# Find the mass and density of a beam

1. Oct 15, 2014

### Dustinsfl

1. The problem statement, all variables and given/known data
I have a steel cantilever beam of length 5m, width 0.5m, and thickness 0.1m. The beam has uniform density.

2. Relevant equations
\begin{align*}
M &= \iint_D\rho(x, y)dxdy\\
\rho &= M/\ell
\end{align*}

3. The attempt at a solution
If I don't know the mass or density, how can I find either one when each is defined with the other?

2. Oct 15, 2014

### LCKurtz

The density is given to be constant, so just call it $\rho$. You have to decide what the units are, depending on whether it is a linear or volume density. Given your formulas above, maybe it's a linear density. In any case, since it is constant, you don't need an integral to calculate the mass.

3. Oct 15, 2014

### Dustinsfl

How do I find the mass then? Will it just be called $M = 5\rho$ or can I get an explicit value for $\rho$?

4. Oct 16, 2014

### Staff: Mentor

With the given information all you can do is write expressions that represent mass and density. If the density is volume density ($\rho$ in units of kg/m3), then the mass would be $V\rho$.

5. Oct 16, 2014

### vela

Staff Emeritus
Perhaps you're meant to look up the density of steel.