7-46 할리데이 11판 솔루션 일반물리학

$$ \begin{cases} F_{ax}&=9x-3x^2\\ x_i&=0\\ v_0&=0\\ v_f&=0\\ \end{cases} $$ $$\ab{a}$$ $$W_{i\rarr f}=\int_{i}^{f} \vec F \cdot \dd \vec S,$$ $$ \begin{aligned} W(x)&=\int_{0}^{x} (9x-3x^2) \cdot \dd x\\ &=\frac{9}{2}{x}^2-x^3 \end{aligned} $$ $$\ab{b}$$ $$ \begin{aligned} \dyx{W}&=\dx\int_{0}^{x} F \cdot \dd x\\ &=F\\ &=9x-3x^2=0,\\ \end{aligned} $$ $$\therefore x_{W \max}=3\ut{m}$$ $$\ab{c}$$ $$W(x)=\frac{9}{2}{x}^2-x^3,$$ $$ \begin{aligned} W(3)&=\frac{9}{2}{(3)}^2-(3)^3\\ &=\frac{27}{2}\ut{J}\\ &=13.5\ut{J} \end{aligned} $$ $$\ab{d}$$ $$W(x)=\frac{9}{2}{x}^2-x^3,$$ $$ \begin{aligned} W(x)&=\frac{9}{2}{x}^2-x^3=0\\ x_{W=0}&=\frac{9}{2}\ut{m}\\ &=4.5\ut{m} \end{aligned} $$ $$\ab{e}$$ $$ \begin{aligned} v&=0\Harr K=0 \Harr W=0\\ &\because K_i=K_j=0,\\ &\because \Delta K = W=0 \end{aligned} $$ $$ \begin{aligned} \therefore x_{\text{stop}}&=x_{W=0}\\ &=\frac{9}{2}\ut{m}\\ &=4.5\ut{m} \end{aligned} $$