Question

14. A leaky 10-kq bucket is lifted from the ground to a height of 12 m at a constant speed with a rope that weighs 0.8 kg/m. Initially the bucket contains 36 kg of water, but the water leaks at a constant rate and finishes draining just as the bucket reaches the 12-m level. Find the work done. (Use 9.8 m/s2 for g.) Evaluate the integral. cind the wwork reauired to pump the water out of the spout. 16. A tank is full of water. Find the work required to pump the water out of the spout. Use the fact that water weighs 62.5 lb/ft. (Assume r 6 ft, R 12 ft, and h 13 ft.) R

Answer 1

14 bucket e force the bucket i my= 10x 9-5 e distanco the bucket iy Ufkd in 12 the work inrilred in iftng the empty bedet ix mgh hei thtm (0yE n), the Mas i 08 m C2-9)m the gex.812 = IL7.6J Pope the rpe 80 Lhe sork done toift the rope i 2 12 J9.8x8-8 (12-)a X ) 564.48 of the war at height 3-3 Watr the Mass 3 6 m(12-2) 12 the olixtance the Ur iffed i 4x the watr iA 30 thcaorkK to lift (26x-3 9.8 9-8/36-) 2116 8j Adding all the work done to Li ft th backet, rope water /17 564. 48 + i 6 8 3857.23 J