Calculus Work Rope problem helpp ?

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SUMMARY

The discussion focuses on calculating work done in two scenarios involving a mountain climber and a bucket being lifted. In the first scenario, the work required to lift a 50-meter rope weighing 0.624 N/m is calculated using the integral W = ∫(0.624x)dx from 0 to 50. In the second scenario, the work done to lift a 5 lb bucket with a 20 ft rope weighing 0.08 lb/ft is determined using the integral W = ∫(0.08)(20-x)dx from 0 to 20. The key difference in the setup of the integrals is based on the coordinate system chosen, which affects how the variables are defined.

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Calculus Work Rope problem helpp pleasezz!?

1.) A mountain climber is about to haul up a 50M length of hanging rope. How much work will it take if the rope weighs .624 N/m?

The Work on the rope is W= integral of 0.624xdx from 0 to 50.

2) A 5 lb bucket is lifted from the ground into the air by pulling in 20ft of rope at aconstant speed. The rope weighs 0.08lb/ft. How much much work was spend lifting the bucket and rope.

Just the work on rope = integral of (.08)(20-x)dx from 0 to 20.

My question is how come the work in question one is not 0.624(50-x), and question to is. When do you use the (L-x)? thank you
 
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1) This should be in homework help
2) It all depends on how you set up coordinates. Does x=0 at the bottom? Does x=0 at the top? Somewhere inbetween? Is x+ going up? Is x+ going down? Coordinates are a convention, you can set them up HOWEVER you'd like.
 

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