(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A particle of mass m is acted on by a force F(x) = -k/x^{2}. The particle is released from rest a distance b from the origin of the attractive force F(x). Show that the time to reach the origin is given by t = [tex]\pi[/tex](mb^{3}/8k)^{1/2}.

2. Relevant equations

F(x) = -k/x^{2}

F = ma = m dv/dt = m dv/dx dx/dt = m v dv/dx

3. The attempt at a solution

m v dv = -k/x^{2}

v dv = -k/mx^{2}dx

[tex]\int[/tex] v dv = -k/m [tex]\int[/tex] x^{-2}dx

Integrating the left from zero to v and the right side from b to zero:

1/2 v^{2}= an integral that diverges???!!!

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# Homework Help: Force as a function of position

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