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HW 18 Prob extra 5_128 - PROBLEM 5.128 Locate the centroid...

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Unformatted text preview: PROBLEM 5.128* Locate the centroid of the volume generated b of the sine curve shown about the x axis. y revolv1ng the portion SOLUTION First, note that symmetry implies El H 0 2:0 Choose as the element of Volume a disk of radius r and thickness dx. Then , dV = m'zdx, in = x New r = lasing— . 2a so that i dV = flbz sin2 _7z_x 2a 2a Then _ V = I 7:222 sin2 fidx a 2a = 72‘ 2 [£- Sinfifa 2 E. a a _ 2 a a ~ flb [(27) ~ (5)] ——1-7tab2 2 _-__ _ 2a 2 . 2 fl and . J-xELdV — L x[7rb sun 2a dx Use integration by parts With . fix u=x dV=srn2— 2a x Sin—7L3“ du=dx =—— ‘ a 2 27: = 0.648687za2b2 35V: [315,3de 3c‘(—;-7zab2]= 0.64868n'a2b2 or 2:129752 4 ...
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