Question

A heavy rope, 40 ft long, weighs 0.8 lb/ft and hangs over the edge of a building 110 ft high. How much work is done in pulling the rope to the top of the building

Answer 1

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 $=\int_0^{40}(40-x)0.8 dx$

                            $=[32x-\frac{0.8x^2}{2}]_0^{40}$

                            $=[(32\times 40)-0.4(40)^2]$

                            =640 ft pound.

Therefore the work done is 640 ft pound.