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)=   Express the answer as a formula. (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.

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