- #1

Phymath

- 184

- 0

[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)

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?

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?

Last edited: