Unformatted text preview: obeys an inverse square law, F = k/r 2 and 9 . 8 m = k/ 6378100 2 , k = 398665564178000 m and W = 62505380 m . Now suppose that the initial velocity of the object, v , is just enough to get it to inﬁnity, that is, just enough so that the object never slows to a stop, but so that its speed decreases to zero, i.e., so that v 1 = 0. Then 62505380 m = W =mv 2 1 2 + mv 2 2 = mv 2 2 so v = √ 125010760 ≈ 11181 meters per second , or about 40251 kilometers per hour. This speed is called the escape velocity . Notice that the mass of the object, m , cancelled out at the last step; the escape velocity is the same for all objects. Of course, it takes considerably more energy to get a large object up to...
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 Spring '07
 JonathanRogawski
 Math, Calculus, Energy, Kinetic Energy, Mass, dx

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