Center of mass

  • Thread starter MozAngeles
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  • #1
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Homework Statement


Find teh center of mass of a thin infinite refion in the first quadrant bounded by the coordinate axes and the curve y=e-2x, if ρ(density)= xy


Homework Equations





The Attempt at a Solution


I set M= ∫∫ xy dydx where y goes from 0 to y=e-2x, and x goes from 0 to infinity. I solved this and got 1/8

but when i try to calculate Mx and My the integration are impossible.
 

Answers and Replies

  • #2
You're doing the integral wrong, mate! What have you got so far?
I get [tex] \int_0^{e^{-2x}} y dy = \left[y^2/2\right]_0^{e^{-2x}} = e^{-4x}/2[/tex]
[tex] M = \int_0^\infty dx \int_0^{e^{-2x}} dy xy = \int_0^\infty dx x \int_0^{e^{-2x}} dy y = \int_0^\infty x e^{-4x}/2 = 1 / 32[/tex]
Now put one additional x or y, respectively into your integrand and do the calculation for Mx and My.
 

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