10-17 할리데이 11판 솔루션 일반물리학

$$ \begin{cases} r&=2.40\ut{cm}=2.4\times10^{-2}\ut{m}\\ I&=7.40\times10^{-4}\ut{kg\cdot m^2}\\ m&=6.20\ut{kg}\\ v_i&=0\\ t&=91.0\ut{ms}=9.1\times10^{-2}\ut{s}\\ \Delta \theta&=0.130\ut{rad}\\ g&=9.80665\ut{m/s^2} \end{cases} $$ $$\ab{a}$$ $$\Delta \theta=\omega_0t+\frac{1}{2}\alpha t^2,$$ $$ \begin{aligned} \alpha &=\frac{2\Delta \theta}{t^2}\\ &=\frac{20000}{637}\ut{rad/s^2}\\ &\approx 31.39717425431711\ut{rad/s^2}\\ &\approx 31.4\ut{rad/s^2}\\ \end{aligned} $$ $$\ab{b}$$ $$ \begin{aligned} a&=r \alpha\\ &=\frac{480}{637}\ut{m/s^2}\\ &\approx 0.7535321821036107\ut{m/s^2}\\ &\approx 0.754\ut{m/s^2}\\ &\approx 75.4\ut{cm/s^2}\\ \end{aligned} $$ $$\ab{c}$$ $$ \begin{aligned} \Sigma F_1&=ma\\ mg-T_1&=ma\\ T_1&=m(g-a)\\ &=\frac{31 g}{5}-\frac{2976}{637}\\ &\approx 56.12933047095761\ut{N}\\ &\approx 56.1\ut{N}\\ \end{aligned} $$ $$\ab{d}$$ $$ \begin{aligned} \Sigma \tau&=I\alpha\\ T_1-T_2&=I\alpha\\ \end{aligned} $$ $$ \begin{aligned} T_2&=m(g-a)-I\alpha\\ &=\frac{31 g}{5}-\frac{14954}{3185}\\ &\approx 56.10609656200942\ut{N}\\ &\approx 56.1\ut{N}\\ \end{aligned} $$