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Centroid of cylindrical cone

by zandria
Tags: centroid, cone, cylindrical
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zandria
#1
Jun2-09, 01:47 PM
P: 15
1. The problem statement, all variables and given/known data

Determine the centroid of volume for a right circular cone with base diameter of 100mm and an altitude of 200mm.

2. Relevant equations

I know that if the my xy-plane is parallel to the base of the cylindrical cone then the x and y coordinates of the centroid must be zero and therefore I only need to find the z coordinate of the centroid.

The equation I am using is

[tex]z_c = \frac{1}{M} \int_{body} z dm[/tex]

where M is the total mass and [tex]dm = \rho dV[/tex]

3. The attempt at a solution

I am trying to use cylindrical coordinates but I think my limits of integration are incorrect. I have tried to solve the integral above with the following limits.

[tex]0<\theta<2\pi [/tex]

[tex]0<r<50 [/tex]

[tex]0<z<(200-r/4)[/tex]

I'm not sure if the limits for the z coordinate is correct. Am I on the right path?
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LowlyPion
#2
Jun2-09, 02:12 PM
HW Helper
P: 5,341
Well, I wouldn't worry with polar coordinates, because you are dealing with basically a stack of disks aren't you?

They are each have a weight of ρ*πrē

Exploit then the fact that r is a function of z, and your integral should be pretty straight forward shouldn't it?
zandria
#3
Jun2-09, 02:28 PM
P: 15
Thank you. I was essentially doing the right thing on my first try before I changed everything, but I made an algebra mistake when trying to use cylindrical coordinates. Thanks for the short cut ... less room for stupid mistakes.


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