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ME_410_Mid2_p2at8-30_sol2

ME_410_Mid2_p2at8-30_sol2 - F2 =(d-2 γ(2(3 F3 = ½(d γ...

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2) Figure ( a ) shows a cross section of a rectangular gate that is 3 m wide (perpendicular to the page). The gate blocks the end of a freshwater channel. The gate opens automatically when the water reaches a certain depth as shown in figure ( b ). Determine the depth d at which the gate just begins to open. Not so Easy Way (Complicated Way): See the next solution done in an EASY WAY. Ay F1 Ax F2 F3 Bx d γ F1 = ½ (d-2) γ (d-2) (3)

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Unformatted text preview: F2 = (d-2) γ (2) (3) F3 = ½ (d γ – (d-2) γ ) (2) (3) = 6 γ Bx = 0 when it begins to open. Sum of moments about A: -F1 ( d-2)/3 + F2 ( 2/2) + F3 (2/3) (2) = 0 -3/2 (d-2) 2 γ + 6 (d-2) γ + 8 γ = 0 Solving for d , d = 6 m See the attached Maple worksheet. EASY WAY: Ay Ax 2m F d/3 Bx d γ F = ½ d γ d (3) Bx = 0 when it begins to open. Sum of moments about A: -F ( 2-d /3) = 0 From which, d = 6 m...
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ME_410_Mid2_p2at8-30_sol2 - F2 =(d-2 γ(2(3 F3 = ½(d γ...

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