Answer:
Therefore the work done is 640 ft pound.
Step-by-step explanation:
Given that, a heavy rope 40 ft long, weighs 0.8 lb/ft.
Force = weight.
Let we pull x ft. Then the remain rope = (40-x)ft.
(40-x) ft it is variable.
The weight of (40-x) ft is =(40-x)0.8 lb
∴ Force =(40-x)0.8 lb
Work done = Force × displacement
= (40-x)0.8 Δx [ displacement = Δx]
Therefore ΔW =(40-x)0.8 Δx
Since total rope is pulling up on the top of the building. Total displacement = 40 ft.
Total work done [tex]=\int_0^{40}(40-x)0.8 dx[/tex]
[tex]=[32x-\frac{0.8x^2}{2}]_0^{40}[/tex]
[tex]=[(32\times 40)-0.4(40)^2][/tex]
=640 ft pound.
Therefore the work done is 640 ft pound.
