Two plastic spheres, each carrying charge uniformly distributed throughout its i

Question

Two plastic spheres, each carrying charge uniformly distributed throughout its interior, are initially placed in contact and then released. One sphere has a diameter of 65.0cm , a mass of m1= 55.0g , and contains -12.0?C of charge. The other sphere has a diameter of 40.0cm , a mass ofm2 = 160.0g and contains -26.0 microC of charge. Assume that no other forces are acting on them.

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a.Find the maximum speed achieved by the sphere of mass 55.0

g

b.Find the maximum speed achieved by sphere of mass 160.0

Explanation / Answer

the electrostatic potential energy of the two spheres whenthey are in contact is E = k * (q1 * q2/r^2) k = (1/4??o) = 9 * 10^9 Nm^2/C^2,q1 =-12.0 ?C = -12.0 * 10^-6 C,q2 = -29.0 ?C = -29.0 * 10^-6C and r = (d1 + d2) = (60.0 + 43.0) cm = 103 cm = 103 * 10^-2m half of the electrostatic potential energy is given to one ofthe spheres and the other half is given to the other spheretherefore (1/2)m1 * v1^2 = (E/2) or v1 = (E/m1)^(1/2) similarly,the speed of second sphere is v2 = (E/m2)^(1/2) the electrostatic force between the two spheres is F = k * (q1 * q2/r^2) or F = k * (q1 * q2/(d1 + d2)^2) therefore the acceleration of 55.0 g sphere is m1 * a1 = k * (q1 * q2/(d1 + d2)^2) or a1 = (k/m1) * (q1 * q2/(d1 + d2)^2) and the acceleration of 160.0 g sphere is a2 = (k/m2) * (q1 * q2/(d1 + d2)^2)

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