QUESTION: How do I derive Equations 3, 4a, and 4b? Helpandexplanations are greatly appreciated!
Consider an elastic(H) collision between two particles moving in ID. We have particles m1 and m2 moving with velocities mu 1 and mu 2 before the collision and v1 , v2 after the collision. We know that kinetic energy (KE) and linear momentum (P) are conserved, as Delta P = (Pf-Pi) = 0 Eq. 1 Delta KE = (KEf - KEi) = 0 Eq.2 It is also useful to formulate these fundamental relations in terms of velocities (see your phyl21 textbook). Thus we have (for elastic collisions) (v2-v1)(mu 2-u1)=-1 eq.3 or in other words "the relative velocities after/before are equal but opposite". This is true for any mass values. A somewhat more restrictive case is for mu 2 = 0 (stationary "target" m2). Then it can be shown that v1 = (m 1 -m2)u 1 /(m 1 +m2) Eq. 4a v2 = (2m 1 )u 1 /(m 1 +m2). Eq. 4b Note that the ratio r = v1/v2 is constant here where u2=0.
