11-13 할리데이 11판 솔루션 일반물리학

$$ \begin{cases} m_1&=4.2\ut{kg}\\ \vec v_1&=2.2\i\ut{m/s}\\ \vec r_1&=1.5\j\ut{m} \end{cases} $$ $$ \begin{cases} m_2&=3.1\ut{kg}\\ \vec v_2&=3.6\j\ut{m/s}\\ \vec r_2&=2.8\i\ut{m} \end{cases} $$ $$\vec L=\vec r\times\vec p,$$ $$ \begin{cases} \vec L_1&= \vec r_1\times\vec p_1\\ \vec L_2&= \vec r_2\times\vec p_2\\ \end{cases} $$ $$ \begin{cases} \vec L_1&= m_1(\vec r_1\times\vec v_1)\\ \vec L_2&= m_2(\vec r_2\times\vec v_2)\\ \end{cases} $$ $$ \begin{cases} \vec L_1&= m_1(r_{1x} v_{1y}-r_{1y} v_{1x})\k\\ \vec L_2&= m_2(r_{2x} v_{2y}-r_{2y} v_{2x})\k\\ \end{cases} $$ $$ \begin{cases} \vec L_1&= -m_1r_{1y} v_{1x}\k\\ \vec L_2&= m_2r_{2x} v_{2y}\k\\ \end{cases} $$ $$ \begin{cases} \vec L_1&= -m_1r_1 v_1\k\\ \vec L_2&= m_2r_2 v_2\k\\ \end{cases} $$ $$ \begin{aligned} \Sigma \vec L &= \vec L_1+\vec L_2\\ &= (m_2r_2 v_2-m_1r_1 v_1)\k\\ &= \frac{4347}{250}\k\ut{kg\cdot m^2/s}\\ &=17.388\k\ut{kg\cdot m^2/s}\\ \end{aligned} $$ $$\ab{a}$$ $$ \begin{aligned} L&=17.388\ut{kg\cdot m^2/s}\\ &\approx 17\ut{kg\cdot m^2/s}\\ \end{aligned} $$ $$\ab{b}$$ $$ \begin{aligned} \vec L \gt0 \Rarr\text{CounterClockwise} \end{aligned} $$