Ejercicio Exercise 2.b - Effective Central Potential Curves · Física I URV Setembre

Exercise 2. Qualitative Analysis of 1D and Effective Central Potential Curves

Consider the potential energy representations below for a one-dimensional system $U(x)$ and for the radial motion in a central force field under an effective potential $U_{\text{eff}}(r)$ (notated as $U'(r)$):

b.

For the radial effective potential $U'(r)$ of a particle in a $1/r$ attractive central potential, classify the type of orbit (geometry and turning points) according to the value of the total mechanical energy: $E_{\text{mec}} = E_{\text{mec, min}}$, $E_{\text{mec, min}} < E_{\text{mec}} < 0$, $E_{\text{mec}} = 0$, and $E_{\text{mec}} > 0$.