Central-Force Motion Problem

  • #1
sams
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Main Question or Discussion Point

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...
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  • #2
PeroK
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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
 
  • #3
sams
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Thank you so much @PeroK for your continuous support...
 

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