A small metal sphere, carrying a net charge of q1- -2.80 pC, is held in a statio

Question

A small metal sphere, carrying a net charge of q1- -2.80 pC, is held in a stationary position by insulating supports. A second small metal sphere, with a net charge of 2 A second small metal sphere, with a net charge of q2-8.20 uC and mass 1.20 g, is projected toward q1. When the two spheres are 0.800 m apart, q2 is moving toward o, with speed 22.0 m/s (see figure below). Assume that the two spheres can be treated as point the force of gravity. u = 22.0 m/s -0.800 m- (a) what is the speed of q2 when the spheres are 0.400 m apart? m/s (b) How close does get q2 to q1? My

Explanation / Answer

a)

vi = speed of q2 when at distance 0.8 m from q1 = 22 m/s

vf = speed of q2 when at distance 0.4 m from q1 = 22 m/s

ri = initial distance between the spheres = 0.8 m

rf = final distance = 0.4 m

using conservation of energy

k q1 q2/ri + (0.5) m vi2 = k q1 q2/rf + (0.5) m vf2

(9 x 109) (- 2.80 x 10-6) (- 8.20 x 10-6)/(0.8) + (0.5) (0.0012) (22)2 = (9 x 109) (- 2.80 x 10-6) (- 8.20 x 10-6)/(0.4) + (0.5) (0.0012) vf2

vf = 7.31 m/s

b)

rf = closest distance between the two spheres

vf = final speed of q2 = 0

using conservation of energy

k q1 q2/ri + (0.5) m vi2 = k q1 q2/rf + (0.5) m vf2

(9 x 109) (- 2.80 x 10-6) (- 8.20 x 10-6)/(0.8) + (0.5) (0.0012) (22)2 = (9 x 109) (- 2.80 x 10-6) (- 8.20 x 10-6)/rf + (0.5) (0.0012) (0)2

rf = 0.377 m

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