A rope holds up a rectangular, hinged gate, as shown in the figure. Derive expressions for the vertical and horizontal reaction forces, per unit depth into the page, at the hinge. Your expressions should contain only the tension in the rope (T), the angle of the gate (θ), the height of the fluid (hf), the height of the rope (hr), and the specific weight of the fluid (γ). You may assume the gate is effectively massless

Mechanics of Materials (MindTap Course List)
9th Edition
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Barry J. Goodno, James M. Gere
Chapter5: Stresses In Beams (basic Topics)
Section: Chapter Questions
Problem 5.12.11P: A cylindrical brick chimney of height H weighs w = 825 lb/ft of height (see figure). The inner and...
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A rope holds up a rectangular, hinged gate, as shown in the figure. Derive expressions for the vertical and
horizontal reaction forces, per unit depth into the page, at the hinge. Your expressions should contain only
the tension in the rope (T), the angle of the gate (θ), the height of the fluid (hf), the height of the rope (hr),
and the specific weight of the fluid (γ). You may assume the gate is effectively massless. 

A rope holds up a rectangular, hinged gate, as shown in the figure. Derive expensions for the vertical and
borinottal reacticn forces, per unit depth into the page, at the hinge. Your experssices should contain only
the tesion in the rope (T), the ange of the gate (), the beight of the fuid (Ay), the beight of the rope (A,)
and the specific weight of the fuid (). You may aosume the gate is effecetively maoles.
Ropey
Transcribed Image Text:A rope holds up a rectangular, hinged gate, as shown in the figure. Derive expensions for the vertical and borinottal reacticn forces, per unit depth into the page, at the hinge. Your experssices should contain only the tesion in the rope (T), the ange of the gate (), the beight of the fuid (Ay), the beight of the rope (A,) and the specific weight of the fuid (). You may aosume the gate is effecetively maoles. Ropey
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