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?

Question

Elena Albarran · Accepted Answer

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John needs to work against gravity to increase the sail's gravitational potential energy in order to raise it 4 meters (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. Power is energy over time, and we are not given the time it takes John to hoist the sail, so my assumption may not be totally accurate. However, efficiency is a measure of output power/input power.

Adam Arnold · Answer

undefined The work done to lift the sail is 600 J. John must do 1200 J of work on the rope.