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

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 2.50 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.)

? 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 = ?.)

less than ?

greater ?

the same?

Explanation / Answer

given

Two insulating spheres have radii

r1 = 0.300 cm = 0.3 X 10-2 m

and 0.500 cm = r2 = 0.5 X 10-2 m

m1 = 0.500 kg

m2 = 0.700 kg

distributed charges of

q1 = - 2.00 µC

and

q2 = 2.50 µC

d = separated by 1.00 m.

a )

using conservation of momentum

0 - k q1 q2 / d = 1/2 m1 v12 + 1/2 m2 v22 - k q1 q2 / ( r1 + r2 )

so re-writing for v1 , we get

v1 = [ 2 k m2 q1 q2 ( (1/r1 + r2 ) - (1/d)) / (m1 ( m1 + m2 )) ]1/2

=[ 2 X 9 X 109 X 0.7 X 2 X 10-6 X 2.5 X 10-6 X ((1/0.0003 + 0.005) - (1/1)) /(0.5 ( 0.5 + 0.7 )) ]1/2

= 4.41 m/sec

and then

m1 v1 = m 2 v2

v2 = ( m1 / m2 ) v1

= ( 0.5 / 0.7 ) X 4.41

= 3.15 m/sec

b )

when just the masses are in touch , then the effective distance between charges is lessthan

( r1 + r2 ) and the spheres can moves greater than calculated in part (a) .

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