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