Question

Prove that the efficiency of a machine is the ratio between mechanical advantage and the velocity ratio?

Answer 1

Explanation

Relation between the efficiency mechanical advantage and velocity ratio of a practical machine

Assumptions

Consider a practical machine that displaces a useful load 'l' through a distance ‘d’, when an effort ‘E’, causes a displacement through distance D.

$$\begin{gathered} \therefore Output=Workdoneinthedisplacingtheload \\ =l\times d \\ Input=workdonebytheefoortincau\sin gthedisplacement \\ =E\times d \\ \therefore Efficiency=\eta =\frac{output}{input}=\frac{l\times d}{E\times D} \\ =\frac{l}{E}\times \left(\frac{1}{{\displaystyle \frac{D}{d}}}\right) \\ =\frac{\frac{l}{E}}{\frac{D}{d}}=\frac{Mechanialadvantage}{VelocityRatio}\because MA=\frac{l}{E}\&VR=\frac{D}{d} \\ \eta =\frac{Mechanialadvantage}{VelocityRatio} \end{gathered}$$