A particle of mass 100 g travelling at an initial speed u collides with another particle of the same mass initially at rest. If the total kinetic energy after the collision becomes 0.2 J , determine the minimum and maximum values of u .

Step-by-step solution

Given mass of each particle, m = 100 g = 0.1 kg . Let the initial velocity of the first particle be u and the coefficient of restitution be e . The velocity of the center of mass is v_ cm = m u + m(0) m + m = u 2 . The final kinetic energy of the system can be written as the sum of the kinetic energy of the center of mass and the kinetic energy relative to the center of mass: K_f = 1 2 (2m)v_ cm ^2 + 1 2 v_ rel,f ^2 where reduced mass = m m m + m = m 2 and final relative velocity v_ rel,f = e u . Substituting these