Finding the Center of Mass of a Meter Stick with Variable Mass Density

[XwakeriderX]

Homework Statement

A meter stick has constant thickness and width , but the material that the stick is constructed from is very strange ... it has a variable mass density that is given by, ρ(x) = 0.800(1 + 0.00250x) grams/cm3 where x is measured in cm. Find the center of mass of the meter stick, as measured from it's left end.

The problem shown asks for the center of mass of a meter stick with a variable mass density, the picture is the solution to the problem! where did this formula come from??

Homework Equations

Xcm=(M1X1+m2x2)/(M1+m2)

The Attempt at a Solution

The hint says to use two simple integrals using the volume element dV=Adx
Can someone please help me understand where they got these 2 integrals from?

 

[tiny-tim]

Hi XwakeriderX!

The hint says to use two simple integrals using the volume element dV=Adx
Can someone please help me understand where they got these 2 integrals from?

The first is the integral of the mass, ∫ ρ dx

The second is the integral of the moment of the mass, ∫ xρ dx

 

[XwakeriderX]

Ahh i see now thanks!