A proton of mass m P and a positively charged nucleus of mass 7 m P are widely s

Question

A proton of mass mP and a positively charged nucleus of mass 7mP are widely separated and traveling towards each other at the same speed of 2492 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 elastic when 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 '7', since mP will cancel out of both of your equations.)

Explanation / Answer

conservation of momentum
7 m 2492 - m 2492 = m x - 7m y

so 6*2492 = x - 7 y

y = (6*2492 -x)/7

conservation of energy
7 m 2492^2 + m 2492^2 = m x^2 +7m y^2

7 2492^2 + 2492^2 = x^2 + 7((6*2492 -x)/7)^2

x=6230 m/s

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