6-9 할리데이 11판 솔루션 일반물리학

$$ \begin{cases} \mu_s&=0.70 \end{cases} $$ $$\ab{a}$$ $$\Sigma \vec F = 0 \Harr \Delta \vec v=0,$$ $$ \begin{cases} \Sigma F_x &= 0\\ \Sigma F_y &= 0\\ \end{cases} $$ $$ \begin{cases} F\cos\theta-\mu_sF_N &= 0\\ F_N-mg-F\sin\theta &= 0\\ \end{cases} $$ $$ \begin{aligned} F&=\frac{\mu_s mg}{\cos\theta-\mu_s \sin\theta}\\ \frac{F}{mg}&=\frac{\mu_s}{ \cos\theta-\mu_s \sin\theta}\\ &=\frac{7\mu_s}{10 \cos\theta-7 \sin\theta}\\ \end{aligned} $$ $$\ab{b}$$ $$ \begin{aligned} \cos\theta_{\inf}-\mu_s\sin\theta_{\inf}&=0\\ \tan\theta_{\inf}&=\frac{1}{\mu_s}=\frac{10}{7}\\ \end{aligned} $$ $$ \begin{aligned} \theta_{\inf}&\approx 0.960070362405688\ut{rad}\\ &\approx 0.960\ut{rad}\\ \end{aligned} $$ $$\ab{c}$$ $$ \begin{aligned} \tan\theta_{\inf}&=\frac{1}{\mu_s}=\frac{100}{55}\\ &\approx 1.0679531158670357\ut{rad}\\ &\approx 1.07\ut{rad}\\ \end{aligned} $$