A pulley system with 75% efficiency is set up to lift a 21kg bag of nails. The bag is lifted to a height of 2.3m by a person pulling on the rope with a force of 91.5N. What is the mechanical advantage of this pulley system?

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Answer 1 · 2018-05-15T14:36:35

We know #"efficiency"(eta)="work output"/"work input"#

Here #eta=75%=3/4#

Work output =# Load (L)xx "Displacement of Load"(D_L)#

#=21xx9.8xx2.3# #J#

Work input =# "Effort" (E)xx "Displacement of Effort"(D_E)#

#=91.5xxD_E# #J#

So #3/4=(21xx9.8xx2.3)/(91.5xxD_E)#

#=>D_E=(21xx9.8xx2.3xx4)/(91.5xx3)#

#=>D_E=(28xx9.8xx2.3)/91.5#

Velocity Ratio #=D_E/D_L#

Now

Mechanical Advantage#=etaxx"V.R"#

#=3/4xxD_E/D_L#

#=3/4xx(28xx9.8xx2.3)/(91.5 xx2.3)#

#=(21xx9.8)/91.5~~21.66 #