8-2 할리데이 11판 솔루션 일반물리학

$$ \put \begin{cases} \KE : \text{Kinetic Energy}\\ \GE : \text{Gravitational Potential Energy}\\ \TE : \text{Thermal Energy}\\ \end{cases} $$ $$\ab{a}$$ $$ \begin{cases} v_A&=9.00\ut{m/s}\\ h_1&=y_A=7.00\ut{m}\\ \end{cases} $$ $$ \begin{aligned} \Sigma E_A&=\Sigma E_B,\\ \KE_A+\GE_A&=\KE_B+\GE_B\\ \frac{1}{2}m{v_A}^2+mgy_A&=\frac{1}{2}m{v_B}^2+mgy_B\\ {v_A}^2+2gy_A&={v_B}^2~~(\because y_B=0)\\ \end{aligned} $$ $$ \begin{aligned} v_B&=\sqrt{{v_A}^2+2gy_A}\\ &=\sqrt{81+14g}\\ &\approx 14.77474534467515\ut{m/s}\\ &\approx 14.8\ut{m/s}\\ \end{aligned} $$ $$\ab{b}$$ $$ \begin{cases} v_A&=9.00\ut{m/s}\\ h_1&=y_A=7.00\ut{m}\\ h_2&=y_C=3.00\ut{m}\\ \end{cases} $$ $$ \begin{aligned} \Sigma E_A&=\Sigma E_C,\\ \KE_A+\GE_A&=\KE_C+\GE_C\\ \frac{1}{2}m{v_A}^2+mgy_A&=\frac{1}{2}m{v_C}^2+mgy_C\\ {v_A}^2+2gy_A&={v_C}^2+2gy_C\\ \end{aligned} $$ $$ \begin{aligned} v_C&=\sqrt{{v_A}^2+2gy_A-2gy_C}\\ &=\sqrt{{v_A}^2+2g(y_A-y_C)}\\ &=\sqrt{81+8g}\\ &\approx 12.627477974639277\ut{m/s}\\ &\approx 12.6\ut{m/s}\\ \end{aligned} $$ $$\ab{c}$$ $$ \begin{cases} v_A&=9.00\ut{m/s}\\ h_1&=y_A=7.00\ut{m}\\ h_2&=y_D=3.00\ut{m}\\ \mu &=0.70\\ L&=12\ut{m}\\ \end{cases} $$ $$ \begin{aligned} \TE_D&=f_{A\rarr D}d_{A\rarr D}\\ &=\mu mgL \end{aligned} $$ $$ \begin{aligned} \Sigma E_A&=\Sigma E_D,\\ \KE_A+\GE_A&=\KE_D+\GE_D+\TE_D\\ \frac{1}{2}m{v_A}^2+mgy_A&=\frac{1}{2}m{v_D}^2+mgy_D+\mu mgL\\ {v_A}^2+2gy_A&={v_D}^2+2gy_D+2\mu gL\\ \end{aligned} $$ $$ \begin{aligned} {v_D}^2&={v_A}^2+2gy_A-(2gy_D+2\mu gL)\\ &={v_A}^2+2g(y_A-y_D-\mu L)\\ &=-5.29852\\ \end{aligned} $$ $$\title{Impossible to Arrive}$$ $$\put C\rarr E\rarr D$$ $$ \begin{aligned} \Sigma E_A&=\Sigma E_E,\\ \KE_A+\GE_A&=\GE_E+\TE_E\\ &(\because \KE_E=0)\\ \frac{1}{2}m{v_A}^2+mgy_A&=mgy_E+\mu mgS_E\\ \frac{1}{2}{v_A}^2+gy_A&=gy_E+\mu gS_E\\ \end{aligned} $$ $$ \begin{aligned} S_E&=\frac{{v_A}^2}{2\mu g}+\frac{y_A-y_E}{\mu}\\ &=\frac{5}{7g}(81+8g)\\ &\approx 11.614072375086584\ut{m}\\ &\approx 11.6\ut{m}\\ \end{aligned} $$