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MasteringPhysics_ GRAVITY View

# MasteringPhysics_ GRAVITY View - MasteringPhysics...

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MasteringPhysics: Assignment Print View http://session.masteringphysics.com/myct/assignmentPrint?assignm... 1 of 10 10/11/08 11:52 PM [ Print View ] Physics 2211-001, Fall 2008 Gravity Due at 11:00pm on Saturday, October 4, 2008 View Grading Details Escape Velocity Learning Goal: To introduce you to the concept of escape velocity for a rocket. The escape velocity is defined to be the minimum speed with which an object of mass must move to escape from the gravitational attraction of a much larger body, such as a planet of total mass . The escape velocity is a function of the distance of the object from the center of the planet , 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?" Part A The key to making a concise mathematical definition of escape velocity is to consider the energy. If an object is launched at its escape velocity, what is the total mechanical energy 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. Hint A.1 Consider various cases Hint not displayed ANSWER: = 0 Consider the motion of an object between a point close to the planet and a point very very far from the planet. Indicate whether the following statements are true or false. Part B Angular momentum about the center of the planet is conserved. ANSWER: true false Part C Total mechanical energy is conserved. ANSWER: true false [ Print ]

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MasteringPhysics: Assignment Print View http://session.masteringphysics.com/myct/assignmentPrint?assignm... 2 of 10 10/11/08 11:52 PM Part D Kinetic energy is conserved. ANSWER: true false Part E The angular momentum about the center of the planet and the total mechanical energy will be conserved regardless of whether the object moves from small to large (like a rocket being launched) or from large to small (like a comet approaching the earth). ANSWER: true false What if the object is not moving directly away from or toward the planet but instead is moving at an angle from the normal? In this case, it will have a tangential velocity and angular momentum . Since angular momentum is conserved, for any , so will go to 0 as goes to infinity. This means that angular momentum can be conserved without adding any kinetic energy at . The important aspect for determining the escape velocity will therefore be the conservation of total mechanical energy. Part F Find the escape velocity for an object of mass that is initially at a distance from the center of a planet of mass . Assume that , the radius of the planet, and ignore air resistance. Part F.1 Determine the gravitational potential energy Part not displayed Part F.2 Determine the kinetic energy Part not displayed Hint F.3 Putting it all together Hint not displayed Express the escape velocity in terms of , , , and , the universal gravitational constant.
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MasteringPhysics_ GRAVITY View - MasteringPhysics...

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