Classical Mechanics Solutions

Classical Mechanics Solutions - Classical Mechanics...

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Solution 1 Conservation of energy given by the sum of potential energy due to gravity and kinetic energy can be used to determine escape velocity. In the case of Earth along the potential is given by: r m M G r E = ) ( φ where m is the mass of the book. The book will escape if initial kinetic energy is high enough to overcome the potential at E R r = . Thus E E E R m M G mv = 2 2 thus s km R GM v E E E / 11 2 = = In the Earth-Moon case the potential is r R m M G r m M G r EM M E = ) ( where MM = ME. The potential is a symmetric double-well and in order to leave the surface of the earth the kinetic energy must be high enough to overcome a saddle point right in the middle between earth and moon. Thus the condition for escape velocity is ME E E EM E E E R m GM R R R m GM mv 4 1 1 2 2 = + This equation solved for escape velocity gives . / 7 . 7 s km v E = Solution 2 Introduce the generalized coordinates as in the figure below. and
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Classical Mechanics Solutions - Classical Mechanics...

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