Homework SourseA cable 100 foot cable with density 2lbft hangs vertically f
A cable 100 foot cable with density 2lb/ft hangs vertically from the top of a tall building. Set up an integral to determine how much work is required to lift the cable to the top of the building. You dont need to evaluate your integral.
Solution
take help 1) A 60 foot length of steel chain weighing 10 pounds per foot is hanging from the top of a building. How much work is required to pull half of it to the top? The total weight of the chain is 10 x 60 = 600 lbs Because you are pulling the entire chain, the work or energy needed to pull half the length of the chain = Force x distance Force = total weight of the chain = 600 lb Work = 600 x 30 = 18,000 ft-lbs ** This assumes you are pulling the entire length of chain at one time and not letting portion of it rest on top of the building while pulling. In other words, if you were to pull say 10 feet at a time, then 1st pull will be 600 lbs x 10\'; 2nd pull will be 500 lbs x 10\'; 3rd pull will be 400 lbs x 10\'. The total energy or work done will be 6000 + 5000 + 4000 = 15,000 ft-bs. In calculus, Let x = length of the chain suspended dx = differential length of chain pulled dW = 10x dx <== 10 lb/ft W = ?10 x dx from x = 60 to 30 W = 10?xdx W = 10 (x^2/2) = 5x^2 W = 5(60^2 - 30^2) = 13,500 ft-bs.
