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Question
Establish a relationship between efficiency, M.A., and V.R.
Solution
Let a machine overcome a load L by applying an effort E. In time t, the displacement of effort is dE, and displacement of load is dL. Then
Work input = Effort × Displacement of effort = E × dE
Work output = Load × Diaplacement of load = L × dL
Efficiency = `("Work output")/("Work input ")=("L" × "d"_"L") /("E" × "d"_"E")=("L"//"E")/("d"_"E"//"d"_"L")`
L / E = M.A. and dE / dL = V.R.
Efficiency =`("M.A.")/("V.R.")`
M.A. = V.R. × Efficiency.
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