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physics test 4 review

physics test 4 review - 12-1 12-2 Newton's Law of Universal...

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12-1 - 12-2 Newton's Law of Universal Gravitation and the Attraction of Spherical Bodies Gravitation is the phenomenon that between every two objects there is a force of attraction. Newton’s law of universal gravitation describes the behavior of this force. Between any two point masses m 1 and m 2 , the magnitude of the gravitational force on each mass due to the other is given by where r is the distance between the two masses and G is a constant called the universal gravitational constant . The value of this constant is The force on each mass points directly at the other mass because each mass attracts the other toward it. For situations involving more than two masses we apply the principle of superposition : The net gravitational force on any given mass due to two or more other masses is the vector sum of the gravitational forces due to each of the other masses individually. Exercise 12-1 Earth and Venus On average Earth and Venus are separated by about 4.14 x 10 10 m. What is the magnitude of the gravitational force between them at this separation? Solution : In this problem we are given only the distance between Earth and Venus. To calculate the gravitational force between them we will need to look up their masses. The masses are as follows: M E = 5.97 x 10 24 kg; M V = 4.87 x 10 24 kg Having all the data we need, the force can now be calculated. Remember, this is the magnitude of the force exerted on both Earth and Venus. The above law of universal gravitation is stated for point masses. The detailed calculations for extended bodies can become complicated, but Newton figured out that the final result for spherical bodies becomes simple again. Basically, Newton showed that two completely separated, uniform spherical bodies attract each other as if they were point masses with all their mass located at their respective centers. This fact explains why the point-mass formula given above works so well for large objects like Earth and the Moon. Treating the Earth as a point mass M E located at the center of the Earth provides further insight into the acceleration due to gravity that we measure near Earth’s surface. Objects near the surface are a distance from the center roughly equal to the radius of the Earth, R E . Using Newton's law of gravity we can conclude that the acceleration due to gravity near the surface is given by
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With this result you can also see that the higher you go above the surface, the farther you are from Earth’s center, and therefore the weaker the effect of gravity, resulting in a smaller acceleration. Example 12-2 Martian Gravity What is the acceleration due to gravity on the surface of Mars? Picture the Problem The sketch is a representation of the planet Mars, with its radius extending from the center to the surface.
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