Lecture06 - Universal Gravitation Newtons Law of Universal...

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Unformatted text preview: Universal Gravitation Newtons Law of Universal Gravitation Every particle in the Universe attracts every other particle with a force that is directly proportional to the product of their masses and inversely proportional to the distance between them G is the universal gravitational constant and equals 6.673 x 10-11 Nm 2 / kg 2 Law of Gravitation, cont This is an example of an inverse square law The magnitude of the force varies as the inverse square of the separation of the particles The law can also be expressed in vector form Notation F 12 is the force exerted by particle 1 on particle 2 The negative sign in the vector form of the equation indicates that particle 2 is attracted toward particle 1 F 21 is the force exerted by particle 2 on particle 1 More About Forces F 12 = - F 21 The forces form a Newtons Third Law action-reaction pair Gravitation is a force that always exists between two particles, regardless of the medium between them The force decreases rapidly as distance increases A consequence of the inverse square law G vs. g Always distinguish between G and g G is the universal gravitational constant It is the same everywhere g is the acceleration due to gravity g = 9.80 m/s 2 at the surface of the Earth g will vary by location Gravitational Force Due to a Distribution of Mass The gravitational force exerted by a finite-size, spherically symmetric mass distribution on a particle outside the distribution is the same as if the entire mass of the distribution were concentrated at the center For the Earth, Newtons Verification He compared the acceleration of the Moon in its orbit with the acceleration of an object falling near the Earths surface He calculated the centripetal acceleration of the Moon from its distance and period The high degree of agreement between the two techniques provided evidence of the inverse square nature of the law Moons Acceleration Newton looked at proportionality of accelerations between the Moon and objects on the Earth Centripetal Acceleration The Moon experiences a centripetal acceleration as it orbits the Earth Newtons Assumption Newton treated the Earth as if its mass were all concentrated at its center He found this very troubling When he developed calculus, he showed this assumption was a natural consequence of the Law of Universal Gravitation Measuring G G was first measured by Henry Cavendish in 1798 The apparatus shown here allowed the attractive force between...
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This note was uploaded on 10/25/2009 for the course PHYS 1501Q taught by Professor Bloomfield during the Fall '08 term at UConn.

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Lecture06 - Universal Gravitation Newtons Law of Universal...

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