. Derive the relationship between mechanical advantage, velocity ratio and efficiency of a machine


Best Answer

Let a machine overcome a load L by the application of an effort E. In time t, let the displacement of effort be dE and the displacement of load be dL.

Work input = Effort X displacement of effort

= E X dE

Work output = Load X displacement of load

= L X dL

Efficiency η = work output / work input

η = (L × dL) / (E × dE)

= L / E × dL / dE

= L / E × 1 / (dE / dL)

But L / E = M.A.

dE / dL = V.R.

η = M.A. / V.R.

M.A. = V.R. × η

Hence, the mechanical advantage of a machine is equal to the product of its efficiency and velocity ratio.

 

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