Calculating Mass of Cloud with Density D(ro)

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i had to do this some time ago:

assume you have a large cloud or radius 2 km, and its density is defined as D(ro) = 3 - ro (btw i can't find the letter 'ro' anywhere... )

what i the mass of the cloud?

i did it this way: mass = density * volume, so in this case it equals D(ro) * dV, so integrating (triple integral) over V yeilds (triple integral) (3 - ro) * (ro)^2 sin (phi) d ro d theta d phi. is that right?

i hope you can understand my *terrible* notation
 
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Is this what you meant?
\int_{0}^{\pi}\int_{0}^{2\pi}\int_{0}^{2}(3-\rho)\rho^{2}\sin\phi{d}\rho{d}\theta{d}\phi
If that's what you meant, I agree with you :smile:
 
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T@P said:
i had to do this some time ago:

assume you have a large cloud or radius 2 km, and its density is defined as D(ro) = 3 - ro (btw i can't find the letter 'ro' anywhere... )

what i the mass of the cloud?

i did it this way: mass = density * volume, so in this case it equals D(ro) * dV, so integrating (triple integral) over V yeilds (triple integral) (3 - ro) * (ro)^2 sin (phi) d ro d theta d phi. is that right?

i hope you can understand my *terrible* notation


For me it doesn't seem a problem in three dimentions,but rather in 2.I mean the cloud cound have a shape of a circle,and in this case,there should be integrations only after 2 coordinates:\rho and \phi.

It looks that way to me,since u're given the radius (of the circle).I've never heard of cilindric clouds,neither of circular ones.But since you aren't given the height,then it should be a circle.
Try to make calcuations for this case and cf.to the result.

Daniel.

EDIT:On the other hand,it might be a sphere.Though it's weird.Anyway,Arildno may be right and disregard what I've written above.
 
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On second thought, I guess they assumed a "disk-like" cloud.
So I would go with dexter's first suggestion.
 
actually the problem was supposed to come out as a triple integral, and yes that was what i meant arildno thanks. ( i think they might have specified a spherical cloud too)
 
You said "assume you have a large cloud or radius 2 km"

I would have assume a spherical cloud. In that case, the simplest thing to do is set up a coordinate system with (0,0,0) at the center of the cloud. The mass then is exactly what arildno said.
 
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