posted by Jessica on .
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?
I know to use the Work integral, but im not sure wat equation to use
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