7-27 할리데이 11판 솔루션 일반물리학

$$ \begin{cases} m&=3.05\ut{kg}\\ F&=50.0\ut{N}\\ F_N&=14.97\ut{N}\\ S&=1.85\ut{m}\\ g&=9.80665\ut{m/s^2}\\ \end{cases} $$ $$ \begin{cases} \Sigma F_x &= F-mg\sin\theta\\ \Sigma F_y &= F_N-mg\cos\theta=0 \end{cases} $$ $$ \begin{aligned} \cos\theta &= \frac{F_N}{mg},\\ \sin\theta &=\sqrt{1-\(\frac{F_N}{mg}\)^2} \end{aligned} $$ $$ \begin{aligned} \Sigma F_x&=F-mg\sqrt{1-\(\frac{F_N}{mg}\)^2}\\ &=F-\sqrt{(mg)^2 -{F_N}^2} \end{aligned} $$ $$ \begin{aligned} K&=\Sigma W\\ \frac{1}{2}mv^2&=\Sigma \vec F\cdot \vec S\\ \end{aligned} $$ $$ \begin{aligned} v&=\sqrt{\frac{2\Sigma \vec F\cdot \vec S}{m}}\\ &\approx 5.407657705118534\ut{m/s}\\ &\approx 5.41\ut{m/s}\\ \end{aligned} $$