Explanation Formula used: “ Centroid of a thin, flat plate by integration : If a thin, flat plate covers the region bounded by y 1 = f 1 ( x ) , y 2 = f 2 ( x ) , x = a and x = b , the moment of the mass of the element of area about the y- axis is given by ( kdA ) x, where k is the mass per unit area. The element dA is written as ( y 2 − y 1 ) d x and so the sum of moments of all the elements is expressed as, k ∫ a b x ( y 2 − y 1 ) d x . If we consider all the mass of the plate to be concentrated at one point x ¯ units from the y- axis , then we can equate the expressions, k ∫ a b x ( y 2 − y 1 ) d x = k A x ¯ . k will divide out as it appears on both sides. The area A is found by the integral ∫ a b ( y 2 − y 1 ) d x . The x- coordinate of the centroid of the plate is given by the equation, x ¯ = ∫ a b x ( y 2 − y 1 ) d x ∫ a b ( y 2 − y 1 ) d x Similarly, if a thin, flat plate covers the region bounded by x 1 = g 1 ( y ) , x 2 = g 2 ( y ) , y = c and y = d , the y- coordinate of the centroid of the plate is given by the equation as follows.” y ¯ = ∫ c d y ( x 2 − x 1 ) d y ∫ a b ( x 2 − x 1 ) d y Calculation: The equation of a circle with radius a is, x 2 + y 2 = a 2 . Note that, a hemisphere is generated by rotating a quarter circle about the y axis. Therefore, x ¯ = 0

11th Edition

ISBN: 9780134437705

Author: Washington

Publisher: PEARSON

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Chapter 26.4, Problem 31E

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The centroid of the northern hemisphere of Earth with radius 6370 km.

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Chapter 26.4, Problem 30E

Chapter 26.4, Problem 32E

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Chapter 26 Solutions

Basic Technical Mathematics

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Ch. 26.1 - A car crosses an intersection as a fire engine...Ch. 26.1 - In designing a highway, a civil engineer must...Ch. 26.1 - Prob. 11E Ch. 26.1 - Prob. 12E Ch. 26.1 - A certain Chevrolet Corvette goes from 0 mi/h to...Ch. 26.1 - Prob. 14E Ch. 26.1 - Prob. 15E Ch. 26.1 - Prob. 16E Ch. 26.1 - Prob. 17E Ch. 26.1 - Prob. 18E Ch. 26.1 - Prob. 19E Ch. 26.1 - Prob. 20E Ch. 26.1 - Prob. 21E Ch. 26.1 - Prob. 22E Ch. 26.1 - Prob. 23E Ch. 26.1 - Prob. 24E Ch. 26.1 - Prob. 25E Ch. 26.1 - Prob. 26E Ch. 26.1 - The voltage across a 3.75-μF capacitor in a...Ch. 26.1 - Prob. 28E Ch. 26.1 - Prob. 29E Ch. 26.1 - Prob. 30E Ch. 26.1 - Prob. 31E Ch. 26.1 - Prob. 32E Ch. 26.1 - Prob. 33E Ch. 26.1 - Prob. 34E Ch. 26.1 - Prob. 35E Ch. 26.1 - Prob. 36E Ch. 26.2 - Find the area in the first quadrant bounded by y =...Ch. 26.2 - Prob. 2PE Ch. 26.2 - In Exercises 1 and 2, make the given changes in...Ch. 26.2 - In Exercises 1 and 2, make the given changes in...Ch. 26.2 - Prob. 3E Ch. 26.2 - Prob. 4E Ch. 26.2 - 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