8-31 할리데이 11판 솔루션 일반물리학

$$ \begin{cases} v_0 &= 0\\ m &= 5.0\ut{kg}\\ k &= 640\ut{N/m}\\ \mu &= 0.25\\ D&=8.5\ut{m}\\ v_2&=0\\ g&=9.80665\ut{m/s^2} \end{cases} $$ $$ \put \begin{cases} \KE : \text{Kinetic Energy}\\ \LE : \text{Elastic Potential Energy}\\ \TE : \text{Thermal Energy}\\ \end{cases} $$ $$\ab{a}$$ $$ \begin{aligned} \Delta \TE &= fD\\ &=\mu m g D\\ &=\frac{85g}{8}\\ &=104.19565625\ut{J}\\ &=1.0\times10^2\ut{J}\\ \end{aligned} $$ $$\ab{b}$$ $$ \begin{aligned} \KE_{\max}&=\Delta \TE \\ &=\mu m g D\\ &=\frac{85g}{8}\\ &=104.19565625\ut{J}\\ &=1.0\times10^2\ut{J}\\ \end{aligned} $$ $$\ab{c}$$ $$ \begin{aligned} \LE &=\Delta \TE \\ \frac{1}{2}kx^2&=\mu m g D\\ \end{aligned} $$ $$ \begin{aligned} x&=\sqrt \frac{2\mu mgD}{k}\\ &=\frac{1}{16}\sqrt{\frac{17g}{2}}\\ &\approx 0.5706237164552925\ut{m}\\ &\approx 0.57\ut{m}\\ &\approx 57\ut{cm}\\ \end{aligned} $$