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 distance the rope must be pulled in order to lift the bag of nails?

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Answer 1 · 2015-11-18T22:46:22

#6.9"m"#

Work done on the load = Work done by the effort.

Since work done = force x distance moved in direction of force we can write:

#F_lxxD_l=F_exxD_e#

#:.( F_lD_l)/(F_eD_e)=1#

This is when the system is 100% efficient. Since it is 75% efficient we can write:

#(F_lD_l)/(F_eD_e)=0.75#

The load #F_l=21xx9.8=205.8"N"#

We need to find #D_e# so we can write:

#D_e= (F_lD_l)/(F_exx0.75)#

#:.D_e=(205.8xx2.3)/(91.5xx0.75)#

#D_e=6.9"m"#