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 1763 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 '5', since mP will cancel out of both of your equations.)

Explanation / Answer

For a perfectly elastic collision, equations are ;

v1 = [u1(m1-m2) - 2m2u2]/(m1+m2)

and v2 = [u1(m2-m1) - 2m1u1]/(m1+m2)

Here v1 and v2 are the final velocities and u1 and u2 are the initial velocities of masses m1 and m2 respectively.

Putting values, m1 = m; m2 = 5m; u1 = v, u2 = -v.

v1 = 6v

v2 = 0.33v

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