8-10 할리데이 11판 솔루션 일반물리학

$$ \begin{cases} 0:\text{Start}\\ 1:\text{End}\\ \end{cases} $$ $$ \begin{cases} R&=12\ut{m}\\ h_0&=4.0\ut{m}\\ m&=25\ut{kg}\\ v_1&=6.2\ut{m/s} \end{cases} $$ $$\ab{a}$$ $$\theta=\frac{L}{R}=\cos^{-1}\frac{R-h_0}{R},$$ $$ \begin{aligned} L &= R\cos^{-1}\frac{R-h_0}{R}\\ &=12\cos^{-1}\frac{2}{3}\\ &\approx 10.092824046815164\ut{m}\\ &\approx 10\ut{m}\\ \end{aligned} $$ $$\ab{b}$$ $$\Sigma E_0=\Sigma E_1,$$ $$ \begin{aligned} \GE_0&=\KE_1+\TE_1\\ mgh_0&=\frac{1}{2}m{v_1}^2+fL\\ \end{aligned} $$ $$ \begin{aligned} f&=\frac{mgh_0-\frac{1}{2}m{v_1}^2}{L}\\ &=\frac{200 g-961}{24 \cos ^{-1}\frac{2}{3}}\\ &\approx 49.556496544476005\ut{N}\\ &\approx 5.0\times10\ut{N}\\ \end{aligned} $$ $$\ab{c}$$ $$\theta=\frac{L}{R}=\sin^{-1}\frac{h_0}{R},$$ $$ \begin{aligned} L &= R\sin^{-1}\frac{h_0}{R}\\ &=12\sin^{-1}\frac{1}{3}\\ &\approx 4.078042913449464\ut{m}\\ &\approx 4.1\ut{m}\\ \end{aligned} $$ $$\ab{d}$$ $$\Sigma E_0=\Sigma E_1,$$ $$ \begin{aligned} \GE_0&=\KE_1+\TE_1\\ mgh_0&=\frac{1}{2}m{v_1}^2+fL\\ \end{aligned} $$ $$ \begin{aligned} f&=\frac{mgh_0-\frac{1}{2}m{v_1}^2}{L}\\ &=\frac{200 g-961}{24 \sin^{-1}\frac{1}{3}}\\ &\approx 122.64829248128957\ut{N}\\ &\approx 1.2\times10^2\ut{N}\\ \end{aligned} $$