6-66 할리데이 11판 솔루션 일반물리학

$$ \begin{cases} \theta&=2.5\degree\\ mg&=69\ut{N}\\ g&=9.80665\ut{m/s^2}\\ \end{cases} $$ $$\Sigma \vec F = m\vec a,$$ $$ \begin{aligned} m a &= mg\sin\theta-f\\ f&=mg\sin\theta-ma\\ &=69 \sin2.5\degree-\frac{1380000}{196133}a \end{aligned} $$ $$\ab{a}$$ $$v=0,a=0$$ $$ \begin{aligned} f&=69 \sin2.5\degree\ut{N}\\ &\approx 3.009737728208184\ut{N}\\ &\approx 3.0\ut{N}\\ \end{aligned} $$ $$\text{Down}$$ $$\ab{b}$$ $$v=0.65\ut{m/s},a=0$$ $$ \begin{aligned} f&=69 \sin2.5\degree\ut{N}\\ &\approx 3.009737728208184\ut{N}\\ &\approx 3.0\ut{N}\\ \end{aligned} $$ $$\text{Down}$$ $$\ab{c}$$ $$v=0.65\ut{m/s},a=0.20\ut{m/s^2}$$ $$ \begin{aligned} f&=69 \sin2.5\degree-\frac{276000}{196133}\ut{N}\\ &\approx 1.602529354298643\ut{N}\\ &\approx 1.6\ut{N}\\ \end{aligned} $$ $$\text{Down}$$ $$\ab{d}$$ $$v=0.65\ut{m/s},a=-0.20\ut{m/s^2}$$ $$ \begin{aligned} f&=69 \sin2.5\degree+\frac{276000}{196133}\ut{N}\\ &\approx 4.416946102117725\ut{N}\\ &\approx 4.4\ut{N}\\ \end{aligned} $$ $$\text{Down}$$ $$\ab{e}$$ $$v=0.65\ut{m/s},a=0.57\ut{m/s^2}$$ $$ \begin{aligned} f&=69 \sin2.5\degree-\frac{786600}{196133}\ut{N}\\ &\approx -1.000806137434008\ut{N}\\ &\approx -1.0\ut{N}\\ \end{aligned} $$ $$\text{Up}$$ $$\ab{f}$$ $$\text{e Case}$$