A small metal sphere, carrying a net charge of q1 = -2.70 ?C , is held in a stat

Question

A small metal sphere, carrying a net charge of q1 = -2.70 ?C , is held in a stationary position by insulating supports. A second small metal sphere, with a net charge of q2 = -7.70 ?C and mass 1.40 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 (Figure 1) . Assume that the two spheres can be treated as point charges. You can ignore the force of gravity.

A) What is the Speed of q2 When the spheres are .430 m apart?

B) How close does q2 to q1?

Explanation / Answer

Initially the total energy is
E = PE + KE = kQq / d + ½mv²
E = 8.99e9N·m²/C² * 2.7e-6C * 7.7e-6C / 0.8m + ½ * 0.0014kg * (22m/s)²
E = 0.572 J

(a) When d = 0.430 m, PE = 8.99e9N·m²/C² * 2.7e-6C * 7.7e-6C / 0.43m = 0.434 J
so KE = 0.572J - 0.434J = 0.138 J = ½ * 0.0014kg * v²
v = 14.04 m/s

(b) When it gets as close as it can, KE = 0, and
PE = 0.572 J = 8.99e9N·m²/C² * 2.7e-6C * 7.7e-6C / d
d = 0.3267 m

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