Find the efficiency of a pulley system which has a mechanical advantage of 2.5 and where the load lifts by 2.5 meters on pulling the rope by 10 m.

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, \(\eta=\frac{mechanical\, \, advantage}{velocity \, \, ratio}\)

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.
• Formula, \(velocity\, \, ratio=\frac{distance\, \, moved\,\, by\,\, effort}{distance \,\, moved\,\, by\,\, load}\)
• In the case of an ideal (frictionless and weightless) machine, velocity ratio = mechanical advantage.

Calculation:

Given: mechanical advantage, MA = 2.5, length of load lift, L_R = 2.5 m, length of effort, L_E = 10 m

Velocity ratio, \(v=\frac{10}{2.5}=4\)

Efficiency, \(\eta=\frac{mechanical \, \, advantage}{velocity \,\, ratio}\)

\(\eta=\frac{2.5}{4}=0.625\)

In percentage, the efficiency is 62.50 %.