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?

1 Answer
Apr 8, 2018

Answer:

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, #mg=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=mgDeltah#
#mg=150#
#h= 4m#

#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.