What is the strength of the gravitational field?

AI Thread Summary
The discussion centers on calculating the strength of the gravitational field just above an oil deposit, considering it as a sphere with negative mass. The initial gravitational field strength is given as 9.81 N/kg, but it is noted that this value would be slightly less above the oil deposit due to the missing mass. Participants suggest using the hint provided in the problem to account for the negative mass effect, which is necessary to adjust the density from 2700 kg/m^3 to 900 kg/m^3. The calculations involve determining the gravitational effect of a sphere with a density of -1800 kg/m^3 to accurately reflect the reduced density caused by the oil. Ultimately, the correct approach is emphasized to compute the gravitational field strength above the oil deposit accurately.
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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.
 
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Workout said:

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.
 
Ok. How do I start this problem?
 
Workout said:
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.
 
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.
 
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Workout said:
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.
 
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