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Question
The pulley system shown in the figure is to be used to lift a load W. If the man applying the effort cannot apply a force exceeding 1000 N, what is the maximum load that can be lifted?
The actual load that the man is finally able to lift turns out to be 2700 N. What are the values of the actual M.A., obtained, and the efficiency of the actual set-up?
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Solution
The load lifted would be a maximum when conditions are ideal. Since this set-up uses three strands of string, the load gets raised only through 1/3rd of the distance through which the effort moves.
Hence,
Velocity ratio =`("Distance moved by the effort")/("Distance moved by the load")`
`=1/(1//3)=3.`
Under ideal conditions, V.R. = M.A.
Hence, Ideal M.A. of the set-up = 3.
∴ Maximum load that can be lifted = Effort × 3 = 100 N × 3
= 3000 N.
Under actual conditions, M.A. =`"Load"/"Effort"`
=`(2700"N")/(1000"N")`
= 2.7
Efficiency = `"M.A."/"V.R."=2.7/3`
= 0.9 = 90%.
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