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

Question

Two insulating spheres have radii 0.300 cm and 0.500 cm, masses 0.300 kg and 0.700 kg, and uniformly distributed charges of -2.00 µC and 4.50 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.)

(b)If the spheres were conductors, would the speeds be greater, less than, or equal to those calculated in part (a)? [Note: Assume a reference level of potential V=0 and r=infinity)

Explain.

Explanation / Answer

a)

Suppose the velocity of mass1 is v1 and mass 2 have v2 velocity after colliding, then

from conservation of momentum, m1v1 = m2v2 = p(say) or v2 = (3/7)v1 --------------(1)

Now from the conservation of energy,

kinetic energy + potential energy = constant.

0 - kq1q2/r1 = p^2/2m1 + p^2/2m2 - kq1q2/r2

hence  (p^2/2)(1/m1+1/m2) = kq1q2(1/r2-1/r1)

now plugging in the values we get p = 2.05 kg.m/s

velocity of m1 = 6.85 m/s

velocity of m2 = 2.93 m/s

b) If they were conductor, electrons will move around on them with negligible energy loss to place the centers of excess charge on the insides of the spheres. Then just before they touch, the effective distance between charges will be less than r1 + r2 and the spheres will really be moving faster.

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