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Answer:
Therefore total work done =2050 ft-lb
Step-by-step explanation:
Given that, a bucket are used to drawn water from a well that is 50 ft deep.
(1)
Work done = Force×displacement.
Work done to pull the bucket is
= Weight of the bucket × displacement
=(6×50) ft-lb
=300 ft-lb
(2)
The bucket fill with 40 lb of water and is pulled up at a rate of 2ft/s, but leaks out of a hole in the bucket at a rate of 0.2 lb/s.
Since the well is 50 ft deep.
It takes =25 s to pull the bucket at the top of the well.
After 25 s it lost (25×0.2)lb =5 lb water.
So the remaining water is = (40-5) lb= 35 lb
Let y is distance above the original depth of 50 ft.
When y=50 ft, weight of the bucket= 40 lb,when y=0 weight of the bucket= 35 lb
The slope of the of water leakage is
The bucket holds lb of water when it is y ft above the original depth.
Work done to pull the water in the bucket is
=1750 ft-lb
Therefore total work done
=Work done to pull the bucket+Work done to pull the water in the bucket
=(300+1750) ft-lb
=2050 ft-lb