A worker on scaffolding 75 ft above the ground needs to lift a 500 lb bucket of cement from the ground to point 30 ft above the ground by pulling on a opre weighing .5 lb/ft. how much work is required?

Question

I know to use the Work integral, but im not sure wat equation to use

Answer 1

The 500 lb bucket of cement is raised 30 ft. That part of the work required is 500x30 = 15,000 ft-lb. A 75 ft length of rope weighing 75/2 = 37.5 lb has its center of mass raised from 75/2 = 37.5 ft elevation to a situation where 30 feet is at 75 ft elevation, and a 45 feet length has a center of mass at (75+30/2) =52.5 ft. The potential energy increase of the rope is [15*37.5 + 22.5*52.5 - 37.5*37.5]= 337.5 ft lb

The total work required is 15,337.5 ft-lb