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(III) The center of a 1.00 $\mathrm{km}$ diameter spherical pocket of oilis 1.00 $\mathrm{km}$ beneath the Earth's surface. Estimate by whatpercentage $g$ directly above the pocket of oil would differfrom the expected value of $g$ for a uniform Earth Assumethe density of oil is $8.0 \times 10^{2} \mathrm{kg} / \mathrm{m}^{3} .$

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gravity will decrease

Physics 101 Mechanics

Chapter 6

Gravitation and Newton's Synthesis

Physics Basics

Newton's Laws of Motion

Applying Newton's Laws

Gravitation

Feemo Fellow

August 31, 2020

why we minus accellration due to bubble earth

University of Michigan - Ann Arbor

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03:43

In physics, dynamics is the branch of physics concerned with the study of forces and their effect on matter, commonly in the context of motion. In everyday usage, "dynamics" usually refers to a set of laws that describe the motion of bodies under the action of a system of forces. The motion of a body is described by its position and its velocity as the time value varies. The science of dynamics can be subdivided into, Dynamics of a rigid body, which deals with the motion of a rigid body in the frame of reference where it is considered to be a rigid body. Dynamics of a continuum, which deals with the motion of a continuous system, in the frame of reference where the system is considered to be a continuum.

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In physics, orbital motion is the motion of an object around another object, which is often a star or planet. Orbital motion is affected by the gravity of the central object, as well as by the resistance of deep space (which is negligible at the distances of most orbits in the Solar System).

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So I have a pocket of oil. Ah, kilometer deep in to earth. So we're essentially trying to find is the dance of the grab the acceleration due to gravity on top of this oil bubble. So we can say that the gravity of the oil present is going to be equal to the gravity due to the uniform earth minus thie Exactly acceleration due to gravity of the Earth double and then plus thie specific the ex effective gravity of the oil bubble. Thus we can say that the change n g is simply going to be equal to the acceleration of gravity of thie oil present minus the acceleration of gravity of a uniform earth. And this is furthermore equaling Jesu bubble of oil minus g of the earth of the bubble of Earth matter So now we can say that Delta G equals g mass of the bubble of oil divided by r squared minus the gravitational constant terms the mass of thie Earth matter bubble again divide by r squared And this is giving us g over r squared times the mass of the bubble of oil minus the mass of the bubble of earth and So at this point we can say that Delta G is going to be equal to G over r squared times the density of the oil minus the density of a uniform earth multiplied by for thirds pi times the radius of the bubble Cute. So at this point, then we can solve for the density of a uniformed earth. This is going to be equal to the mass of the earth, divided by 4/3 4/3 pi times the radius of the earth Cute. And this is giving us again. 4/3 pi the radius of the earth 6.38 times 10 to the sixth meters quantity cubed. And then for the numerator 5.98 times 10 to the 24th kilograms. And this is giving us approximately 5.50 times 10 to the 30 kilograms per cubic meter. So keep this value in mind. So when we we can actually solve this, solve this now and send it out, the gene equals 6.67 times 10 to the negative 11th. The gravitational constant divided by the radius squared, so 1000 meters squared. So that's how that's the how far beneath the earth's surface. This bubble is and then times 800 the density of oil minus 5500 the density of the earth times 4/3 pi times 500 quantity cute and this equals negative. 1.6414 times 10 to the negative forthe meters per second squared. Now we're not done yet just yet. Just keep note of that. At this point, we need to find Delta G over G times 100% and so this would simply be equal to negative 1.6414 times 10 to the negative fourth meters per second squared, divided by 9.8 meters per second squared and then again times 100%. And this is giving us negative 1.7 times 10 to the negative third percent. So here, because because it's negative, this means that the effective gravity will decrease. This is our final answer. That is the end of the solution. Thank you for watching

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