A trough is 7 feet long and 1 foot high. The vertical cross-sections of the trou

Question

A trough is 7 feet long and 1 foot high. The vertical cross-sections of the trough parallel to its ends are shaped like the graph offromto. The trough is completely filled with 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 ispounds per cubic foot.

Work =ft-lb A trough is 7 feet long and 1 foot high. The vertical cross-sections of the trough parallel to its ends are shaped like the graph of 62.5 pounds per cubic foot. Work =ft-lb x=1 . The trough is completely filled with 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 x=-1 to Y = x^8 from

Explanation / Answer

W = F S dW = 62 L (2X) dy (2-y) dW = 124(7) y^(1/8)(2-y)dy W= SUM 868 (2y^(1/8) - y^(9/8))dy, from y = 2 to y = 1 SUM means integral of W =868 (2(8/9)y^(9/8) - (8/17)y^(17/8)) from y=2 to y=1 W = 449.147335 ft -lbs

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