Review 5: Problem 44 Pevious Problem List Next (1 point) A trough is 2 feet long

Question

Review 5: Problem 44 Pevious Problem List Next (1 point) A trough is 2 feet long and 1 foot high. The vertical cross-section of the trough parallel to an end is shaped like the graph of y-x6 from x =-1 to x = 1 . The trough is full of water. Find the amount of work required to empty the trough by pumping the water over the top. Note: The weight of water is 62 pounds per cubic foot. Your answer must include the correct units. (You may enter Ibf or lb'ft for ft-lb.) Work 98.11ft-lbs Preview My Answers Submit Answers You have attempted this problem 5 times. Your overall recorded score is 0%. You have unlimited attempts remaining. Email instructor

Explanation / Answer

Solution :- We'll assume that each molecule of water is pumped from its current level, over the top. So the pump floats on the surface of the water.

Since the trough is 1 foot high, we will pump from a depth of 0 feet below the surface to 1-foot below the surface. So our integration will go from y=0 to y=1
also Work W=F*d
At a particular height, y (taking y=0 to be the bottom of the trough), we have a differential volume of water l*w*(dy), where l=2 feet, w=2*y^(1/6) (2 due to doubling the width since we go from +x to -x), and dy is just the differential.
Now we know that weight = volume * density

Weight = (4y^(1/6)dy)(62) = 248y^(1/6) dy

So the total work is W = ?(y=0 to y=1) 248 y^(1/6)*(1-y) dy

W = ?(y=0 to y=1) 248 {y^(1/6)(1-y) } dy = 8928 /91
W = 98.11 Foot-Pounds of Force

Related Questions

Navigate

• Browse (All)
• Browse R
• Subjects

---

---

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