Two plastic beads, Bead C and D, are spaced 10-mm apart, measured between their

Question

Two plastic beads, Bead C and D, are spaced 10-mm apart, measured between their centers. Each has a diameter of 2.0-mm. Bead C had a mass of 1.0-g and is charged to 2.0 nC. Bead D has a mass of 2.0 g and is charged to -1.0 nC. If the beads are real send from rest what will be the final speeds of each of them before impact? Draw a before-and-after pictorial representation, identifying all important symbols. (Hint: energy is not the only quantity conserved)

Also draw a before and after pictorial representaition identifying all important symbols.

Explanation / Answer

the electric force between the beads is

F = k x (q1q2/r^2)

where k = (1/4pi x e_o) = 9 x 10^9 Nm^2/C^2,q1 = 2.0 nC = 2.0 x 10^-9 C,q2 = -1.0 nC = -1.0 x 10^-9 C and r = 10 mm = 10 x 10^-3 m

let v1 and v2 be the speeds of the beads before impact

we know that

(1/2)m1 x v1^2 = U

and (1/2)m2 x v2^2 = U

or v1 = (2U/m1)^1/2

and v2 = (2U/m2)^1/2

where U = F x r

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