5-43 할리데이 11판 솔루션 일반물리학

$$\begin{cases} a_1&=10.0\ut{m/s^2}\\ a_2&=6.20\ut{m/s^2}\\ \end{cases}$$ $$\ab{a}$$ $$\begin{cases} m_1&=\cfrac{F}{a_1}\\ m_2&=\cfrac{F}{a_2}\\ \end{cases}$$ $$\begin{aligned} a_a&=\frac{F}{m_2-m_1}\\ &=\frac{F}{\frac{F}{a_2}-\frac{F}{a_1}}\\ &=\frac{1}{\frac{1}{a_2}-\frac{1}{a_1}}\\ &=\frac{310}{19}\ut{m/s^2}\\ &= 16.3158\ut{m/s^2}\\ &\approx 16.3\ut{m/s^2}\\ \end{aligned}$$ $$\ab{b}$$ $$\begin{aligned} a_b&=\frac{F}{m_2+m_1}\\ &=\frac{F}{\frac{F}{a_2}+\frac{F}{a_1}}\\ &=\frac{1}{\frac{1}{a_2}+\frac{1}{a_1}}\\ &=\frac{310}{81}\ut{m/s^2}\\ &= 3.82716\ut{m/s^2}\\ &\approx 3.83\ut{m/s^2}\\ \end{aligned}$$