 A block of weight W...

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PROBLEM 10.47 A block of weight W is pulled up a plane forming an angle α with the horizontal by a force P directed along the plane. If µ is the coefficient of friction between the block and the plane, derive an expression for the mechanical efficiency of the system. Show that the mechanical efficiency cannot exceed 1 2 if the block is to remain in place when the force P is removed. SOLUTION Input work P x δ = ( ) Output work sin W x α δ = Efficiency: sin sin or W x W P x P αδ α η η δ = = (1) 0: sin 0 or sin x F P F W P W F α α Σ = = = + (2) 0: cos 0 or cos y F N W N W α
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