Two insulating spheres have radii 0.300 cm and 0.500 cm, masses 0.250 kg and 0.7

Question

Two insulating spheres have radii 0.300 cm and 0.500 cm, masses 0.250 kg and 0.700 kg, and uniformly distributed charges of -2.00 µC and 5.00 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)
(b) If the spheres were conductors, would the speeds be greater or less than those calculated in part (a)? (Note: Assume a reference level of potential V = 0 at r = .)

Explanation / Answer

let

m1 = 0.25 kg

m2 = 0.7 kg

q1 = -2 micro C

q2 = 5 micro C

initail distance between the sphere, d1 = 1m

final distance between the sphere, d2 = 0.3+0.5

= 0.8 cm

= 0.008 m

a) let v1 and and v2 are velocities of m1 and m2 when they collide

Apply conservation of momentum

0 = m1*v1 + m2*v2

v1 = (m2/m1)*v2

= (0.7/0.25)*v2

= 2.8*v2

now Apply conservation of energy

kKEi + Ui = KEf + Uf

0 + k*q1*q2/d1 = 0.5*m1*v1^2 + 0.5*m2*v2^2 + k*q1*q2/d2

0.5*m1*(2.8*v2)^2 + 0.5*m2*v2^2 = k*q1*q2*(1/d1 - 1/d2)

0.5*0.25*7.84*v2^2 + 0.5*0.7*v2^2 = 9*10^9*(-2)*5*10^-12*(1/1 - 1/0.008)

1.33*v2^2 = 11.16

v2 = sqrt(11.16/1.33)

= 2.9 m/s (heavier sphere)

v1 = 2.8*v2

= 2.8*2.9

= 8.4 m/s (lighter sphere)

b) same.

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