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**1. Homework Statement**

Two insulating spheres having radii 0.300 cm and 0.500 cm, masses 0.100 kg and 0.700 kg, and charges -2.000 micro-C and 3.00 micro-C 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 linear momentum.) (b) If the spheres were conductors would the speeds be larger or smaller than those calculated in part (a)? Explain.

**2. Homework Equations**

[tex]U = K_e \frac{q_1 q_2}{r_{12}}[/tex]

[tex]E_1 = U = E_2 = \frac{1}{2} m v^2[/tex]

**3. The Attempt at a Solution**

Let the radii be r_1 and r_2, masses m_1, m_2, charges q_1, q_2, and distance separated d.

so we have:

[tex]U = K_e \frac{q_1 q_2}{r_{12}} = K_e \frac{q_1 q_2}{d + r_1 + r_2}[/tex]

Since the charges are at rest at first, they have only electrical potential energy (given above) and they're the same, and when they collide, I assume they have only kinetic energy.

[tex]U = KE_1 = \frac{1}{2}m_1 v_{1}^2[/tex]

[tex]K_e \frac{q_1 q_2}{d + r_1 + r_2} = \frac{1}{2}m_1 v_{1}^2[/tex]

solving for V we have [tex]v = \sqrt { \frac{2 K_e q_1 q_2}{(d + r_1 + r_2) m}[/tex]

but this fails to provide the proper solution. what's wrong with it? How is linear momentum involved?