How fast is each particle moving when the separation between them is one-half its initial value?

Question

Two particles each have a mass of 5.90 10-3 kg. One has a charge of +5.0 10-6 C, and the other has a charge of -5.0 10-6 C. They are initially held at rest at a distance of 0.95 m apart. Both are then released and accelerate toward each other. How fast is each particle moving when the separation between them is one-half its initial value?_______m/s

Answer 1

Energy conservation.
The initial energy: Ei = -q^2/(4*pi*Epsilon_0*r)
The final energy: Ef = -q^2/(4*pi*Epsilon_0*(0.5r)) = 2*Ei
Let the final particle speed be v, we have:
2*(0.5mv^2) = Ei - Ef = q^2/(4*pi*Epsilon_0*r)
Therefore v = sqrt(q^2/(4*pi*Epsilon_0*r*m))
= sqrt{[5.0x10^(-6)]^2*8.99x10^9
/[0.95*5.90x10^(-3)]} (m/s)

Answer 2

Use the expression for skill potential of each can charge: PE = -ok*q1*q2/r Calculate it on the preliminary distance. Calculate it on the appropriate distance. the version between those is how plenty PE each particle loses, and how plenty KE each particle has gained. So set that equivalent to (a million/2)mv^2 and sparkling up for v.