Question

Derive the 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 load be dL.
Work input = Effort X displacement of effort
= E X dE

Efficiency 𝔫 = `"𝑤𝑜𝑟𝑘 𝑜𝑢𝑡𝑝𝑢𝑡 "/"𝑤𝑜𝑟𝑘 𝑖𝑛𝑝𝑢𝑡"`

𝔫 = `"𝐿 ×𝑑𝐿"/"𝐸 × 𝑑𝐸"`= `"𝐿"/"𝐸"`  ×  `"1"/"𝑑𝐸/𝑑𝐿"`

But `"𝐿"/"𝐸"`=𝑀.𝐴

`"𝑑𝐸"/"𝑑𝐿"`=𝑉.𝑅

𝔫 = `"𝑀.𝐴"/"𝑉.𝑅"`

M.A = n × V.R  

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