Question

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

Answer 1

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 the load be dL.

Work input = Effort $\times$ displacement of effort

= E $\times$ dE

Work output = Load $\times$ Displacement of load

= L $\times$ dL

But,

=




M.A. = V.R. $\times$


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