Question

Prove the following about two objects colliding elastically in one dimension. Note: each step helps with the next, and all of this is useful for 1D elastic collisions of two objects. (a) For an incident particle A of mass mA and a target particle B (mB), the initial (vA,o and vB,o) and final (vA,f and vB,f) velocities are related as follows: (b) If the target B is initially stationary (VB,0 -0), show that the final velocity of particle A is: UA,0 (c) If the target B is initially stationary (VB,o -0), show that its final velocity is: 2mA A,0 (d) Under the same condition, show that the fraction of kinetic energy lost by the incident particle is: 4mAmB where mB is generically the mass of the stationary target particle.

Answer 1

uh("So+4f)(2Ao. 2시)-ug(も1%。)( %)--:@ A,D b) ,o A,O "A-uィ Α,ο

A b A,D 2 K. Ao A,0