Question

2) Two small balls have the net charges ??1=?3.0 ??C and ??2=?8.0 ??C and masses ??1=20g and ??2=10g. The first ball, ??1, is hold in at point (1.0 m,0.0, 0.0) and ??2 is initially at point (0.0, 0.0, 0.0) and has initial velocity ??0???? =25 ??? m/s. Suppose both balls are very small and you consider them as point charge.
a) Find velocity of the second ball, ??2, when it is at point (0.5 m,0.0, 0.0).
b) How close does the second mass, ??2, get to the first mass , ??1?

Please do explain how to do this homework. Thank you!

Answer 1

let

m1 = 20 g = 0.02 kg

m2 = 10 g = 0.01 kg

q1 = -3 micro C

q2 = -8 micro C

a) Apply conservation of energy

k*q1*q2/d1 + (1/2)*m2*vo^2 = k*q1*q2/d2 + (1/2)*m2*v^2

9*10^9*(-3*10^-6)*(-8*10^-6)/1 + (1/2)*0.01*25^2 = 9*10^9*(-3*10^-6)*(-8*10^-6)/0.5 + (1/2)*0.01*v^2

==> v = 24.1 m/s <<<<<<-----------Answer

b) let d is the closest distance.

Apply conservation of energy

k*q1*q2/d1 + (1/2)*m2*vo^2 = k*q1*q2/d

9*10^9*(-3*10^-6)*(-8*10^-6)/1 + (1/2)*0.01*25^2 = 9*10^9*(-3*10^-6)*(-8*10^-6)/d

==> d = 0.0646 m or 6.46 cm <<<<<<-----------Answer