- #1

- 43

- 0

## Homework Statement

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

## Homework Equations

Circle equation: x

^{2}+y

^{2}=r

^{2}

Mass density: rho=x+y

## 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.