8-35 할리데이 11판 솔루션 일반물리학

$$ \begin{cases} v_0&=0\\ m&=70\ut{kg}\\ \Delta y &= -6.0\ut{m}\\ \Delta d&=-\Delta y \end{cases} $$ $$ \put \begin{cases} \KE : \text{Kinetic Energy}\\ \GE : \text{Gravitational Potential Energy}\\ \TE : \text{Thermal Energy}\\ \end{cases} $$ $$\Sigma E_i=\Sigma E_f,$$ $$\KE_i+\GE_i+\TE_i=\KE_f+\GE_f+\TE_f$$ $$ \begin{aligned} \KE_f&=-\Delta \TE-\Delta \GE\\ \frac{1}{2}mv^2&=-\Delta (fd)-\Delta (mgy)\\ &=-f\Delta d-mg\Delta y\\ &=-f(-\Delta y)-mg\Delta y\\ &=f\Delta y-mg\Delta y\\ \end{aligned} $$ $$ \begin{aligned} v&=\sqrt\frac{2(f \Delta y-mg \Delta y)}{m}\\ &=\sqrt\frac{2\Delta y(f -mg)}{m}\\ &=\sqrt\frac{6(70g -f)}{35}\\ \end{aligned} $$ $$\ab{a}$$ $$f=0,$$ $$ \begin{aligned} v&=\sqrt\frac{6(70g -0)}{35}\\ &=2\sqrt{3g}\\ &\approx 10.848032079598585\ut{m/s}\\ &\approx 11\ut{m/s}\\ \end{aligned} $$ $$\ab{b}$$ $$f=500\ut{N},$$ $$ \begin{aligned} v&=\sqrt\frac{6(70g -500)}{35}\\ &=2\sqrt{3g-\frac{150}{7}}\\ &\approx 5.653805292518861\ut{m/s}\\ &\approx 5.7\ut{m/s}\\ \end{aligned} $$