Artificial gravity in Monolith Burger is created by a heavy plate of ultra-dense metal?

Question

installed under the floor.

http://www.spacequest.net/misc/fanfiction/fanstories/sq3fanfiction.shtml

The plate has a shape of uniform disk of radius
R=10m and induces gravity 1g (9.8m/s²) in the
center of the diner.

What is the mass of the plate?

Answer 1

Assume that R is big compared to your distance from the plate, so that the gravitational field is uniform.

Gauss' Law for gravity:
Gravitational flux = 4 pi G M,
where M is the mass enclosed by the surface

Make a Gaussian pillbox or area A, so flux = 2gA

M = gA / 2 pi G
A = pi r^2,
so M = g r^2 / 2G--about 10^13 kg

Answer 2

The monolitic burger induced gravity pressure is 4.9510^20 Newton per square metres.
So the weight of the mass on a disc 10m radius would be the area times the induced gravity pressure times the area of the disk.
Weight =1.555x10^23 Newtons.
If the acceleration on that surface = 9.8 m /sec^2 then the mass would be force (weight) divide by acceleration=1.587 x10^22 kilogrames.
The acceleration postulated on the disc has to be greater than 9.8 otherwise its mass is almost the mass of the earth.

Answer 3

The equation I would use would be the following:

F(i) = M(i)m/R(i)^2

Problem is you have the Force and the radius but there are two variables still left. Mass of the disc = M(i) and mass of another object = m.

I don't know how you would solve for that.

OR you could use from Newton's Laws:

g = GM/R^2

where G = universal constant and you have g and R already given to you so it seems a pretty straightforward equation to solve.

Peace

Answer 4

I think that the answer has already been worked out above, I just wanted to point out that it isn't "artificial gravity" any more than the Earth has "artificial gravity". Gravity is gravity, "artificial gravity" refers to an acceleration (elevator going up or spinning space station) that acts like gravity.

Answer 5

Hi. I would guess an amount equal to the Earth's. It would be a very thick plate, more like a cylinder, in this case so it does not meet the requirement. Ultra-dense indeed!