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 65.0 cm , a mass of m1 = 53.0 g , and contains -12.0 μC of charge. The other sphere has a diameter of 45.0 cm , a mass of m2 = 160.0 g and contains -29.0 μC of charge. Assume that no other forces are acting on them.

a)Find the maximum speed achieved by the sphere of mass 53.0 g .

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

c)Find the maximum acceleration achieved by the sphere of mass 53.0 g .

d)Find the maximum acceleration achieved by the sphere of mass 160.0 g .

Answer 1

Given,

d1 = 65 cm ; m1 = 53 g ; q1 = -12 uC ; d2 = 45 cm ; m2 = 160 g ; -29 uC

a)The electric force between them will be:

F = k q1q2/r^2

F = 9 x 10^9 x 12 x 10^-6 x 29 x 10^-6/(0.65/2 + 0.45/2)^2 = 10.35 N

a)from conservation of energy

U = 1/2 m1v1^2 + 1/2 m2v2^2

m1v1 + m2v2 = 0

U = 1/2 (m1 + m1^2/m)v1^2

v1 = sqrt (2Um2/m1(m1+m1))

U = k q1q2/r = 9 x 10^9 x 12 x 10^-6 x 29 x 10^-6/(0.65/2 + 0.45/2) = 5.69 J

v1 = sqrt (2 x 5.69 x 0.16/0.053(0.053 + 0.16)) = 12.7 m/s

Hence, v1 = 12.7 m/s

b)v2 = m1v1/m2

v2 = 0.053 x 12.7/0.16 = 4.21 m/s

Hence, v2 = 4.21 m/s

c)a1 = 10.35/0.053 = 195.28 m/s^2

Hence, a1 = 195.28 m/s^2

d)a2 = 10.35/0.16 = 64.69 m/s^2

Hence, a2 = 64.69 m/s^2