hw5_PHYS3318 - February 26, 2010 Cornell University,...

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Unformatted text preview: February 26, 2010 Cornell University, Department of Physics P3318, Analytical Mechanics, HW#5, due: 3/5/10, 2:30PM (at section) Question 1 : Using conservation laws This question shows the power of conserved quantities. Consider a particle in a smooth monotonic attractive central potential V ( r ). At time t = 0 the particle is at a point ~ r and has velocity ~v . It is given that the velocity is inward, that is, r ( t = ) < r ( t = 0) (where, as always, it is implicit that is very small compared to all other time scales in the problem). 1. What are the two conserved quantities in the problem? Calculate them based on the initial conditions. 2. In terms of angles, the above conserved quantities should depend only on the angle between ~ r and ~v . Verify that this is indeed the case in your answer and explain why. 3. We try to find the point the particle is closest to the origin, r min . What is the value of the radial velocity at that point, r | r min ? What is the angle between ~ r and ~v there?...
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hw5_PHYS3318 - February 26, 2010 Cornell University,...

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