8-42 할리데이 11판 솔루션 일반물리학

$$ \begin{cases} 0:\text{Start}\\ 1:x_{1}=2.0\ut{m}\\ 2:x_{2}=14\ut{m}\\ \end{cases} $$ $$ \begin{cases} v_0&=0\\ v_1&=4.2\ut{m/s}\\ v_2&=0\\ \end{cases} $$ $$ \begin{cases} m&=0.69\ut{kg}\\ a_{0\rarr1}&=\Cons\\ a_{1\rarr2}&=0\\ f_{0\rarr2}&=\Cons\\ \end{cases} $$ $$ \put \begin{cases} \KE : \text{Kinetic Energy}\\ \TE : \text{Thermal Energy}\\ \end{cases} $$ $$\ab{a}$$ $$\Sigma \Delta E=0,$$ $$\Delta \KE+\Delta \TE=0$$ $$ \begin{aligned} \Delta \TE_{1\rarr2} &=-\Delta \KE_{1\rarr2}\\ &=-\Delta \(\frac{1}{2}mv^2\)_{1\rarr2}\\ &=-\frac{1}{2}m\Delta \(v^2\)_{1\rarr2}\\ &=\frac{m}{2}\({v_1}^2-{v_2}^2\)\\ &=\frac{30429}{5000}\ut{J}\\ &= 6.0858\ut{J}\\ &\approx 6.1\ut{J} \end{aligned} $$ $$\ab{b}$$ $$\Delta \TE=fd,$$ $$ \begin{aligned} \Delta \TE_{0\rarr2}&=\Delta \TE_{0\rarr1}+\Delta \TE_{1\rarr2}\\ &=\Delta \TE_{1\rarr2}\cdot\frac{d_{0\rarr1}}{d_{1\rarr2}} +\Delta \TE_{1\rarr2}\\ &=\Delta \TE_{1\rarr2}\cdot\(\frac{d_{0\rarr1}}{d_{1\rarr2}} +1\)\\ &=7.1001\ut{J}\\ &\approx 7.1\ut{J}\\ \end{aligned} $$ $$\ab{c}$$ $$ \begin{aligned} W_{0\rarr2}&=\Delta \KE_{0\rarr2}+\Delta \TE_{0\rarr2},\\ &=\Delta \TE_{0\rarr2}\\ &\approx 7.1\ut{J}\\ \end{aligned} $$