8-50 할리데이 11판 솔루션 일반물리학

$$ \begin{cases} \theta &= 30\degree\\ m&= 42.0\ut{kg}\\ d&=5.20\ut{m}\\ \mu &= 0.170 \end{cases} $$ $$\Sigma \vec F =0\Harr \Delta \vec v=0$$ $$ \begin{cases} \Sigma F_x &=0\\ \Sigma F_y &=0\\ \end{cases} $$ $$ \begin{cases} F-\mu N-mg\sin\theta &=0\\ N-mg\cos\theta &=0\\ \end{cases} $$ $$\therefore F=mg(\mu \cos\theta+\sin\theta)$$ $$\ab{a}$$ $$ \begin{aligned} W&=Fd\\ &=mgd(\mu \cos\theta+\sin\theta)\\ &=\frac{273}{250} \(100+17 \sqrt{3}\) g\\ &\approx 1386.2071563901695\ut{J}\\ &\approx 1.4\times 10^3\ut{J}\\ &\approx 1.4\ut{kJ}\\ \end{aligned} $$ $$\ab{b}$$ $$ \begin{aligned} \Delta \TE&=fd\\ &=\mu N d\\ &=\mu mg d \cos \theta \\ &=\frac{4641 \sqrt{3} g}{250}\\ &\approx 315.3209763901695\ut{J}\\ &\approx 3.2\times 10^2\ut{J}\\ \end{aligned} $$