Two plastic spheres, each carrying charge uniformlydistributed throughout its in

Question

Two plastic spheres, each carrying charge uniformlydistributed throughout its interior, are initially placed incontact and then released. One sphere has a diameter of55.0 cm , a mass of m1 = 55.0 g, and contains -11.0 C of charge. The other spherehas a diameter of 45.0 cm, a massof m2 = 140.0 g and contains-30.0 C of charge. Assume that no other forces areacting on them. a)Find the maximum speed achieved by the sphere of mass55.0 g b)Find the maximum speed achieved by sphere of mass140.0 g c)Find the maximum acceleration achieved by the sphere of mass55.0 g d)Find the maximum acceleration achieved by the sphere of mass140.0 g Two plastic spheres, each carrying charge uniformlydistributed throughout its interior, are initially placed incontact and then released. One sphere has a diameter of55.0 cm , a mass of m1 = 55.0 g, and contains -11.0 C of charge. The other spherehas a diameter of 45.0 cm, a massof m2 = 140.0 g and contains-30.0 C of charge. Assume that no other forces areacting on them. a)Find the maximum speed achieved by the sphere of mass55.0 g b)Find the maximum speed achieved by sphere of mass140.0 g c)Find the maximum acceleration achieved by the sphere of mass55.0 g d)Find the maximum acceleration achieved by the sphere of mass140.0 g

Explanation / Answer

The total initial energy is E = qQ/(4D) where D is the initial separation D= r+R after they are released, the energy equation, when the centers ared apart, is (1/2)mv^2 + (1/2)MV^2 + qQ/(4d) = E =qQ/(4D) but, treating the 2 spheres as a system, electric force is internaland so total momentum must be conserved, mv + MV = 0 solving for v and plugging into the energy equation, (1/2)(M^2/m + M)V^2 + qQ/(4d) =qQ/(4D) V is max when d goes to , and so (1/2)(M^2/m + M)Vmax^2 = qQ/(4D) Vmax = [2qQ/(4D)/(M^2/m + M)]           = ____m/s vmax = MVmax/m = ______ m/s

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