A proton of mass m P and a positively charged nucleus of mass 5 m P are widely s

Question

A proton of mass mP and a positively charged nucleus of mass 5mP are widely separated and traveling towards each other at the same speed of 2855 m/s along the same line. Because they are both positively charged, they repel each other and undergo a soft head-on collision. As you'll learn in Phys 126, the electrostatic repulsive force is a conservative force so the 'collision' is perfectly elasticwhen we consider the speeds a long time before and a long time after the collision (when they are essentially no longer interacting).

What is the final speed of the proton (in m/s) when they are again widely separated? (i.e. when they exert negligible forces on each other, and their speeds are no longer changing.)

(Note: you don't actually need the mass of the proton here, only the mass ratio '5', since mP will cancel out of both of your equations.)

Explanation / Answer

electrostatic repulsive force is a conservative force so we can consider as general collision problem

let velocity be v1 and v2 of proton after collison

5mpv1+mpv2=5mpv-mpv

5v1+v2=4v

for perfect elastic collison

v2-v1=2v

v2=2v+v1.....putting this in above eqn

5v1+2v+v1=4v

v1=1/3v

v2=7/3v

v1of 5mp=1/3*2855=951.67m/s

v2of mp=6661.7m/s

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