6-60 할리데이 11판 솔루션 일반물리학

$$ \begin{cases} \theta&=30\degree\\ \mu_1&=\mu\\ \mu_2&=0\\ t_1&=2t_2 \end{cases} $$ $$S=v_0t+\frac{1}{2}at^2,$$ $$S=(0)t+\frac{1}{2}a{t}^2$$ $$a=\frac{2S}{t^2}$$ $$ \begin{aligned} a_2&=\frac{2S}{{t_2}^2}\\ a_1&=\frac{2S}{(2t_2)^2}=\frac{1}{4}a_2 \end{aligned} $$ $$\Sigma \vec F = m\vec a,$$ $$ \begin{aligned} \Sigma F_2 &= m a_2\\ m a_2 &= mg\sin\theta\\ a_2&=g\sin\theta=\frac{g}{2}\\ a_1&=\frac{1}{4}a_2=\frac{g}{8} \end{aligned} $$ $$\Sigma \vec F = m\vec a,$$ $$ \begin{cases} \Sigma F_{1x} &= m a_1\\ \Sigma F_{1y} &= 0\\ \end{cases} $$ $$ \begin{cases} m a_1 &= mg\sin\theta-\mu N\\ 0 &= N-mg\cos\theta\\ \end{cases} $$ $$ \begin{aligned} a_1&=g\sin\theta-\mu g\cos\theta\\ \mu&=\frac{g\sin\theta-a_1}{g\cos\theta}\\ &=\tan\theta-\frac{a_1}{g\cos\theta}\\ &=\frac{\sqrt3}{4}\\ &\approx 0.4330127018922193\\ &\approx 0.4\\ \end{aligned} $$