A small metal sphere, carrying a net charge of q_1 = -2.90 mu C, is held in a st

Question

A small metal sphere, carrying a net charge of q_1 = -2.90 mu C, is held in a stationary position by insulating supports. A second small metal sphere, with a net charge of q_2 = -7.70 mu C and mass 1.40 g, is projected toward q_1. When the two spheres are 0.800 m apart, q_2 is moving toward q_1 with speed 22.0 m/s (Figure 1). Assume that the two spheres can be treated as point charges. You can ignore the force of gravity. What is the speed of q_2 when the spheres are 0.430 m apart? How close does q_2 get to q_1?

Explanation / Answer

Initially the total energy is
E = PE + KE = kQq / d + ½mv²
E = 8.99e9N·m²/C² * 2.9e-6C * 7.7e-6C / 0.8m + ½ * 0.0014kg * (22m/s)²
E = 0.589 J

(a) When d = 0.430 m, PE = 8.99e9N·m²/C² * 2.9e-6C * 7.7e-6C / 0.43m = 0.467 J
so KE = 0.589J - 0.467J = 0.122 J = ½ * 0.0014kg * v²
v = 13.20 m/s

(b) When it gets as close as it can, KE = 0, and
PE = 0.589 J = 8.99e9N·m²/C² * 2.9e-6C * 7.7e-6C / d
d = 0.341 m

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