7-34 할리데이 11판 솔루션 일반물리학

$$ \begin{cases} m&= 72\ut{kg}\\ S&=1.5\ut{m}\\ h&=0.85\ut{m}\\ \end{cases} $$ $$\Sigma \vec F = 0 \Harr \Delta \vec v=0,$$ $$ \begin{cases} \Sigma F_x &= 0\\ \Sigma F_y &= 0\\ \end{cases} $$ $$ \begin{cases} 0&=F-mg\sin\theta \\ 0&=N-mg\cos\theta \\ \end{cases} $$ $$\ab{a}$$ $$ \begin{aligned} \sin\theta&=\frac{h}{S}\\ &=\frac{17}{30}\\ \end{aligned} $$ $$ \begin{aligned} F&=mg\sin\theta\\ &=\frac{204}{5}g\\ &=400.11132\ut{N}\\ &\approx 4.0\times10^2\ut{N} \end{aligned} $$ $$\ab{b}$$ $$W=\vec F \cdot \vec S,$$ $$ \begin{aligned} W_{F}&=\frac{204}{5}g\i \cdot (-1.5)\i\\ &=-\frac{306}{5}g\\ &= -600.16698\ut{J}\\ &\approx -6.0\times10^2\ut{J}\\ \end{aligned} $$ $$\ab{c}$$ $$ \begin{aligned} W_{mg}&=(-72g\sin\theta\i-72g\cos\theta\j)\cdot(-1.5\i)\\ &=\frac{306}{5}g\\ &=600.16698\ut{J}\\ &\approx 6.0\times10^2\ut{J}\\ \end{aligned} $$ $$\ab{d}$$ $$ \begin{aligned} W_{N}&=(N\j)\cdot(-1.5\i)\\ &=0 \end{aligned} $$ $$\ab{e}$$ $$ \begin{aligned} \Sigma W&=W_{mg}+W_{F}+W_{N}\\ &=\frac{306}{5}g-\frac{306}{5}g+0\\ &=0 \end{aligned} $$