8-80 할리데이 11판 솔루션 일반물리학

$$ \begin{cases} L&=230\ut{cm}\\ g&=9.80665\ut{m/s^2} \end{cases} $$ $$ \put \begin{cases} 0:\text{Start}\\ 1:\text{Lowest Point}\\ 2:\text{Over P Highest Point} \end{cases} $$ $$ \begin{cases} y_0&=L\\ y_1&=0\\ y_2&=2r\\ \end{cases} $$ $$\Sigma \Delta E=0,$$ $$\Delta \KE+\Delta \GE=0$$ $$ \begin{aligned} \Delta \KE&=-\Delta \GE\\ \Delta \(\frac{1}{2}m{v}^2\)&=-\Delta (mgy)\\ \Delta \({v}^2\)&=2g(-\Delta y)\\ {v_2}^2-{v_0}^2&=2g( y_0-y_2)\\ {v_2}^2&=2g(L-2r)\taag1\\ \end{aligned} $$ $$ \begin{aligned} \Sigma F_{R2}&=mg=\frac{m{v_2}^2}{R}\\ gR&={v_2}^2\\ &=2g(L-2r)\\ \end{aligned} $$ $$ \begin{aligned} r&=2(L-2r)\\ r&=\frac{2}{5}L\\ \end{aligned} $$ $$d=L-r,$$ $$ \begin{aligned} d&=\frac{3}{5}L\\ &=138\ut{cm}\\ &\approx 1.4\ut{m} \end{aligned} $$