# John uses a pulley to lift the sail on his sailboat. The sail weighs 150 N, and he must lift it 4.0 m. The pulley is 50% efficient. How much work must be done to lift the sail? How much work must John do on the rope to lift the sail?

Apr 8, 2018

See below:

#### Explanation:

In order to lift the sail upward 4 meters, John must increase its Gravitational potential energy by doing work against gravity (i.e hoisting the sail).

We are given the weight of the sail due to gravity, $m g = 150 N$, which is convenient as we are going to use it to calculate the increase in gravitational potential energy.

Using the formula for Gravitational potential energy.
${E}_{p} = m g \Delta h$
$m g = 150$
$h = 4 m$

${E}_{p} = 150 \times 4 = 600 J$

This is how much work must be done to lift the sail 4 meters. However, using a pulley, like John's, it is only 50% efficient. I assume this would mean John would have to put in twice as much energy, $1200 J$ , to hoist the sail to the given position.

However, efficiency is a measure of output power/input power, So my assumption might not be entirely correct. Power is energy over time- and we are not given the time it takes for John to hoist the sail.