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Physics Regents 2013-2014 Video Project! ● Crafted by Robert Richner

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Goal: To be able to calculate the acceleration due to gravity at various locations on earth which have greatly differing altitudes. Using only physics and math, deduce the difference of the force due to gravity between the highest point on earth and the lowest.

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The Locations ● Mt. Chimborazo, Ecuador – While not as high as Mt. Everest, Chimborazo is located on the equator and actually is a farther distance from the earths center. ● The Dead Sea, which borders Jordan and Israel, is 427 meters below sea level making it one of the lowest places on earth's surface.

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Equations Fg = Gm1m2 r² Fg = mg (mg) = Gm1m2 r² g = Gm2 r²

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Definitions ● Fg = Force due to gravity ● G = Universal gravitational constant 6.67x10 - ¹¹ Nxm²/kg² ● m1 = mass of object being affected ● M2 = mass of the Earth = 5.98x10 24 kg ● r = Distance from center of the earth ● g = acceleration due to gravity

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Distances = r Mean radius of Earth – 6371 km = 6,371,000 m Elevation of Chimborazo – 6268 m above sea level BUT because of bulge it is 6384.4 km from the center of the earth. Elevation of Dead Sea – 427 m below sea level 6,370,573 m

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Chimborazo, Ecuador ● g = 6.67x10 -11 Nm²/kg² x 5.98x10 24 kg ● (6,384,400 m)² ● g = 9.785586045 m/s²

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The Dead Sea ● g = 6.67x10 -11 Nm²/kg² x 5.98x10 24 kg (6,370,573 m)² ● g = 9.82811036 m/s²

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Explanation ● The force due to gravity exerted by earth is proportional to the distance from earth's center. The farther away from the center the weaker the force will be. ● Therefore the closer you are to the Earth's center the stronger the force of gravity will be due to the force being exerted over a smaller distance.

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The Difference ● The determined difference of the force of gravity was approximately 0.04 m/s² ● While a small difference, it demonstrates the relationship between the distance (radius) and the acceleration due to gravity. ● The smaller the radius the larger the force of gravity will be due to the nature of division.

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The Breakdown ● By using the altered equation: g = Gm2 ● r² ● We are able to solve for g at various points on earth. These calculations are not perfectly correct because earth is not a perfect sphere, so unlike a perfect sphere the radius varies depending upon the location. ● By making a rough estimate of what the radius will be at a certain point an answer can be found.

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Finale ● Using Physics almost all questions can be eventually answered based on the scope. ● While a trivial matter, calculating the force due to gravity is a teaching experience and very informative about the world we live in and the force we are constantly subjected to, gravity.

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