8-19 할리데이 11판 솔루션 일반물리학

$$ \begin{cases} m&=1750\ut{kg}\\ \theta&=5.0\degree\\ S&=65\ut{m}\\ v_i&=32\ut{km/h}=\frac{80}{9}\ut{m/s}\\ v_f&=40\ut{km/h}=\frac{100}{9}\ut{m/s}\\ g&=9.80665\ut{m/s^2} \end{cases} $$ $$ \put \begin{cases} \KE : \text{Kinetic Energy}\\ \GE : \text{Gravitational Potential Energy}\\ \ME : \text{Mechanical Energy} \end{cases} $$ $$ \begin{aligned} \Delta y &= -S\sin\theta\\ &=-65\sin5\degree\\ \end{aligned} $$ $$\ME=\KE+\GE,$$ $$\ab{a}$$ $$ \begin{aligned} \Ans&=-\Delta \ME\\ &=-\Delta(\KE+\GE)\\ &=-\Delta \KE-\Delta \GE\\ &=-\Delta \(\frac{1}{2}mv^2\)-\Delta (mgy)\\ &=-\frac{1}{2}m\Delta (v^2)-mg\Delta y\\ &=-\frac{1}{2}m\Delta (v^2)-mg(-S\sin\theta)\\ &=\frac{8750}{9} (117 g \sin5\degree-40)\\ &\approx 58333.90321121774\ut{J}\\ &\approx 5.8\times 10^4\ut{J}\\ &\approx 58\ut{kJ}\\ \end{aligned} $$ $$\ab{b}$$ $$-\Delta \ME = fS,$$ $$ \begin{aligned} f&= \frac{-\Delta \ME}{S}\\ &= \frac{\frac{8750}{9} (117 g \sin5\degree-40)}{65}\\ &=1750 g \sin5\degree-\frac{70000}{117}\\ &\approx 897.4446647879653\ut{N}\\ &\approx 9.0\times10^2\ut{N}\\ \end{aligned} $$