Question

Two insulating spheres have radii 0.300 cm and 0.500 cm, masses 0.500 kg and 0.700 kg, and uniformly distributed charges of -2.00 µC and 3.00 µC. They are released from rest when their centers are separated by 1.00 m.

(a) How fast will each be moving when they collide? (Hint: Consider conservation of energy and of linear momentum.)
m/s (lighter sphere)
m/s (heavier sphere)

Answer 1

lnitial ptential energy of spheres,

Ui = kq1q2 / d^2

where d = 1 m

Potential energy when the collide,

Uf = kq1q2 / d'^2

where d = r1 + r2

From conservation of energy,

U = KE

kq1q2 / d'^2 -  kq1q2 / d^2 = (1/2)m1v1^2 + (1/2)m2v2^2 ......(1)

From conservation of linear momentum,

m1v1 = m2v2

v2 = m1v1 / m2

Put the value of v2 in eq1 and Put d' = r1 + r2,

(1/2)*(m1 + m2)*(m1v1^2 / m1) = kq1q2 *[1 / (r1+r2) - 1 / d]

v1 = sqrt [(2*m2*k*q1q2 / m*(m1 + m2)) * (1 / (r1 + r2) - 1 / d)]

Put the values,

v1 = sqrt [2*0.7*9*10⁹*2*10^-6*3*10^-6 / 0.5*(0.5 + 0.7)) * (1 / (0.003 + 0.005) - 1 / 1)]

v1 = 3.95 m/s (lighter sphere)

v2 = m1v1 / m2 = 0.5*3.95 / 0.7

v2 = 2.82 m/s (heavier sphere)