Posted by James on .
The density of a 5.0m long rod can be described by the linear density function λ(x) = 140 g/m + 14.8x g/m2. One end of the rod is positioned at x = 0 and the other at x = 5 m.
(a) Determine the total mass of the rod.
(b) Determine the centerofmass coordinate.
I found the total mass of the rod to be 885 g, how does one find the center of mass coordinate in the xdirection given this information?
Thank you in advance.

Physics 
Elena,
m=∫ρ•dx =∫(140+14.8x) •dx =
= ∫140•dx+∫14.8•x•dx =
=140•x + 14.8x²/2=
=140•5 + 14.8•25/2 =885 g.
Calculate the integral
∫ρ•x•dx =
=∫(140+14.8x) •x •dx =
= ∫140•x•dx+∫14.8•x²•dx =
=140•x²/2 + 14.8x³/3=
=140•25/2 + 14.8•125/3=2367 kg.
x(c/m/) =∫ρ•x•dx/∫ρ•dx =2367/885=2.67 m.
C.M. (2.67 m; 0)