Change in Magnitude of Accleration due to gravity

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SUMMARY

The discussion focuses on calculating the change in the magnitude of the acceleration due to gravity (g) above a spherical oil deposit with a diameter of 350 m, using the densities of oil (1590 kg/m³) and normal soil (2500 kg/m³). The user initially calculated the masses of both substances as 3.57E10 kg and 5.612E10 kg, respectively, and derived acceleration values of 1.2228E-5 m/s² and 7.777E-6 m/s². However, the user reported an incorrect final result for the change in acceleration due to gravity, indicating a need for further verification of calculations.

PREREQUISITES
  • Understanding of gravitational acceleration and its formula (a = GM/r²)
  • Knowledge of density and its role in mass calculations
  • Familiarity with spherical volume calculations (4/3πr³)
  • Basic algebra for manipulating equations and solving for unknowns
NEXT STEPS
  • Review the gravitational acceleration formula and its application in real-world scenarios
  • Recalculate the mass of the oil deposit using the correct volume formula
  • Verify the calculations for acceleration due to gravity with accurate values
  • Explore methods for detecting subsurface density variations in geophysical studies
USEFUL FOR

Students in physics or geology, geophysicists, and professionals involved in mineral exploration or subsurface resource detection will benefit from this discussion.

mandi182
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Homework Statement



When searching for gold, measurements of g can be used find regions within the Earth where the density is larger than that of normal soil. Such measurements can also be used to find regions in which the density of the Earth is smaller than normal soil; such regions might contain a valuable fluid (oil). Consider a deposit of oil that is 350 m in diameter and just below the surface of the Earth. For simplicity, assume the deposit is spherical. Estimate the change in the magnitude of the acceleration due to gravity on the surface above this deposit. Assume that the density of the oil is 1590 kg/m3 and the density of normal soil and rock is 2500 kg/m3. Note: Companies that search for valuable minerals actually use this method.

Homework Equations


a=GM/r^2 and also 4/3pi (r^3)



The Attempt at a Solution


I solved for the Mass of each which was 3.57E10 and 5.612E10. Then I solved for accelaration due to gravity on both, which was 1.2228168630857E-5 and 7.777E-6
and then subtracted those numbers to get the change in acceleration due to gravity.

The answer I got was incorrect, so I am not sure what to do next.

Thanks!
 
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I get the same numbers for the masses, but not for the accelerations.
Try that last calc again and show your work if you would like more feedback.
 

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