10-15 할리데이 11판 솔루션 일반물리학

$$ \put \begin{cases} \RE : \text{Rotational Kinetic Energy}\\ \KE : \text{Kinetic Energy}\\ \GE : \text{Gravitational Potential Energy}\\ \end{cases} $$ $$ \begin{cases} r&=0.20\ut{m}\\ I&=0.40\ut{kg\cdot m^2}\\ m&=6.0\ut{kg}\\ \KE&=6.0\ut{J}\\ g&=9.80665\ut{J}\\ y_i&=0\\ \KE_i&=0\\ \RE_i&=0 \end{cases} $$ $$\ab{a}$$ $$ \begin{cases} \KE&=\frac{1}{2}mv^2\\ \RE&=\frac{1}{2}I\omega^2\\ v&=r\omega\\ \end{cases} $$ $$ \begin{aligned} \RE&=\frac{I}{mr^2}\cdot\KE\\ &=10\ut{J}\\ &=1.0\times10\ut{J} \end{aligned} $$ $$\ab{b}$$ $$ \begin{aligned} -\Delta \GE&=\Delta(\KE+\RE)\\ mg(-y)&=\KE_f+\RE_f\\ \end{aligned} $$ $$ \begin{aligned} h&=\frac{\KE_f+\RE_f}{mg}\\ &=\frac{8}{3g}\\ &\approx 0.2719243234607809\ut{m}\\ &\approx 0.27\ut{m}\\ &\approx 27\ut{cm}\\ \end{aligned} $$