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

Therefore the work done is 640 ft pound.

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-(0.8x^2)/(2)]_0^(40)`

`=[(32* 40)-0.4(40)^2]`

=640 ft pound.

Therefore the work done is 640 ft pound.