Question

Cathy, a 125lb actress playing Peter Pan, is hoisted above the stage in order to “fly” by a stagehand pulling on a compound pulley system that has 6 supporting strands with a force of 30lbs. C) What is the efficiency of the pulley?

Answer 1

The efficiency of the pulley, % Efficiency is
`69.\overline 4`%

Step-by-step explanation:

The given parameters in the question are;

The mass of the actress playing Peter Pan (the pulley load) = 125 lb

The force applied to hoist the actress by the stage hand = 30 lbs

The actual mechanical advantage, AMA = Load/Force applied

Therefore, the AMA of the pulley = 125 lbs/(30 lbs) = 25/6 =
`4.1 \overline 6`

The pulley's Ideal mechanical advantage, IMA = The number of stands in the pulley = 6

The efficiency of a pulley is given by the following formula;

`\% \ Efficiency = (AMA)/(IMA) * 100`

Where

AMA = The actual mechanical advantage

IMA = The ideal mechanical advantage

Therefore, the efficiency of the pulley, % Efficiency, is given by plugging in the values of the AMA and the IMA in the efficiency formula as follows;

`\% \ Efficiency = ((25)/(6) )/(6) * 100 = (625)/(9)\% = 69.\overline 4\%`

The efficiency of the pulley, % Efficiency =
`69.\overline 4`%