11-28 할리데이 11판 솔루션 일반물리학

$$\begin{cases} m&=2.90\times10^{-4}\ut{kg}\\ v&=3.03\ut{m/s}\\ 2d&=4.20\ut{cm}=4.20\times10^{-2}\ut{m}\\ \end{cases}$$ $$\begin{cases} \vec v&=v\i\\ \vec S&=vt\i+d\j\\ \vec O&=x\i+y\j+z\k\\ \vec r&=\vec S - \vec O=(vt-x)\i+(d-y)\j-z\k\\ \end{cases}$$ $$\begin{aligned} \vec L&=m(\vec r\times\vec v)\\ &=mv\bra{-z\j+\br{y-d}\k}\\ \end{aligned}$$ $$L=\abs{mv}\sqrt{\br{y-d}^2+{z}^2}$$ $$\begin{cases} d_1&=+d\\ d_2&=-d\\ \end{cases}$$ $$\therefore \begin{cases} L_{1}&=\abs{mv_{1}}\sqrt{\br{y-d}^2+{z}^2}\\ L_{2}&=\abs{mv_{2}}\sqrt{\br{y+d}^2+{z}^2}\\ \end{cases}$$ $$\ab{a}$$ $$\begin{cases} v_{a1}&=v\\ v_{a2}&=-v\\ \vec O_a&=0 \end{cases}$$ $$\begin{cases} L_{a1}&=\abs{mv_{a1}}\sqrt{\br{y_a-d}^2+{z_a}^2}\\ L_{a2}&=\abs{mv_{a2}}\sqrt{\br{y_a+d}^2+{z_a}^2}\\ \end{cases}$$ $$\begin{cases} L_{a1}&=\abs{mvd}\\ L_{a2}&=\abs{mvd}\\ \end{cases}$$ $$\begin{aligned} L_{a1}&=L_{a2}\\ &=1.84527\times10^{-5}\ut{kg\cdot m^2/s}\\ &\approx 1.85\times10^{-5}\ut{kg\cdot m^2/s}\\ \end{aligned}$$ $$\ab{b}$$ $$\begin{cases} v_{b1}&=v\\ v_{b2}&=-v\\ \vec O_b&=\vec X \end{cases}$$ $$\begin{cases} L_{b1}&=\abs{mv_{b1}}\sqrt{\br{y_b-d}^2+{z_b}^2}\\ L_{b2}&=\abs{mv_{b2}}\sqrt{\br{y_b+d}^2+{z_b}^2}\\ \end{cases}$$ $$\begin{cases} L_{b1}&=\abs{mv}\sqrt{\br{y-d}^2+{z}^2}\\ L_{b2}&=\abs{mv}\sqrt{\br{y+d}^2+{z}^2}\\ \end{cases}$$ $$\begin{cases} L_{b1}&=8.787 \sqrt{\br{10^3 y-21}^2+\br{10^3 z}^2}\times10^{-7}\\ L_{b2}&=8.787 \sqrt{\br{10^3 y+21}^2+\br{10^3 z}^2}\times10^{-7}\\ \end{cases}$$ $$\ab{c}$$ $$\begin{cases} v_{c1}&=v\\ v_{c2}&=v\\ \vec O_c&=0 \end{cases}$$ $$\begin{cases} L_{c1}&=\abs{mv_{c1}}\sqrt{\br{y_c-d}^2+{z_c}^2}\\ L_{c2}&=\abs{mv_{c2}}\sqrt{\br{y_c+d}^2+{z_c}^2}\\ \end{cases}$$ $$\begin{cases} L_{c1}&=\abs{mvd}\\ L_{c2}&=\abs{mvd}\\ \end{cases}$$ $$\begin{aligned} L_{c1}&=L_{c2}\\ &=1.84527\times10^{-5}\ut{kg\cdot m^2/s}\\ &\approx 1.85\times10^{-5}\ut{kg\cdot m^2/s}\\ \end{aligned}$$ $$\ab{d}$$ $$\begin{cases} v_{d1}&=v\\ v_{d2}&=v\\ \vec O_d&=\vec X \end{cases}$$ $$\begin{cases} L_{d1}&=\abs{mv_{d1}}\sqrt{\br{y_d-d}^2+{z_d}^2}\\ L_{d2}&=\abs{mv_{d2}}\sqrt{\br{y_d+d}^2+{z_d}^2}\\ \end{cases}$$ $$\begin{cases} L_{d1}&=\abs{mv}\sqrt{\br{y-d}^2+{z}^2}\\ L_{d2}&=\abs{mv}\sqrt{\br{y+d}^2+{z}^2}\\ \end{cases}$$ $$\begin{cases} L_{d1}&=8.787 \sqrt{\br{10^3 y-21}^2+\br{10^3 z}^2}\times10^{-7}\\ L_{d2}&=8.787 \sqrt{\br{10^3 y+21}^2+\br{10^3 z}^2}\times10^{-7}\\ \end{cases}$$