Ringling Brothers Bamum and Bailey Circus is using a pulley to lift an Elephant on to a ship. If the Elephant is 2200kg and you have to raise her 15m with a pulley that has an efficiency of 60%, then how much rope do the handlers, who can pull with a combined force of 115 N, hope is available to them.
The force due to gravity on the elephant is 21,506 N (2200kg*9.8m/s^2)=F_e
The force of the combined humans is 115N=F_p
The Attempt at a Solution
The work needed to raise an 2200kg elephant 15 meters is 323,400 J
W=21,560 * 15=323,400 J
Since the efficiency is 60% the output and the work done to lift the elephant is the output, I divided 323,400 by 0.6 to get 539,000 J for the input.
I then divided by the force the combined handlers make up which is 115 N and got
4,687 m for the distance which mean the rope has to be more than 4,687 meters + at least 15m needed on the elephants side.
So would a rope greater than 4702 be the right answer?