11-7 할리데이 11판 솔루션 일반물리학

$$ \begin{cases} m &= 8.1\ut{kg}\\ \vec r_0 &= 3.0\i+8.0\j\ut{m}\\ \vec v_0 &= 5.0\i-6.0\j\ut{m/s}\\ \vec F &= -7.0\i\ut{N}\\ \end{cases} $$ $$\vec a=\frac{\vec F}{m}=-\frac{70}{81}\i\ut{m/s^2}\taag1$$ $$ \begin{aligned} \vec v &=\vec v_0+\vec a t,\\ &=\(-\frac{70}{81}t+5\)\i-6\j\ut{m/s}\taag2\\ \end{aligned} $$ $$ \begin{aligned} \vec r &=\vec r_0+\Delta \vec r,\\ &=\vec r_0+\vec v_0t+\frac{1}{2}\vec a t^2\\ &=\(-\frac{35 t^2}{81}+5 t+3\)\i+(- 6 t+8 )\j\ut{m}\taag3\\ \end{aligned} $$ $$\ab{a}$$ $$\vec L=\vec r\times\vec p,$$ $$ \begin{aligned} \vec L&=m(\vec r\times\vec v)\\ &=m(r_xv_y-r_yv_x)\k\\ &=\(-21 t^2+56 t-\frac{2349}{5}\)\k\ut{kg\cdot m^2/s} \end{aligned} $$ $$\ab{b}$$ $$\vec \tau = \vec r\times \vec F,$$ $$ \begin{aligned} \vec \tau &= \vec r\times \vec F\\ &=(r_xF_y-r_yF_x)\k\\ &=-r_yF_x\k\\ &=(-42t+56)\k\ut{N\cdot m}\\ \end{aligned} $$ $$\ab{c}$$ $$ \begin{aligned} \Ans &=\dyt{\vec L}\\ &=\Sigma \vec \tau\\ &=(-42t+56)\k\ut{N\cdot m}\\ \end{aligned} $$