A small metal sphere, carrying a net charge of g-3.00 C, is held in a stationary

Question

A small metal sphere, carrying a net charge of g-3.00 C, is held in a stationary position by insulating supports. A second smal metal sphere, with a net charge of g -7.20 C and mass l.50 g , is projected toward 1. When the two spheres are 0.800 m apart, q2 is moving toward gi with speed 22.0 m/s 222.0 m/s 91 0.800 m Q Tap image to zoom Assume that the two spheres can be treated as point charges. You can ignore the force of gravity You may want to review (Pages 752-758 For related problem-solving tips and strategies, you may want to view a Video Tutor Solution of Conservation of energy with Part A What is the speed of q2 when the spheres are 0.400 m apart? ANSWER: m/s

Explanation / Answer

(1)

Given that,

q1 = -3 uC

q2 = -7.2 uC

u = 22 m/s

d1 = 0.80 m

d2 = 0.40 m

m = 1.5 g

(a)

From conservation of total energy,

KEi + PEi = KEf + PEf

(1/2)mu^2 + kq1q2 / d1 = (1/2)mv^2 + kq1q2 / d2

0.5*1.5*10-3*222 + 9*109*3*10-6*7.2*10-6 / 0.8 = (1/2)*1.5*10-3*v2 + 9*109*3*10-6*7.2*10-6 / 0.4

0.363 + 0.243 = 0.486 + 0.75*10-3 *v^2

v = 12.6 m/s

(b)

Closest distance,

(1/2)mu^2 + kq1q2 / d1 = kq1q2 / d

0.5*1.5*10-3*222 + 9*109*3*10-6*7.2*10-6 / 0.8 = 9*109*3*10-6*7.2*10-6 / d

0.606 = 0.1944 / d

d = 0.32 m

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