lab11_solns_f11

lab11_solns_f11 - MATH 116 Lab 11 Solutions 1 For the...

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Unformatted text preview: MATH 116 - Lab 11 - Solutions 1. For the following lamina, compute i) the mass of the lamina, ii) the first moment of the lamina with respect to the y-axis, iii) the first moment of the lamina with respect to the x-axis, iv) the center of mass of the lamina. a) Bounded by x = 0, y = √ x , x = 1 with ρ = 5 kg/m 2 Solution: i) Mass = Z 1 ρ √ xdx = 5 x 3 / 2 3 / 2 1 x =0 = 10 3 kg ii) M y = Z 1 ρx √ xdx = Z 1 5 x 3 / 2 dx = 5 x 5 / 2 5 / 2 1 x =0 = 2 iii) M x = Z 1 ρ 2 ( √ x 2 ) dx = Z 1 5 2 xdx = 5 2 x 2 2 1 x =0 = 5 4 iv) The center of mass is at M y Mass , M x Mass = 2 10 / 3 , 5 / 4 10 / 3 = 3 5 , 3 8 b) Bounded by x = 0, y = √ x , y = 1 with ρ = 5 kg/m 2 Solution: i) Mass = Z 1 ρ (1- √ x ) dx = 5 x- x 3 / 2 3 / 2 1 x =0 = 5 3 kg ii) M y = Z 1 ρx (1- √ x ) dx = Z 1 5( x- x 3 / 2 ) dx = 5 x 2 2- x 5 / 2 5 / 2 1 x =0 = 1 2 iii) M x = Z 1 ρ 2 (1 2- √ x 2 ) dx = Z 1 5 2 (1- x ) dx = 5 2 x- x 2 2 1 x =0 = 5 4 iv) The center of mass is at M y Mass , M x Mass = 1 / 2 5 / 3 , 5 / 4 5 / 3 = 3 10 , 3 4 c) Bounded by x = 1, x = 3, y = 5 x- 5, y = x 2 + x- 5 with ρ = 3 kg/m...
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lab11_solns_f11 - MATH 116 Lab 11 Solutions 1 For the...

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