Question

Two stationary frictionless pucks are placed on a level surface at an initial distance of 3.0m. The mass of puck 1 is 0.55kg and it has a charge of

+5.0 x 10^-4C,

while puck 2 has a mass of 0.25kg and a charge of +3.5 x 10^-4C. Find the velocity of each puck after they have moved very far apart.

Answer 1

$F_1=\frac{Gm_1m_2}{r^2},$

$F_2=\frac{kq_1q_2}{r^2},$

$p_1=m_1v_1,$

$p_2=m_2v_2,$

$\begin{cases} (F_2-F_1)r=\frac{m_1v_1^2}{2}+\frac{m_2v_2^2}{2}\\ p_1=p_2 \end{cases}$

$\begin{cases} \frac{2kq_1q_2}{r}-\frac{2Gm_1m_2}{r}=m_1v_1^2+m_2v_2^2 \\ m_1v_1=m_2v_2 \end{cases}$

where

$v_1=\sqrt{\frac{2m_2(kq_1q_2-Gm_1m_2)}{m_1r(m_1+m_2)}}$

$v_2=\sqrt{\frac{2m_1(kq_1q_2-Gm_1m_2)}{m_2r(m_1+m_2)}}$

$v_1\approx 24.4~\frac ms$

$v_2\approx 53.7~\frac ms$