## Essential University Physics: Volume 1 (4th Edition)

$F_{21} = -F_{12} = \frac{m_1}{m_1+m_2}F$
We start with the equation for acceleration, and then we simplify: $a = \frac{F}{m} \\ a = \frac{F}{m_1+m_2}$ We know that $F_{12} = m_2a$, so it follows: $F_{12} = \frac{m_2}{m_1+m_2}F$ Thus: $F_{21} = -F_{12} = \frac{m_1}{m_1+m_2}F$