9-58 할리데이 11판 솔루션 일반물리학

$$ \put \begin{cases} 0:\text{Start}\\ 1:\text{After Burst}\\ 2:\text{Stop} \end{cases} $$ $$ \begin{cases} m_L&=3.0\ut{kg}\\ \mu_L&=0.40\\ \mu_R&=0.50\\ d_L&=0.15\ut{m}\\ d_R&=0.25\ut{m}\\ g&=9.80665\ut{m/s^2} \end{cases} $$ $$\Delta \Sigma \vec p=0,$$ $$0=m_Lv_{L1}+m_Rv_{R1}$$ $$W=\Delta \KE,$$ $$f d=\frac{1}{2}mv^2,$$ $$ \begin{aligned} {v_1}^2&=2\mu gd\\ \end{aligned} $$ $$ \begin{cases} {v_{L1}}^2&=2\mu_L gd_L\\ {v_{R1}}^2&=2\mu_R gd_R\\ 0&=m_Lv_{L1}+m_Rv_{R1} \end{cases} $$ $$ \begin{aligned} m_R&=m_L\sqrt{\frac{d_L}{d_R}\cdot\frac{\mu_L}{\mu_R}}\\ &=\frac{6}{5}\sqrt3\ut{kg}\\ &\approx 2.0784609690826525\ut{kg}\\ &\approx 2.1\ut{kg}\\ \end{aligned} $$