8-50 할리데이 11판 솔루션 일반물리학

$$ \begin{cases} \theta &= 30\degree\\ m&= 42.0\ut{kg}\\ d&=5.20\ut{m}\\ \mu &= 0.170 \end{cases} $$ $$\Sigma \vec F =0\Harr \Delta \vec v=0$$ $$ \begin{cases} \Sigma F_x &=0\\ \Sigma F_y &=0\\ \end{cases} $$ $$ \begin{cases} F\cos\theta-\mu N-mg\sin\theta &=0\\ N-F\sin\theta-mg\cos\theta &=0\\ \end{cases} $$ $$ \therefore\begin{cases} F=\cfrac{\mu+\tan \theta}{1-\mu\tan\theta}mg\\ N=\cfrac{mg}{\cos \theta -\mu \sin \theta } \end{cases} $$ $$\ab{a}$$ $$ \begin{aligned} W&=Fd\\ &=\frac{\mu+\tan \theta}{1-\mu\tan\theta}mgd\\ &=\frac{1092 \left(6800+10289 \sqrt{3}\right) g}{148555}\\ &\approx 1774.8554012114564\ut{J}\\ &\approx 1.8\times 10^3\ut{J}\\ &\approx 1.8\ut{kJ}\\ \end{aligned} $$ $$\ab{b}$$ $$ \begin{aligned} \Delta \TE&=fd\\ &=\mu N d\\ &=\mu \frac{mg}{\cos \theta -\mu \sin \theta }d\\ &=\frac{37128 g}{500 \sqrt{3}-85}\\ &\approx 466.18368549314334\ut{J}\\ &\approx 4.7\times 10^2\ut{J}\\ \end{aligned} $$