7-38 할리데이 11판 솔루션 일반물리학

$$ \begin{cases} m&=31.0\ut{kg}\\ \theta&=25.0\degree\\ F&=350\ut{N}\\ S&=2.30\ut{m}\\ g&=9.80665\ut{m/s^2}\\ \end{cases} $$ $$\ab{a}$$ $$W=\vec F \cdot \vec S,$$ $$ \begin{aligned} W_F&=350\cdot2.30\\ &=805\ut{J} \end{aligned} $$ $$\ab{b}$$ $$ \begin{aligned} W_{mg}&=mgS\cos(90\degree+\theta)\\ &=-\frac{713}{10}g\sin25\degree\\ &\approx -295.5006665444094\ut{J}\\ &\approx -296\ut{J}\\ \end{aligned} $$ $$\ab{c}$$ $$ \begin{aligned} W_{N}&=\vec N\cdot\vec S\\ &=0~~(\because \vec N\perp\vec S ) \end{aligned} $$ $$\ab{d}$$ $$ \begin{aligned} \Sigma W&=W_F+W_{mg}+W_{N}\\ &=805-\frac{713}{10}g\sin25\degree\\ &\approx 509.4993334555906\ut{J}\\ &\approx 509\ut{J}\\ \end{aligned} $$