Two point charges are moving to the right along the x-axis. Point charge 1 has charge q1 =...

Two point charges are moving to the right along the x-axis. Point charge 1 has charge q1 = 2.00 µC, mass m1 = 6.00 × 10−5 kg, and speed υ1. Point charge 2 is to the right of q1 and has charge q2 = −5.00 µC, mass m2 = 3.00 × 10−5 kg. and speed v2. At a particular instant, the charges are separated by a distance of 9.00 mm and have speeds υ1 = 400 m/s and v2 = 1300 m/s. The only forces  on the particles are the forces they exert on each other. (a) Determine the speed υcm of the center of mass of the system. (b) The relative energy Erel of the system is defined as the total energy minus the kinetic energy contributed by the motion of the center of mass:

Where  Is the total energy of the system and r is the distance between the charges Show that   where   is called the reduced mass of the system and υ = υ2−υ1 is the relative speed of the moving particles.  (c) For the numerical values given above, calculate the numerical value of Erel. (d) Based on the result of part (c), for the conditions given above, will the particles escape from one another? Explain.  (e) If the particles do escape, what will be their final relative speed when r → ∞?  If the particles do not escape, what will be their distance of maximum separation? That is, what will be the value of r when υ = 0?  (f) Repeat parts (c) −(e) for υ1 = 400 m/s and v2 = 1800 m/s when the separation is 9.00 mm.