Solve integral in Eng...
Ok..it\'s in Eng...so if you can help me out..that would be awesome!! Here comes the problem...
Water is being drawn from a well 100 ft deep, using a bucket that scoops up 100 lb of water. The bucket is pulled up at the rate of 2 ft/s, but it has a hole in the bottom through which water leaks out at a rate of 0.5 lb/s. Determine how much work is done in pulling the bucket to the top of the well. Neglect the weight of the bucket, the weight of the rope, and any work done in overcoming friction.
Hint: let y=0 correspond to the surface of the water in the well, so that y=100 at ground level, and consider the infinitesimal amount of work dW done to raise the bucket an infinitesimal distance dy, from y to y+ dy.
- 1 decade agoFavorite Answer
則由W=FS公式及y = v*t => t = y/v = y/2 (每秒2ft)
dw=F*dy => dw=(100-0.5t)g*dy => dw=(100-0.5*y/2)g*dy (g為重力常數)
=g∫(0積到100)(100-y/4) dy (g提到外面去)
=g*(100y-y^2/8 |( 0積到100)