Question

What is the horizontal coordinate of the center of mass of this track?

Answer 1

`bar x = 5/4 " m"`

Explanation:

Combining the instructions:

`bar x = (int x dm)/(int dm) = (int_0^5 x * rho W y(x) dx)/(int_0^5 rho W y(x) dx)`

Eliminate constant, express function `y(x)`:

`= (int_0^5 x (x-5)^2/9 \ dx)/(int_0^5 \ (x-5)^2/9 dx)`

`= ([ x^4/36 - (10 x^3)/27 + (25 x^2)/18]_0^5)/([ (x-5)^3/27 ]_0^5) = (625/108)/(125/27) = 5/4`