# p3 - Problem Set 3 Problem 3.1 Center of Gravity for a Bent...

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Problem Set 3 Problem 3.1 Center of Gravity for a Bent Rod Determine the distance x C and y C to the center of gravity of the bent rod. Figure P9.1: Problem 9.1

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Problem 3.2 Centroid of a Composite Section Determine the location y C of the centroid of the beam’s cross sectional area. Neglect the size of the corner welds at A and B for the calculation. Figure P9.2: Problem 9.2
Problem 3.3 Centroid of a Tapered Cross Section Locate the centroid y C of the concrete beam with the tapered cross section shown. Figure P9.3: Problem 9.3

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Problem 3.4 Find the x -coordinate of the centroid of the indicated region where A = 2 m and k = π/ 8 m - 1 . x y O y = A cos( kx ) Figure 3.1: Problem 3.1
Problem 3.5 Determine the area and the centroid of the area. Solution % y(x) = x^(3/2) % where 0<x<a and 0<y<a a = 1; % m % differential element % dA = y dx = x^(3/2) dx % centroid of the differential element is at % x and y/2 = (1/2) x^(3/2) % A = int(dA) where 0<x<a A = int( x^(3/2),x,0,a); % A = 0.400 (m^2) % My = int(x dA) where 0<x<a My = int(x*x^(3/2),x,0,a); xC = My/A; % xC = 0.714 (m)

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% Mx = int(y/2 dA) where 0<x<a Mx = int((1/2)*x^(3/2)*x^(3/2),x,0,a); yC = Mx/A; % yC = 0.312 (m)
Problem 3.6 Determine the area and the centroid of the area.

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Problem 3.7
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## This note was uploaded on 08/29/2011 for the course MECH 2110 taught by Professor Clark,b during the Spring '08 term at Auburn University.

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p3 - Problem Set 3 Problem 3.1 Center of Gravity for a Bent...

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