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Consider an object of mass m in a circular orbit of radius r and angular velocity w about a larger object of mass M and radius R, where M > m. (a) What is the the potential energy of the mass-m in its circular orbit, assuming that r > R? 23 (b) In 1. Vectors and kinematics, we showed that the acceleration in the radial direction of an object in a circular orbital of radius r and angular velocity w is w²r. Use this result, and the result that the velocity of such an object is wr to calculate the mass-m object's kinetic energy in terms of G, M, m, and r. (c) Calculate the corresponding velocity of the mass m object in terms of G, M, m, and r.

Consider an object of mass m in a circular orbit of radius r and angular velocity w about a larger object of mass M and radius R, where M > m. (a) What is the the potential energy of the mass-m in its circular orbit, assuming that r > R? 23 (b) In 1. Vectors and kinematics, we showed that the acceleration in the radial direction of an object in a circular orbital of radius r and angular velocity w is w²r. Use this result, and the result that the velocity of such an object is wr to calculate the mass-m object's kinetic energy in terms of G, M, m, and r. (c) Calculate the corresponding velocity of the mass m object in terms of G, M, m, and r.

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Physics word problem on energy/work/force:

Consider an object of mass m in a circular orbit of radius r and angular velocity w about a larger object of mass M and radius R, where M > m. (a) What is the the potential energy of the mass-m in its circular orbit, assuming that r > R? 23 (b) In 1. Vectors and kinematics, we showed that the acceleration in the radial direction of an object in a circular orbital of radius r and angular velocity w is w²r. Use this result, and the result that the velocity of such an object is wr to calculate the mass-m object's kinetic energy in terms of G, M, m, and r. (c) Calculate the corresponding velocity of the mass m object in terms of G, M, m, and r.
Transcribed Image Text:Consider an object of mass m in a circular orbit of radius r and angular velocity w about a larger object of mass M and radius R, where M > m. (a) What is the the potential energy of the mass-m in its circular orbit, assuming that r > R? 23 (b) In 1. Vectors and kinematics, we showed that the acceleration in the radial direction of an object in a circular orbital of radius r and angular velocity w is w²r. Use this result, and the result that the velocity of such an object is wr to calculate the mass-m object's kinetic energy in terms of G, M, m, and r. (c) Calculate the corresponding velocity of the mass m object in terms of G, M, m, and r.
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  1. What is the total mechanical energy of the mass m-mass M system?

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