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

$6.9 m$ $6.9"m"$

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

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

$F_{l} \times D_{l} = F_{e} \times D_{e}$ $F_lxxD_l=F_exxD_e$

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

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:

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

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

$D_e=6.9"m"$