A small metal sphere, carrying a net charge of q 1 = -2.50 C , is held in a stat

Question

A small metal sphere, carrying a net charge of q1 = -2.50 C , is held in a stationary position by insulating supports. A second small metal sphere, with a net charge of q2 = -7.80 C and mass 1.90 g , is projected toward q1. When the two spheres are 0.800 m apart, q2 is moving toward q1 with speed 22.0 m/s. Assume that the two spheres can be treated as point charges. You can ignore the force of gravity.

The speed of q2 is 16.6 m/s when the spheres are 0.420 m apart.

However, how close does q2 get to q1? Please show work so that I can understand. :)

Explanation / Answer

here

E = K + U

E = 0.5 * m * v^2 + k * q1 * q2 / r

E = 0.5 * 0.0019 * 22^2 + 9 * 10^9 * 2.5 * 10^-6 * 7.8 * 10^-6 / 0.8

E = 0.68 J

so when it gets as close as it can, KE = 0, and

PE = 0.68 = k * q1 * q2 / d

0.68 = 9 * 10^9 * 2.5 * 10^-6 * 7.8 * 10^-6 / d

d = 0.258 m

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