Equation of Efficiency that relates mechanical advantage and velocity ratio of an ideal machine

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In this post, we will find out the equation of Efficiency that relates mechanical advantage and velocity ratio of an ideal machine.

Equation of Efficiency that relates mechanical advantage and velocity ratio of an ideal machine

The efficiency of a machine = Work output / Work input …. (1)

Now, Work output = Load x displacement of the load ….. (2)

And Work Input = Effort X displacement of the effort ….. (3)

From all 3 equations above,

Efficiency = Work output / Work input = (Load x displacement of the load)/(Effort X displacement of the effort)
= (Load/Effort) x (displacement of load/displacement of effort)
= Mechanical Advantage x (1/Velocity Ratio) = Mechanical Advantage/Velocity Ratio

Efficiency= Mechanical Advantage/Velocity Ratio = MA/VR …………………… (2)

For an ideal machine, Work output = Work input
and hence for an ideal machine efficiency = 1 or 100%…. (3)

Hence, for an ideal machine from equation 2 and 3,
1 = MA/VR
so, Hence, for an ideal machine MA = VR

Equation of Efficiency that relates mechanical advantage and velocity ratio of an ideal machine

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