This is a statics of rigid bodies (mechanics) problem 4. Replace the force system on the post by a resultant force,and specify where its line of action intersections the postAB measured from point B.0.5mB500N0.2m1m330°250N1m300N1тA

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Answered: 4. Replace the force system on the post…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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EXAMPLE 1 A dam has the shape of a trapezoid shown in the top figure. The height is 30 m and the width is 60 m at the top and 30 m at the bottom. Find the force on the dam due to hydrostatic pressure if the water level is 2 m from the top of the dam. SOLUTION We choose a vertical x-axis with origin at the surface of the water and directed downward as in the middle figure. The depth of the water is 28 m, so we divide the interval [0, 28] into subintervals of equal length with endpoints x; and we choose x E [X; - 1, x]. The ith horizontal strip of the dam is approximated by a rectangle with height Ax and width wi, where, from similar triangles in the bottom figure, a 15 Xị or a = 24 - Xj 30 2 2 and so - 2(1 ]-) - 54 wj = 2(15 + a) = If Aj is the area of the ith strip, then Aj z WiAx = If Ax is small, then the pressure P; on the ith strip is almost constant and we can use this equation to write Pi x 1000gx;" The hydrostatic force F; acting on the ith strip is the product of the pressure…
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4. Replace the force system on the post by a resultant force, and specify where its line of action intersections the post AB measured from point B. 0.5m B 500N 0.2m 1m 3 30° 4 250N 1m 300N 1m A