8-47 할리데이 11판 솔루션 일반물리학

$$ \put \begin{cases} i : \text{Start}\\ f : \text{Highest Point} \end{cases} $$ $$ \begin{cases} m&=0.750\ut{kg}\\ \vec v_i&=2.75\j\ut{m/s}\\ g&=9.80665\ut{m/s^2}\\ \end{cases} $$ $$ \put \begin{cases} \KE : \text{Kinetic Energy}\\ \GE : \text{Gravitational Potential Energy}\\ \end{cases} $$ $$\ab{a}$$ $$ \begin{aligned} \KE &= \frac{1}{2}mv^2\\ &=\frac{363}{128}\ut{J}\\ &=2.8359375\ut{J}\\ &\approx 2.84\ut{J}\\ \end{aligned} $$ $$\ab{b}$$ $$ \begin{aligned} W_{mg}&=\Delta \KE\\ &=\KE_f-\KE_i\\ &=-\KE_i~~~(\because v_f=0)\\ &=-\frac{363}{128}\ut{J}\\ &=-2.8359375\ut{J}\\ &\approx -2.84\ut{J}\\ \end{aligned} $$ $$\ab{c}$$ $$\Delta E=0$$ $$ \begin{aligned} \Delta \GE+\Delta \KE&=0\\ \end{aligned} $$ $$ \begin{aligned} \Delta \GE&=-\Delta \KE\\ &=2.8359375\ut{J}\\ &\approx 2.84\ut{J}\\ \end{aligned} $$ $$\ab{d}$$ $$\GE_i=0,$$ $$ \begin{aligned} \GE_f&=\GE_i+\Delta \GE\\ &=\Delta \GE\\ &=2.8359375\ut{J}\\ &\approx 2.84\ut{J}\\ \end{aligned} $$ $$\ab{e}$$ $$\GE_f=0,$$ $$ \begin{aligned} \GE_i&=\GE_f-\Delta \GE\\ &=-\Delta \GE\\ &=-2.8359375\ut{J}\\ &\approx -2.84\ut{J}\\ \end{aligned} $$ $$\ab{f}$$ $$ \begin{aligned} \Delta \GE&=\Delta (mgh)\\ &=mg\Delta h\\ \end{aligned} $$ $$ \begin{aligned} \Delta h&=\frac{\Delta \GE}{mg}\\ &=\frac{121}{32g}\\ &\approx 0.38558019303227914\ut{m}\\ &\approx 0.386\ut{m}\\ &\approx 38.6\ut{cm}\\ \end{aligned} $$