EXAMPLE 2 Find the mass and center of mass of a triangular lamina with vertices (0, 0), (1, 0), and (0, 2) if the density function is p(x, y) - 2+ 6x + 2y. SOLUTION The triangle is shown in the figure. (Note that the equation of the upper boundary is y = 2- 2x.) The mass of the lamina is )dA = (2 + 6x + 2y) dy dx L 2y + 6xy + y dx dx Video Example ) 16 Then the formulas for center of mass give xp(x, y) dA (2-2x (2x + 6x + 2xy) dy dx dx x) dx yo(x, y) dA (2y + 6xy + 2y) dy dx y-2-2 dx - 18x - 6x + dx %3D The current center of mass is (x, y) - 2

EXAMPLE 2 Find the mass and center of mass of a triangular lamina with vertices (0, 0), (1, 0), and (0, 2) if the density function is p(x, y) - 2+ 6x + 2y. SOLUTION The triangle is shown in the figure. (Note that the equation of the upper boundary is y = 2- 2x.) The mass of the lamina is )dA = (2 + 6x + 2y) dy dx L 2y + 6xy + y dx dx Video Example ) 16 Then the formulas for center of mass give xp(x, y) dA (2-2x (2x + 6x + 2xy) dy dx dx x) dx yo(x, y) dA (2y + 6xy + 2y) dy dx y-2-2 dx - 18x - 6x + dx %3D The current center of mass is (x, y) - 2

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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