Question
Download Solution PDFFind 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.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
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,
, where, F0 = output force, Fi = 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,
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,
- 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, LR = 2.5 m, length of effort, LE = 10 m
Velocity ratio,
Efficiency,
In percentage, the efficiency is 62.50 %.
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