Answer: Centripetal Force An object of mass moves at a constant speed in a circular path

Chapter 12, Problem 86

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Centripetal Force An object of mass m moves at a constant speed v in a circular path of radius r. The force required to produce the centripetal component of acceleration is called the centripetal force and is given by F=m\(v^{2}\)/r. Newton’s Law of Universal Gravitation is given by F=GMm/\(d^{2}\), where d is the distance between the centers of the two bodies of masses M and m, and G is a gravitational constant. Use this law to show that the speed required for circular motion is \(v=\sqrt{G M} / r\)

Text Transcription:

v^2

d^2

v=\sqrt{G M / r}