Question

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

Answer 1

Let a machine overcome a load L by applying an effort E, in time t. Let the displacement of effort be d_E, and the displacement of the load be d_L.
Work input = Effort × Displacement of effort

Work input = E × D_E 

Work output = Load × Displacement of load

Work output = L x d_L

Efficiency = η

`"Efficiency"="Work output"/"Work input"`

`eta=(L xx d_L)/(E xx d_E)`

`eta=L/E xx d_L/d_E`

Now, we know that

`L/E=M.A`

`d_E/d_L=V.R`

Thus, we get

`eta="M.A"/"V.R."`

`M.A.=V.R. xx eta`

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