The efficiency of a simple machine is defined as ______.

Concept:

Mechanical advantage:

• It is a number that tells us how many times a simple machine multiplies the effort force. 
• is defined as the ratio of output force to input force.
• The mechanical advantage of a machine gives its efficiency. 
• Formula, \(MA=\frac{F_0}{F_i}\), where, F₀ = output force, F_i = input force
• It is a unitless and dimensionless quantity.

Efficiency:

• The efficiency of a machine is the ratio of the work done on the load by the machine to the work done on the machine by the effort.
• Thus, it is the ratio of useful work done by the machine output to the work done by the machine input.
• It is represented by the Greek symbol η.
• Formula, efficiency, \(\eta=\frac{output\, \, work done}{input \, \, workdone}\)

Velocity ratio:

• The ratio of the distance moved by the point at which the effort is applied in a simple machine to the distance moved by the point at which the load is applied at the same time.
• In the case of an ideal (frictionless and weightless) machine, velocity ratio = mechanical advantage.

Explanation:

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

MA = efficiency × velocity ratio

Therefore, \(efficiency=\frac{MA}{velocity\, \, ratio}\)