9-28 할리데이 11판 솔루션 일반물리학

$$\begin{cases} m_1&=200\ut{g}=0.2\ut{kg}\\ v_{1i}&=3.00\ut{m/s}\\ m_2&=400\ut{g}=0.4\ut{kg}\\ v_{2i}&=0\\ \end{cases}$$ $$\put\begin{cases} \vec v_{\text{in}}&=\vec v_{1i}-\vec v_{2i}=v_{1i}\\ \vec v_{\text{out}}&=\vec v_{1f}-\vec v_{2f}\\ \end{cases}$$ $$\Delta \Sigma \vec P=0,$$ $$m_1v_{1i}+m_2v_{2i}=m_1v_{1f}+m_2v_{2f}$$ $$\begin{aligned} J&=\Delta \vec P\\ &=m_1v_{1f}-m_1v_{1i}\\ &=m_1(v_{1f}-v_{1i})\\ &=\frac{m_1m_2}{m_1+m_2}(v_{\text{out}}-v_{\text{in}})\\ &=\frac{2}{15}(v_{\text{out}}-v_{\text{in}})\\ \end{aligned}$$ $$\ab{a}$$ $$\text{Elastic Collision}\Harr\vec v_{\text{in}}+ \vec v_{\text{out}}=0,$$ $$\begin{aligned} \abs{J}&=\abs{\frac{2}{15}(-2v_{\text{in}})}\\ &=\frac{4}{5}\ut{N\cdot s}\\ &=0.8\ut{N\cdot s}\\ &=800\ut{mN\cdot s}\\ \end{aligned}$$ $$\ab{b}$$ $$\text{Perfectly Inelastic Collision}\Harr\vec v_{\text{out}}=0,$$ $$\begin{aligned} \abs{J}&=\abs{\frac{2}{15}(-v_{\text{in}})}\\ &=\frac{2}{5}\ut{N\cdot s}\\ &=0.4\ut{N\cdot s}\\ &=400\ut{mN\cdot s}\\ \end{aligned}$$