Consider a system of two particles with reduced mass p; attracted to each other by the potential Uh") = or;"r4, where the radial coordinate r is the distance between the two particles, 91'; is the angular coordinate associated with their rotation. and a: is a positive constant. The system has positive angular momentum t'. The total energy E is depicted as a dashed line on the plot of the effective potential Fair) = 2:: + Um (1) shown in Fig l. . a '3- Figure l: A plot of Ugly (r) versus r {in some codvenient units). The total energy E is depicted on the plot by the horizontal dashed line. Values of r where Uc{T) = E are labeled n. and re, and the value of 1' that maximizes U03 is labeled r5. Part (a) (15 points): Find the values of Tm 1'5, and n. in terms of p, or, E, and E. Part {b} (5 points}: Find the angular velocity :35 at r = r and r = rd in terms of a, or, 6', and E. Which of these values of T has the larger c5? Part (c) (5 points): Find the value of the radial velocity 1' at r = Ta and r = rd in terms of u, or, t', and E. Consider that the two particles initially have T > Ta and are moving toward each other. Find the minimum energy E needed for the two particles to collide in terms of f, or, and it