8-1 할리데이 11판 솔루션 일반물리학

$$ \put \begin{cases} \KE : \text{Kinetic Energy}\\ \GE : \text{Gravitational Potential Energy}\\ \LE : \text{Elastic Potential Energy}\\ \end{cases} $$ $$\ab{a}$$ $$ \begin{cases} 0:\text{Start}\\ 1:\text{Spring Contact}\\ 2:\text{Spring Contraction}\\ \end{cases} $$ $$ \begin{cases} \theta &= 40\degree\\ k&=220\ut{N/m}\\ d&=0.60\ut{m}\\ m&=1.5\ut{kg}\\ \KE_{0}&=16\ut{J}\\ \end{cases} $$ $$ \begin{cases} x_0&=0\\ x_{2}&=0.20\ut{m}\\ \end{cases} $$ $$ \begin{cases} y_0&=0,\\ y_2&=(d+x_{2})\sin\theta\\ \end{cases} $$ $$ \begin{cases} y_0&=0\\ y_2&=\frac{4}{5}\sin40\degree\ut{m}\\ \end{cases} $$ $$\Sigma E_0=\Sigma E_2,$$ $$\KE_0=\GE_2+\LE_2+\KE_2$$ $$ \begin{aligned} \KE_2&=\KE_0-mgy_{2}-\frac{1}{2}k{x_{2}}^2\\ &=\frac{58}{2}-\frac{6}{5}g\sin40\degree\\ &\approx 4.035688264960999\ut{J}\\ &\approx 4.0\ut{J}\\ \end{aligned} $$ $$\ab{b}$$ $$ \begin{cases} a:\text{Start}\\ b:\text{Spring Contact}\\ c:\text{Spring Contraction}\\ \end{cases} $$ $$ \begin{cases} \theta &= 40\degree\\ k&=220\ut{N/m}\\ d&=0.60\ut{m}\\ m&=1.5\ut{kg}\\ v_{c}&=0\\ \end{cases} $$ $$ \begin{cases} x_a&=0\\ x_c&=0.40\ut{m}\\ \end{cases} $$ $$ \begin{cases} y_a&=0,\\ y_c&=(d+x_c)\sin\theta\\ \end{cases} $$ $$ \begin{cases} y_a&=0\\ y_c&=\sin40\degree\ut{m}\\ \end{cases} $$ $$\Sigma E_a=\Sigma E_c,$$ $$ \begin{aligned} \KE_a&=\GE_c+\LE_c+\KE_c\\ &=\GE_c+\LE_c~~(\because v_c=0)\\ &=mgy_c+\frac{1}{2}k{x_c}^2\\ &=\frac{88}{5}+\frac{3}{2}g\sin40\degree\\ &\approx 27.055389668798753\ut{J}\\ &\approx 27\ut{J}\\ \end{aligned} $$