PHY183-Lecture20-1 - Center of Mass and Center of Gravity...

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1 February 21, 2012 Physics for Scientists&Engineers 1 1 Physics for Scientists & Engineers 1 Fall Semester 2011 Lecture 21 Center of Mass February 21, 2012 Physics for Scientists&Engineers 1 2 Center of Mass and Center of Gravity In our previous discussions this semester we have always treated the location of objects as a single point “A car is located at x = 5.5 m…” Of course, the car is not ALL at x =5.5 m The natural choice for the location of the car is the center of mass of the car The center of mass of also the point at which we can imagine the force of gravity acting Center of gravity The center of mass of an object is defined as the point at which we can imagine all the mass of an object to be concentrated. Combined Center of Mass for Two Objects We have two identical objects of equal mass and want to find the center of mass for the combination of the two The center of mass lies exactly midway between the individual centers of mass of the two objects If one object is more massive than the other object, the center of mass will be closer to the more massive one The general formula for calculating the location of the center of mass for two masses is February 21, 2012 Physics for Scientists&Engineers 1 3 R = r 1 m 1 + r 2 m 2 m 1 + m 2 February 21, 2012 Physics for Scientists&Engineers 1 4 Clicker Quiz In figure above, M represents the center of mass of a system of two masses m 1 and 2 . What can we say about the relative magnitude of the two masses 1 and 2 ? A. 1 < 2 B. 1 > 2 C. 1 = 2 D. Based solely on the information given in this figure, it is not possible to decide which of the two masses is larger February 21, 2012 Physics for Scientists&Engineers 1 5 Clicker Quiz (Solution) In figure above, represents the center of mass of a system of two masses 1 and 2 . What can we say about the relative magnitude of the two masses 1 and 2 ? 1 < 2 B. m 1 > 2 1 = 2 D. Based solely on the information given in this figure, it is not possible to decide which of the two masses is larger Center of Mass of Earth and Moon The Earth has a mass of 5.97·10 24 kg and the Moon has a mass of 7.36·10 22 kg The Moon orbits the Earth at a distance of 384,000 km PROBLEM How far from the center of the Earth is the center of mass of the Earth-Moon system? THINK Take the center of mass of the Earth to be located at x = 0 February 21, 2012 Physics for Scientists&Engineers 1 6
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2 Center of Mass of Earth and Moon Take the center of mass of the Moon to be located at x = 384,000 km The center of mass of the Earth-Moon system will be located along a line connecting their centers of mass SKETCH RESEARCH Define an -axis and place the Earth at E = 0 and the Moon at M = 384,000 km, putting the center of mass of the Earth-Moon system at February 21, 2012 Physics for Scientists&Engineers 1 7 X = x E m E + x M m M m E + m M Center of Mass of Earth and Moon SIMPLIFY Taking E = 0 CALCULATE ROUND DOUBLE-CHECK The center of mass of the Earth-Moon system
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PHY183-Lecture20-1 - Center of Mass and Center of Gravity...

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