# Homework Help: Linear density

1. Apr 30, 2008

### chocolatelover

1. The problem statement, all variables and given/known data
A rod of length 38.5 cm has linear density (mass-per-length) given by the following equation, where x is the distance from one end.

λ=50.0g/m+16.5g/m^2

a. What is its mass in g?

b. How far from the x=0 end is its center of mass in m?

2. Relevant equations

3. The attempt at a solution

For part a., could I just divide by the mass?

Could someone please show me how to do this problem? I really don't understand what it's asking for.

Thank you very much

2. Apr 30, 2008

### CrazyIvan

For part A:

By definition,
$$mass = \lambda \cdot length$$

Since linear density isn't constant, you will need to integrate. But first you need an expression for how the mass of an infinitesimal length of the rod. Can you figure out what this is?

After you have an expression for how $$dm$$ relates to $$dx$$, you can integrate both sides to get the total mass.

For part B, start with the general expression for center of mass.

Last edited: Apr 30, 2008