Introduction to Classical Mechanics · Problem 7.2

Angular momentum, Part I (Constant L) — Morin

Physics — Mechanics · central-forces-effective-potential

Problem

Cross section ** A particle moves in a potential,

V(r) = -C/(3r^3)

. ((a)) Given

L

, find the maximum value of the effective potential. ((b)) Let the particle come in from infinity with speed

v_0

and impact parameter

b

. In terms of

C

m

, and

v_0

, what is the largest value of

b

(call it

b_{\max}

) for which the particle is captured by the potential? In other words, what is the ``cross section'' for capture,

\pi b_{\max}^2

, for this potential?