5-22 할리데이 11판 솔루션 일반물리학

$$ \begin{cases} m&=72.0\ut{kg}\\ \theta&=5.00\degree\\ a&=3.5\ut{m/s^2}\\ g&=9.80665\ut{m/s^2}\\ \end{cases} $$ $$\ab{a}$$ $$ \begin{aligned} \Sigma F&=ma\\ &=72\cdot3.5\\ &=252\ut{N}\\ &\approx 2.5\times10^2\ut{N}\\ \end{aligned} $$ $$\ab{b}$$ $$ \begin{aligned} \Sigma F_y&=F_N-mg\cos\theta=0\\ F_N&=mg\cos\theta, \end{aligned} $$ $$ \begin{aligned} \Sigma \vec F&=\vec F+m\vec g=m\vec a\\ \end{aligned} $$ $$ \begin{aligned} \vec F&=m\vec a-m\vec g\\ &=ma\i-m(-g\sin\theta\i-g\cos\theta\j)\\ &=ma\i+mg\sin\theta\i+mg\cos\theta\j\\ &=(ma+mg\sin\theta)\i+mg\cos\theta\j\\ \end{aligned} $$ $$ \begin{aligned} F&=\sqrt{(ma+mg\sin\theta)^2+(mg\cos\theta)^2}\\ &=m\sqrt{a^2+g^2+2ga\sin\theta}\\ &\approx 770.1083288892785\ut{N}\\ &\approx 7.7\times10^2\ut{N}\\ \end{aligned} $$