What is the strength of the gravitational field?

[Workout]

Homework Statement

What is the strength of the gravitational field on the ground just above the oil deposit? Hint: Consider the missing mass as a sphere with a negative mass.

Given: a spherical oil deposit with radius 200m at a centre of depth 2.0km. The density of the Earth's crust is 2700 kg/m^3 and the crude oil is 900 kg/m^2. The strength of the gravitational field in the surrounding area is 9.81 N/kg.

Homework Equations

a = GM/r^2

The Attempt at a Solution

Okay I'm a little confused with this question. Isn't the strength of the gravitational field on the ground just above the oil deposit 9.81 m/s^2? It already said in the problem that the gravitational field in the surrounding area was 9.81 N/kg in my problem.

 

[Dick]

Homework Statement

What is the strength of the gravitational field on the ground just above the oil deposit? Hint: Consider the missing mass as a sphere with a negative mass.

Given: a spherical oil deposit with radius 200m at a centre of depth 2.0km. The density of the Earth's crust is 2700 kg/m^3 and the crude oil is 900 kg/m^2. The strength of the gravitational field in the surrounding area is 9.81 N/kg.

Homework Equations

a = GM/r^2

The Attempt at a Solution

Okay I'm a little confused with this question. Isn't the strength of the gravitational field on the ground just above the oil deposit 9.81 m/s^2? It already said in the problem that the gravitational field in the surrounding area was 9.81 N/kg in my problem.

They mean that it's 9.81m/s^2 at a large distance from the oil deposit. It will be a little less over the oil deposit. You should take it to mean that it would be 9.81m/s^2 if the oil deposit weren't there.

 

[Workout]

Ok. How do I start this problem?

 

[Dick]

Ok. How do I start this problem?

Follow the hint they gave you. You know the initial g value at the surface due to the solid sphere (without the oil). Add the negative g value you would get from a sphere of negative mass at the position of the oil deposit. Make the negative mass of the sphere enough to reduce the density as much as the oil reduces the density of the earth.

 

[Workout]

So g = G(-m)/r^2

where G = 6.67x10^-11
r = 2000m
So I get m = -5.997x10^16 x g

So then I equate what you were saying about reducing the density as much as the oil reduces the density of the earth.

-5.997x10^16 x g / 900 kg/m^3 = 2700kg/m^3

And I solve for g and I get -4.05x10^-11 m/s^2.

 

[Dick]

So g = G(-m)/r^2

where G = 6.67x10^-11
r = 2000m
So I get m = -5.997x10^16 x g

So then I equate what you were saying about reducing the density as much as the oil reduces the density of the earth.

-5.997x10^16 x g / 900 kg/m^3 = 2700kg/m^3

And I solve for g and I get -4.05x10^-11 m/s^2.

That's not the way to 'reduce the density'. If the Earth has a density of 2700kg/m^3 and you want to reduce it to 900kg/m^3 you need a sphere of density -1800kg/m^3 sitting where the oil is. Compute the g created by that.