# 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?

Nov 18, 2015

$6.9 \text{m}$

#### Explanation:

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

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

${F}_{l} \times {D}_{l} = {F}_{e} \times {D}_{e}$

$\therefore \frac{{F}_{l} {D}_{l}}{{F}_{e} {D}_{e}} = 1$

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

$\frac{{F}_{l} {D}_{l}}{{F}_{e} {D}_{e}} = 0.75$

The load ${F}_{l} = 21 \times 9.8 = 205.8 \text{N}$

We need to find ${D}_{e}$ so we can write:

${D}_{e} = \frac{{F}_{l} {D}_{l}}{{F}_{e} \times 0.75}$

$\therefore {D}_{e} = \frac{205.8 \times 2.3}{91.5 \times 0.75}$

${D}_{e} = 6.9 \text{m}$