7-12 할리데이 11판 솔루션 일반물리학

$$ \begin{cases} K(0\ut{m})&=80.0\ut{J}\\ K(2\ut{m})&=0\\ v_0&=4.00\ut{m/s}\\ \end{cases} $$ $$K=\frac{1}{2}mv^2,$$ $$K(0\ut{m})=\frac{1}{2}m{v_0}^2=80.0\ut{J}$$ $$\therefore m=10.0\ut{kg}$$ $$ \begin{aligned} K_0&=W=F\cdot S\\ &=mg\sin\theta\cdot\frac{\Delta x}{\cos\theta}\\ &=mg\Delta x \tan\theta\\ \end{aligned} $$ $$ \begin{aligned} \tan\theta&=\frac{4}{g},\\ \cos\theta&=\frac{1}{\sqrt{\frac{16}{g^2}+1}}\\ \end{aligned} $$ $$ \begin{aligned} 0&=\Sigma F_y\\ &=F_N-mg\cos\theta\\ \end{aligned} $$ $$ \begin{aligned} F_N&=mg\cos\theta\\ &=\frac{10 g}{\sqrt{\frac{16}{g^2}+1}}\\ &\approx 90.80342865829145\ut{N}\\ &\approx 90.8\ut{N}\\ \end{aligned} $$