How Do You Calculate the Mass of a Rod with Non-Uniform Density?

[AstroturfHead]

I'm having a hard time with this.
A long thin rod lies along the x-axis. One end is at x=2.00 m and the other at x=3.00 m. Its linear mass density λ = 0.300 x2+ 0.500, in kg/m. Calculate mass of the rod.

Can anybody help?

 

[Justin Lazear]

I take it you mean \lambda = .300x^2 + .500?

Note that

m = \int_{x_1}^{x_2}\lambda(x) dx.

--J

 

[AstroturfHead]

But then how would I find the center of mass?

 

[Justin Lazear]

The center of mass is just the weighted average of the density. You really should be able to look these formulas up on your own, or memorize them.

x_{CM}= \frac{1}{m}\int_{x_1}^{x_2} x \lambda(x) dx

--J