12-33 할리데이 11판 솔루션 일반물리학

$$\begin{cases} M&=m_b+m_p=89.00\ut{kg}\\ T_a&=500\ut{N}\\ T_b&=700\ut{N}\\ g&=9.80665\ut{m/s^2} \end{cases}$$ $$\put {x\over L}=k,$$ $$\Sigma \tau=0,$$ $$\begin{aligned} 0&=-{L\over2}m_bg-\br{x\over L}Lm_pg+LT_y \\ &={m_bg}+2km_pg-2T\sin\theta \\ \end{aligned}$$ $$\begin{cases} 0&={m_bg}+2\br{0}m_pg-2\br{500}\sin\theta \\ 0&={m_bg}+2\br{1}m_pg-2\br{700}\sin\theta \\ 89&=m_b+m_p \end{cases}$$ $$\ab{a,b,c}$$ $$\begin{cases} \theta&=\sin^{-1}\br{89g\over1200}\\ m_b&={445\over6}\ut{kg}\\ m_p&={89\over6}\ut{kg}\\ \end{cases}$$ $$\begin{cases} \theta&\approx 0.8144183521806214\ut{rad}\\ m_b&\approx 74.16666666666667\ut{kg}\\ m_p&\approx 14.833333333333334\ut{kg}\\ \end{cases}$$ $$\begin{cases} \theta&\approx 0.814\ut{rad}\\ m_b&\approx 74.2\ut{kg}\\ m_p&\approx 14.8\ut{kg}\\ \end{cases}$$