Center of mass of a cone

1. Oct 13, 2011

GreenPrint

1. The problem statement, all variables and given/known data

Calculate the X_com of the cone of mass M in terms of quantities given in the picture. The density of the cone is uniform.

See the attachments for the picture.

2. Relevant equations

3. The attempt at a solution

When I did it I got

X_com = (3L)/2

and I am unsure if this is correct or not. The infinitely small sections are circular disks of area pi R^2 were r is the radius of the infinitely small disk and a volume just an infinitely small width dx times the area. therefore the density

rho = dm/dV = dm/(pi R^2 dx)

I sort of got confused when I did because the radius changes with respect to x and during the middle of the test I sort of rushed this problem and thought that it just canceled out in the end but believe I may be wrong

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2. Oct 13, 2011

SteamKing

Staff Emeritus
You have shown that the center of mass of the cone in the x-direction lies outside of the cone. Your answer is not correct.

Yes, the radius changes with respect to x, but it does so in a predictable manner.

Care to reformulate your solution to the c.o.m.? Concentrate on writing the moment equation using the origin as the reference point.

3. Oct 13, 2011

GreenPrint

what is the moment equation?

4. Oct 14, 2011

SteamKing

Staff Emeritus
It's an essential component in your c.o.m. calculation.

d(moment)/dx = x * dm

5. Dec 12, 2011

GreenPrint

Im not exactly sure what is meant by moment in your equation. Can someone tell me. I recalculated it except this time I got 3/4 R. I believe the answer is 3/4 L though. I'm not exactly sure what I did wrong. Thanks for any help.

sorry that a four in the denominator magically disappeared from my work towards the end and magically reappeared. I just realized this. Everything else is correct though I believe, except some reason I got 3/4 R instead of 3/4 L

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Last edited: Dec 12, 2011