Taking the potential energy to be zero at infinite separation, find the potentia

Question

Taking the potential energy to be zero at infinite separation, find the potential energy of a 15 kg object at the surface of the Earth. (Use 6.37 times 106 m for the Earth's radius.) -9.39e10 J Find the potential energy of the same object at a height above the Earth's surface equal to the Earth's radius. J Find the escape speed for a body projected from this height. km/s In order for an object to just escape a gravitational field from a particular location, it must have enough kinetic energy so that its total energy is zero.

Explanation / Answer

(a) PE = mgy PE = 15(9.8)(6.37e6) PE = 9.39e8 J (negative because it is trying to escape gravity) (b) at a point R away from the earth's surface, gravity will be decreased g = G(me)/(2re)^2 g = 0.25(Gme/re^2) g = 0.25(9.8) PE = mgy PE = (m)(0.25g)(2re) PE = 0.5(mg)(re) PE = 0.5 (9.39e8) PE = 4.69e8 J (negative again) (c) this energy must be converted to KE KE = 4.69e8 0.5mv^2 = 4.69e8 v = 7.91 km/s BOL

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