Answer
(a) $57.28N$
(b) $85.9\times 10^{-14}J$
(c) $85.9\times 10^{-14}J$
Work Step by Step
(a) We can find the required Coulomb force as follows:
$F=\frac{KqQ}{d^2}$
We plug in the known values to obtain:
$F=\frac{(8.99\times 10^9Nm^2/C^2)(2e)(8e)}{(15\times 10^{-15}m)^2}$
$F=\frac{(8.99\times 10^9Nm^2/C^2)(56)(1.6\times 10^{-19}C)^2}{(15\times 10^{-15}m)^2}$
$F=57.28N$
(b) The required potential energy can be determined as
$U=\frac{KqQ}{d}$
$U=\frac{K(2e)(28e)}{d}$
$U=\frac{56Ke^2}{d}$
We plug in the known values to obtain:
$U=\frac{(56)(8.99\times 10^9Nm^2/C^2)(1.6\times 10^{-19}C)^2}{15\times 10^{-15}m}$
$U=85.9\times 10^{-14}J$
(c) We can find the initial kinetic energy of the particle as follows:
$K_i=U_f$
$\implies K_i=85.9\times 10^{-14}J$
