The escape velocity is defined to be the minimum speed with which an object of m

Question

The escape velocity is defined to be the minimum speed with which an object of mass m must move to escape from the gravitational attraction of a much larger body, such as a planet of total mass M. The escape velocity is a function of the distance of the object from the center of the planetR, but unless otherwise specified this distance is taken to be the radius of the planet because it addresses the question "How fast does my rocket have to go to escape from the surface of the planet?" What is the total mechanical energy Etotal of the object at a very large (i.e., infinite) distance from the planet? Follow the usual convention and take the gravitational potential energy to be zero at very large distances. True or False. Angular momentum about the center of the planet is conserved. Total mechanical energy is conserved. Kinetic energy is conserved.

Explanation / Answer

Angular momentum about the center of the planet is conserved - True

The angular momentum m r^2 ( d /dt ) is constant. As the larger object moves away from the orbit ( takes an orbit with larger radius ), the angular speed is decreases so as to total angular momentum of the object is constant.

Total mechanical energy is conserved : True

As the larger object move farther from planet, its gravitational potential energy is converts into the kinetic energy, however the total mechanical energy of the system is constant throughout the motion of object.

Kinetic energy is conserved. - False

As the object moving away from the planer, the velocity of objects changes, and hence it kineitic energy vaires. It is not constant ( not conserved ). As it reaches infinity, the potential energy approaches zero and kinetic energy is maximum.

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