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.
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.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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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