Answer to Question #186216 in Classical Mechanics for Jethro

Question #186216

A trough of length 6 ft has for its vertical cross section an isosceles trapezoid. The upper and lower bases are 6 ft and 2 ft respectively and the altitude is 2 ft. If the trough is full of water, find the force on the slant side of the trough.


1
Expert's answer
2021-04-29T07:28:21-0400

Given:

b = 2 ft = 0.61 m;

h = 2 ft = 0.61 m;

w = 6 ft = 1.83 m;

l = 6 ft = 1.83 m.

Find the force perpendicular to the vertical plane equal to the slant side in height and width:

"F_p=\\frac12\\rho gh(hw)=\\frac12\u00b71000\u00b79.8\u00b70.61(1.83\u00b70.61)=\\\\=3320\\text{ N}."

Find the volume above the slant:


"V=\\frac14 (w-b)hl=0.34\\text{ m}^3."

The weight of water above the slant side:


"w=V\\rho g= 3330\\text{ N}."

The magnitude of the force is


"R=\\sqrt{w^2+F_p^2}=4700\\text{ N}."


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