12-13 할리데이 11판 솔루션 일반물리학

$$\begin{cases} h&=3.00\ut{cm}\\ r&=6.00\ut{cm}\\ m&=0.415\ut{kg}\\ g&=9.80665\ut{m/s^2}\\ \end{cases}$$ $$\begin{cases} x&=\sqrt{r^2-y^2}\\ y&=r-h\\ \end{cases}$$ $$\begin{aligned} \Sigma \tau&=-yF+xmg=0\\ F&={x\over y} mg\\ &=\frac{ \sqrt{h (2r-h)}}{r-h}mg\\ &={83\sqrt3\over200}g\\ &=\frac{16279039 \sqrt{3}}{4000000}\ut{N}\\ &\approx 7.049030661598812\ut{N}\\ &\approx 7.05\ut{N}\\ \end{aligned}$$