- Homework Statement
- Consider two particles interacting via a repulsive central potential U(r) = k/r with k > 0. Find the minimal distance between particles, when one of them (with mass m1) is coming from infinity with initial velocity v0, and approaching an initially resting particle (with mass m2) with impact parameter ρ.
- Homework Equations
- U(r) = k/r
I have one problem with this question that I've been struggling with. Initially, the total energy should be given by E =m1* v0^2/2 (as U goes to zero, and m2 is at rest). However, if we write r = r1 - r2, we get E = mu*rdot^2/2 + U_eff(r), U_eff(r) also goes to 0, where mu is the reduced mass. However, rdot^2 is exactly v0^2 when r is infinity, as rdot = r1dot - r2dot = r1dot, since m2 is at rest. This seems to imply that m1 = mu, which makes no sense. What am I missing? If I assume that the first energy I stated is incorrect, I have no trouble with the rest of the problem.