Question: Assume the bucket in Example 4 is leaking. It starts with 2 gallons of

Question

Question: Assume the bucket in Example 4 is leaking. It starts with 2 gallons of water (16 lb) and leaks at a constant rate. It finishes draining just as it reaches the top. How much work was spent lifting the water alone? (Hint: do not include the rope and bucket, and find the proportion of water left at elevation x ft.)

"Example 4": A 5-lb bucket is lifted from the ground into the air by pulling in 20 ft of rope at a constant speed. the rope weighs 0.08 lb/ft. (intentionally left out initial example question, because already answered and not needed, to avoid confusion. I need the answer from the first paragraph.

The question is an extension from an example in our book, but the book doesn't give the answer.

Thanks for the help, and sorry for the confusion. Please show work.

Explanation / Answer

work done = mgh
m = 16lbs when h = 20ft
m = 0 when h = 0ft
so at h = xft, m=16 - 16/20*x =16 - (4x/5)
so work done =integral(16 - (4x/5))*g*x) = integral(16gx - (4g/5)*x2) (from 0 to 20)
so work done = 16gx2/2 - (4g/5)(x3/3) from (0 to 20)
so workdone = 8g*202 - (4g/5)(203/3) = (8*32.174*400)-(4*32.174 ft/s2/5)(203/3)

=104684.8-68637.87 foot-pound

=36046.93 foot-pound

At elevation x proportion of water = 16 - (4x/5) lbs

Related Questions

Navigate

• Browse (All)
• Browse Q
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.