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A Central-Force Motion Problem

  1. Sep 30, 2018 #1


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    In Chapter 8: Central-Force Motion, in the Classical Dynamics of Particles and Systems book by Thornton and Marion, Fifth Edition, page 323, Problem 8-5, we are asked to show that the two particles will collide after a time ##\tau/4√2##.

    I don't have any problems with the derivations and with the integrations, but I want to know please why the authors put a negative sign in Equation (6) and what do they mean that the negative sign was included due to the fact that the time increases as the distance decreases?

    Thanks a lot for your help... Central-Force Problem.PNG
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  3. Sep 30, 2018 #2


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    In my opinion the negative sign should have appeared in equation (5). Equation (4) for ##\dot{x}^2## has two solutions. In this case, the negative square root is required as ##\dot{x}## is negative, for the physical reason given
  4. Oct 13, 2018 #3


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    Thank you so much @PeroK for your continuous support...
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