. 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 d_E and the displacement of load be d_L.

Work input = Effort X displacement of effort

= E X d_E

Work output = Load X displacement of load

= L X d_L

Efficiency η = work output / work input

η = (L × d_L) / (E × d_E)

= L / E × d_L / d_E

= L / E × 1 / (d_E / d_L)

But L / E = M.A.

d_E / d_L = 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.