the weight of a thin sheet of water of thickness dy and area 9x is
9x*62 dy
At depth y, the width across the water surface is 2∜y, so the weight of the sheet of water is
1116∜y dy
Now, since work = force * distance, we have to add up all the work lifting thin sheets of water to a height of 1
W = ∫[0,1] 1116∜y(1-y) dy = 396.8 J
A trough is 9 feet long and 1 foot high. The vertical cross-section of the trough parallel to an end is shaped like the graph of y=x4 from x=−1 to x=1 . The trough is full of water. Find the amount of work in foot-pounds required to empty the trough by pumping the water over the top. Note: The weight of water is 62 pounds per cubic foot.
1 answer
1 answer