(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find the mass and the coordinates for the center of mass of a thin wire formed like a quarter circle.

2. Relevant equations

Circle equation: x^{2}+y^{2}=r^{2}

Mass density: rho=x+y

3. The attempt at a solution

I know that: x^{2}+y^{2}=cos^{2}(t)+sin^{2}(t)=1

This leads to: x^{2}+y^{2}=r^{2}(cos^{2}(t)+sin^{2}(t))=r^{2}

x=r*cos(t)

y=r*sin(t)

The quarter circle is described by the vector equation:

r(t)=r*cos(t)i+r*sin(t)j; 0<t<1/2*pi

The density function becomes:

rho=x+y=r*cos(t)+r*sin(t)=r(cos(t)+sin(t))

The line integral that I try to use: (C is the quarter circle wire)

M=∫[itex]_{C}[/itex](rho(x,y)*ds)=∫[itex]^{1/2*pi}_{0}[/itex](rho(x,y)*r'(t)*dt)

=r^{2}∫[itex]^{1/2*pi}_{0}[/itex](cos^{2}(t)-sin^{2}(t))*dt

This ends up in M=0.... FFFUUUU! The right answer is supposed to be 2r^{2}

I can't seem to find the right solution to this... please help.

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# Homework Help: Mass of 2 dimensional object - line integral

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