7-7 할리데이 11판 솔루션 일반물리학

$$ \begin{cases} v_0&=0\\ m&=1.5\ut{kg}\\ \vec F&=(2.5-x^2)\i\ut{N}\\ x_0&=0 \end{cases} $$ $$ \begin{aligned} W(x)&=\int_{0}^{x} F \cdot \dd x\\ &=\int_{0}^{x}(2.5-x^2)\dd x\\ &=\frac{5x}{2}-\frac{x^3}{3}\\ \end{aligned} $$ $$\ab{a}$$ $$x=2.8\ut{m}$$ $$ \begin{aligned} W(2.8)&=-\frac{119}{375}\ut{J}\\ \abs{K}&=\abs{K_0+W}\\ &=\frac{119}{375}\ut{J}\\ &\approx 0.31733333333333336\ut{J}\\ &\approx 0.32\ut{J}\\ \end{aligned} $$ $$\ab{b}$$ $$ \begin{aligned} \frac{\dd W}{\dd x}&=\frac{\dd}{\dd x}\(\int_{0}^{x} F \cdot \dd x\)\\ &=F\\ &=2.5-x^2=0\\ x&=\sqrt{\frac{5}{2}}\ut{m}\\ &\approx 1.5811388300841898\ut{m}\\ &\approx 1.6\ut{m}\lt 2.0\ut{m}\\ \end{aligned} $$ $$ \begin{aligned} K_{\max}&=W\(\sqrt{\frac{5}{2}}\)\\ &=\frac{5}{3}\sqrt{\frac{5}{2}}\ut{J}\\ &\approx 2.63523138347365\ut{J}\\ &\approx 2.6\ut{J}\\ \end{aligned} $$