# Linear Mass Density Problem

1. Mar 2, 2005

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?

2. Mar 2, 2005

### Justin Lazear

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

Note that

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

--J

3. Mar 2, 2005

But then how would I find the center of mass?

4. Mar 2, 2005

### 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