Find Mass & Center of Mass for a Rod of Length 38.5 cm

[chocolatelover]

Homework Statement

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?

Homework Equations

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

 

[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.