The curved and flat plates of width 6-m are connected at A, Band C. They are submerged in water at the depth h=7-m. Thedistance d =4-m and the radius R= 2-m. Find the resultantforce [kN] in the hinge at B.hВRAd

Answered: The curved and flat plates of width 6-m…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Question

The curved and flat plates of width 6-m are connected at A, B
and C. They are submerged in water at the depth h=7-m. The
distance d =4-m and the radius R= 2-m. Find the resultant
force [kN] in the hinge at B.
h
В
R
A
d

Expert Solution

Step 1 Calculate the resultant force at B

First we have to calculate the force on the member AB. We have

$T h e h o r i z o n t a l f o r c e F_{H} = ρ A g \bar{x} = 1000 \times 9.81 \times 6 \times 2 \times (7 + \frac{2}{2}) = 941.76 k N; T h e v e r t i c a l f o r c e F_{V} = 1000 \times 9.81 \times (π \times 2^{2} \times 6 + 6 \times 7 \times 2) = 1563.7 kN; So the net force is acting on AB is = \sqrt{{F_{H}}^{2} + {F_{V}}^{2}} = \sqrt{941 . 76^{2} + 1563 . 7^{2}} = 1825.4 kN;$

The inclination of force on AB is = $θ_{A B} = \tan^{- 1} (\frac{F_{V}}{F_{H}}) = \tan^{- 1} (\frac{1825.4}{941.76}) = 62.7 °$

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