# Relationship between mechanical advantage, velocity ratio, and efficiency – state & derive

Last updated on June 26th, 2023 at 02:04 pm

In this post, we will first state the Relationship between **mechanical advantage**, **velocity ratio**, and efficiency. Then we will derive the relationship between mechanical advantage, velocity ratio, and efficiency of a machine.

**State the Relationship between mechanical advantage, velocity ratio, and efficiency** | formula, equation

Efficiency = Mechanical Advantage/Velocity Ratio

η= M.A. / V.R.M.A. =

[Here,ηx V.R.η= efficiency, M.A. = Mechanical Advantage, and V.R. = Velocity Ratio]

**Derive the Relationship between mechanical advantage, velocity ratio, and efficiency** | derivation

The efficiency of a machine (

η) = 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 ()η= Work output / Work input=>= Work output / Work inputη

=>= (Load x displacement of the load)η/(Effort X displacement of the effort)

=>= (Load/Effort) x (displacement of load/displacement of effort)η

=>= Mechanical Advantage x (1/Velocity Ratio)η

= Mechanical Advantage/Velocity Ratioη

Efficiency= Mechanical Advantage/Velocity Ratio

=ηMA/VR

**Mechanical Advantage equals Velocity Ratio** for an ideal machine – How?

**For an ideal machine**, **Work output = Work input**

and hence **for an ideal machine** **efficiency η** = 1 or 100%

So, for an ideal machine,

**= 1**

*η*As we know,

**=**

*η***MA/VR**

So, in this case of an ideal machine,

**1 = MA/VR**

so, Hence, for an ideal machine

**MA = VR**