[tex] \vec{g}(x,y,z) = -kG((x^3 y^2 z^2)\hat{e_x} + (x^2 y^3 z^2)\hat{e_y} + (x^2 y^2 z^3) \hat{e_z})[/tex] given this grav field (k is constant)(adsbygoogle = window.adsbygoogle || []).push({});

find the mass density of the source of this field, and what is the total mass in a cube of side 2a centered about the origin?

hmmm well we all know...[tex]\int \int \vec{g} \bullet d\vec{a} = 4 \pi G m_{enclosed}[/tex]

and density [tex] p = \frac{m}{V} [/tex] at least the overall density of it is (non-differential)

sooooo...[tex]\frac{1}{4 \pi G}\int\int\int (\nabla \bullet \vec{g}) dV = m_{source/enclosed}[/tex]

now the limits i made a cube of side 2a, because the flux through a box is easier when g is given in cart coords....any way i get...

[tex]m_{source} = \frac{-2}{3 \pi}G k a^9[/tex] how do I get a neg mass (unless this is dark matter which it very well could be) and I'm thinking i missed something about density cause why would it ask that first and then the mass enclosed second?...a lil help?

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# Grav field fun!

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