lab11_solns_f11

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

This preview shows pages 1–3. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

{[ snackBarMessage ]}

### Page1 / 5

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

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online