Question

A 5 lb bucket containing 10 lb of water is hanging at the end of a 30 ft rope which weighs 1 2 lb/ft. The other end of the rope is attached to a pulley. Assume that the rope is wound onto the pulley at a rate of 3 ft/s causing the bucket to be lifted. Find the work done in winding the rope onto the pulley

Answer 1

Workdone=10,800 ft/lb

Explanation:

10lb of water + 5lb bucket+ (12lb/ft× 30ft)=375lb

Workdone= integral(375 -x) dx

Integrating with upper limit 30 gives

W= [375- x^2/2]

W=375(30) -(30^2)/2

W=11250-450 = 10800ft/lb