7-28 할리데이 11판 솔루션 일반물리학

$$ \begin{cases} m&=6.0\ut{kg}\\ v(0\ut{m})&=4.0\ut{m/s} \end{cases} $$ $$ F(x)=\begin{cases} 8-8x&:(0\le x \le2)\\ -8&:(2\le x \le8) \end{cases} $$ $$W_{i\rarr f}=\int_{i}^{f} \vec F \cdot \dd \vec S,$$ $$ \begin{aligned} W_{0\rarr (2+s)}&=\int_{0}^{2+s} F \cdot \dd x\\ &=\int_{0}^{2} F \cdot \dd x+\int_{2}^{2+s} F \cdot \dd s\\ &=0+(-8\cdot s)\\ &=-8s \end{aligned} $$ $$ \begin{aligned} K(2+s)&=K(0)+W_{0\rarr (2+s)}\\ &=\frac{1}{2}m{v_0}^2-8s\\ &=48-8s\\ \end{aligned} $$ $$\ab{a}$$ $$ \begin{aligned} K(3)&=K(2+1)\\ &=48-8\cdot 1\\ &=40\ut{J}\\ &=4.0\times 10\ut{J}\\ \end{aligned} $$ $$\ab{b}$$ $$ \begin{aligned} K(2+s)&=48-8s=32\ut{J}\\ s&=2\ut{m}\\ x&=2+s\\ &=4\ut{m} \end{aligned} $$ $$\ab{c}$$ $$ \begin{aligned} \max(K)&=K(1\ut{m})\\ &=W_{0\rarr 1}\\ &=\int_{0}^{1} F \cdot \dd x\\ &=\frac{1}{2}\cdot1\cdot8\ut{J}\\ &=4\ut{J} \end{aligned} $$