Lifting an elephant with a pulley & rope

[Lamont]

Homework Statement

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.

Homework Equations

The force due to gravity on the elephant is 21,506 N (2200kg*9.8m/s^2)=F_e
15m=d
The force of the combined humans is 115N=F_p

Work W=F*d

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?

 

[SteamKing]

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?

Almost 5 km of rope strong enough to hold the elephant would weigh more than the elephant.

 

[haruspex]

Your calculation looks ok, except I don't understand the extra 15m. There may be a bit extra on the workers' side, but doesn't need to be 15m.

Almost 5 km of rope strong enough to hold the elephant would weigh more than the elephant.

Surely the tension in the rope is the 115N. The only parts that have to take the full weight are the pulley blocks and hooks at top and bottom. Even then, the rope's weight would be significant.

 

[BiGyElLoWhAt]

This question feels weird to me. I don't know how you could get a better answer than what you have, however:
115N*4687m = the amount of energy an applied force of 115N imparts to an object over the course of 4687 meters.

There is still a net force issue between the rope and the elephant. I can't see why the elephant should lift. Asking how many pullies would be necessary would be a better question in my opinion. As this is apparently your homework question, I am somewhat at a loss.

Any mechanics experts around?

 

[Lamont]

Your calculation looks ok, except I don't understand the extra 15m. There may be a bit extra on the workers' side, but doesn't need to be 15m.

Surely the tension in the rope is the 115N. The only parts that have to take the full weight are the pulley blocks and hooks at top and bottom. Even then, the rope's weight would be significant.

If we use Sig Figs the answer because 4700 m regardless so I'll guess go with that.

 

[haruspex]

I can't see why the elephant should lift.

There would be some strapping around the elephant. A large pulley block (many pulleys) immediately above the elephant would hook to the strapping. Numerous turns of rope connect that block to a similar block 15m higher. The other end of the rope goes from top pulley block to workers. Why would the elephant not lift when the workers pull?

 

[BiGyElLoWhAt]

I gotcha, I was thinking 1 pully.

 

[insightful]

Another way is to convert 2200kgf to 21,575N and divide by 115N to get a 188X multiplier divided by the 0.6 efficiency to get 313X. Then 15m times 313X = 4700m of rope needed.