(696) Problem 9: You are given a rectangular block of length a. width b and heig
ID: 1770748 • Letter: #
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(696) Problem 9: You are given a rectangular block of length a. width b and height c that has a non-uniform density such that when the rectangle is placed in the xy-plane with one corner at the origin and the block placed in the first quadrant with the two edges along the x and y-axes, the density is given by the following (x,y,z-P0nz, where 01s a constant 17% Part (a) Write an expression for the center of mass Xcm. 7 8 9 Submit Hint I give up! Hints: 090 deduction per hint Hints remaining Feedback: deduction per feedback. 17% Part (b) Write an expression for the center of mass yen. 17% Part (c) Write an expression for the center of mass Zen. - 17% Part (d) For a = 2.1 cm, b = 1.75 cm , and c = 1.25 crn, determine the center of mass of the block, X,m - 17% Part (e) For a = 2.1 cm, b = 1.75 cm. and c = 1.25 cm, determine the center of mass of the block, Yem. - 17% Part (f) For a = 2.1 cm, b = 1.75 cm, and c = 1.25 cm, determine the center of mass of the block, Zem.Explanation / Answer
a] Xcm = integral rho x dx dy dz / integral rho dx dy dz
= integral x^2yz dx dy dz / integral xyz dx dy dz
= [1/12 a^3 b^2c^2] /[1/8 a^2b^2c^2]
= 2a/3
b] similarly Ycm = 2b/3
c] Similarly Zcm = 2c/3
d] Xcm = 2*2.1/3 = 1.4 cm
e] Ycm = 2*1.75/3 = 1.167 cm
f]Zcm = 2*1.25/3 = 0.833 cm
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