8-55 할리데이 11판 솔루션 일반물리학

$$ \begin{cases} m&=0.50\ut{kg}\\ v_i&=13\ut{m/s}\\ h_{\max}&=7.0\ut{m}\\ g&=9.80665\ut{m/s^2}\\ \end{cases} $$ $$ \put \begin{cases} \KE : \text{Kinetic Energy}\\ \GE : \text{Gravitational Potential Energy}\\ \ME : \text{Mechanical Energy}\\ \end{cases} $$ $$ \begin{aligned} \Delta \ME &= \Delta (\KE+\GE)\\ &=\Delta \KE+\Delta \GE\\ &=\Delta \(\frac{1}{2}mv^2\)+\Delta (mgh)\\ &=\frac{1}{2}m\Delta \(v^2\)+mg \Delta h\\ &=\frac{1}{2}m \({v_f}^2-{v_i}^2\)+mg (h_f-h_i)\\ &=\frac{1}{2}m \(-{v_i}^2\)+mg (h_f)\\ &=mgh_f-\frac{1}{2}m{v_i}^2\\ &=\frac{7 g}{2}-\frac{169}{4}\\ &=-7.926725\ut{J}\\ &\approx -7.9\ut{J} \end{aligned} $$