1. ## Lamina Workouts

Given a lamina of uniform density $\displaystyle \rho$, bounded by $\displaystyle y = \sqrt{x} , y=0 , x=4.$

1. Set up an integral to find m, the mass of the lamina.
2. Find m, the mass of the lamina
3. Set up Integral to find Mx
4. Find Mx
5. Set up integral to find My
6. Find My
7. Find the center of mass.

2. m = $\displaystyle \rho \int_0^4 \sqrt{x} * dx = \frac{16}{3}$

Mx = $\displaystyle \rho \int_0^4 \frac{\sqrt{x}}{2} * \sqrt{x} * dx = 4$

y = $\displaystyle \frac{.25}{3} = \frac{1}{12}$

Center: (x, $\displaystyle \frac{1}{12}$)

My = ?

3. Originally Posted by Selim
m = $\displaystyle \rho \int_0^4 \sqrt{x} * dx = \frac{16}{3}$

Mx = $\displaystyle \rho \int_0^4 \frac{\sqrt{x}}{2} * \sqrt{x} * dx = 4$

y = $\displaystyle \frac{.25}{3} = \frac{1}{12}$

Center: (x, $\displaystyle \frac{1}{12}$)

My = ?
$\displaystyle m= \frac{16}{3}\rho$

$\displaystyle M_x=4\rho$

$\displaystyle y = \frac{M_x}{m} = \frac{3}{4}$

$\displaystyle M_y=\rho\int_0^4x\sqrt{x}\,dx$

$\displaystyle x=\frac{M_y}{m}$