Two particles each have a mass of 66 103 kg One has a charge

Two particles each have a mass of 6.6 10-3 kg. One has a charge of +5.3 10-6 C, and the other has a charge of -5.3 10-6 C. They are initially held at rest at a distance of 0.78 m apart. Both are then released and accelerate toward each other. How fast is each particle moving when the separation between them is one-third its initial value?

___________m/s

Solution

PE=kq1 q1/r

when they are a distance r/3 apart,

they have both PE and KE; the conservation of momentum tells us:

total energy before=total energy after

kq1 q1/r = kq1q2/(r/3) + 2(1/2 mv^2)

and we have 2(1/2mv^2) since there are two particles of mass m moving with speed v

the equation above gives us

-2k q1q2/r = mv^2

for k=9x10^9

q1 x q2 =-5.3*5.3x10^(-12)

q1q2 =-28.09*10^-12

m=6.6*10^-3kg

r=0.75m
we have

(9x10^9)(-28.09x10^(-12)/0.78 = 6.6*10^-3v^2

0.3241 = 6.6*10^-3v^2

v=7.007m/s