A heavy rope 10 meters long, weighs 3.5 N/m and hangs from the roof of a building 30 meters high. We want to lift part of the rope up onto the roof. (i) Suppose that at a given moment, x meters of...

A heavy rope 10  meters long, weighs 3.5 N/m and hangs from the roof of a building 30  meters high. We want to lift part of the rope up onto the roof.




(i) Suppose that at a given moment, x  meters of rope had been lifted up onto the roof. Therefore the amount of work required to lift the rope Δx  meters is approximately w(x)Δx . What is w(x) ?
w(x)=

(ii) What is, in Joules, the amount of work required to lift all of the rope up onto the roof of the building? Give the answer with 3  significant digits.






(iii) What is, in Joules, the amount of work required to lift half of the rope up onto the roof of the building? Give the answer with 3  significant digits.