Question

Application Problems: i. Be sure to draw a picture. 11. Set up the problem using calculus formulas. iii. Solve using the calculator. • A bucket weighs 5 pounds when empty. It is loaded with 60 pounds of sand, and is then lifted (at constant speed) 10 Sana leaks out the bottom at a uniform rate and a third of the sand is lost by the end lifting Find the work done lifting the bucket if the rope weighs 0.2 pounds per foot.

Answer 1

If you have any doubts, feel free to ask.

this problem We can three in devide parts. Work done = work done in lifting the empty - bucket t work done in lifting - the rope t work done in lifting the sand w = WitWztWg W, = mgh = 50x3 2.2710 w=1680 work done in lifting the hope is W for the rope 9 = 0.2 lblft.. mass of a rope length x = ax = Was glo arg de blo = 500g = 50X0.2% was 322 3 322

let - the speed lifted be at which ŕ then the sand is time taken to lift In that time t= bo. dost amout of sand = 1360 = 20 hence rate of sand loss = 20 = 26. amount of hance at any time t'n sand on bucket is m(t)= M-aut the hence Wyr Sm (4) gdz - Smca) v dtg I Ws Slot (M-2 0 1 ) gu de I W3 = 10m-1000g

how putting m=60 . =) W3 = [10x60-100]x32,2 De = 16100 hance W= WitWat Wz W=20930 ft. lbf