8-6 할리데이 11판 솔루션 일반물리학

$$ \put \begin{cases} K : \text{Kinetic Energy}\\ U:\text{Potential Energy}\\ \end{cases} $$ $$ \begin{cases} K(5.00\ut{m})&=14.0\ut{J}\\ U(5.00\ut{m})&=0\\ \vec v(5.00\ut{m})&\lt0\\ \end{cases} $$ $$ \begin{cases} \Delta K_{i\rarr f}&=W_{i\rarr f},\\ \Delta U_{i\rarr f}&=-W_{i\rarr f},\\ \end{cases} $$ $$ \begin{cases} K_f-K_i&=\int_i^f F \dd x\\ U_f-U_i&=-\int_i^f F \dd x\\ \end{cases} $$ $$ \therefore\begin{cases} K_f&=K_i+\int_i^f F \dd x\\ U_f&=U_i-\int_i^f F \dd x \end{cases} $$

$$\ab{a}$$ $$ \begin{aligned} K_2&=K_5+\int_5^2 F \dd x\\ &=K_5-\int_2^5 F \dd x\\ &=14-1\cdot5\\ &=9\ut{J}\\ &=9.00\ut{J}\\ \end{aligned} $$ $$\ab{b}$$ $$ \begin{aligned} U_2&=U_5-\int_5^2 F \dd x\\ &=U_5+\int_2^5 F \dd x\\ &=0+1\cdot5\\ &=5\ut{J}\\ &=5.00\ut{J}\\ \end{aligned} $$ $$\ab{c}$$ $$ \begin{aligned} K_0&=K_5+\int_5^0 F \dd x\\ &=K_5-\int_0^5 F \dd x\\ &=14-(2\cdot3+1\cdot5)\\ &=3\ut{J}\\ &=3.00\ut{J}\\ \end{aligned} $$ $$\ab{d}$$ $$ \begin{aligned} U_0&=U_5-\int_5^0 F \dd x\\ &=U_5+\int_0^5 F \dd x\\ &=0+(2\cdot3+1\cdot5)\\ &=11\ut{J}\\ &=11.0\ut{J}\\ \end{aligned} $$ $$\ab{e}$$ $$ \begin{aligned} K_{11}&=K_5+\int_5^{11} F \dd x\\ &=14+3\cdot(-4)\\ &=2\ut{J}\\ &=2.00\ut{J}\\ \end{aligned} $$ $$\ab{f}$$ $$ \begin{aligned} U_{11}&=U_5-\int_5^{11} F \dd x\\ &=0-\bra{3\cdot(-4)}\\ &=12\ut{J}\\ &=12.0\ut{J}\\ \end{aligned} $$ $$\ab{g}$$ $$ \begin{aligned} K_{12}&=K_5+\int_5^{12} F \dd x\\ &=14+3\cdot(-4)+1\cdot(-1)\\ &=1\ut{J}\\ &=1.00\ut{J}\\ \end{aligned} $$ $$\ab{h}$$ $$ \begin{aligned} U_{12}&=U_5-\int_5^{12} F \dd x\\ &=0-\bra{3\cdot(-4)+1\cdot(-1)}\\ &=13\ut{J}\\ &=13.0\ut{J}\\ \end{aligned} $$ $$\ab{i}$$ $$ \begin{aligned} K_{13}&=K_5+\int_5^{13} F \dd x\\ &=14+3\cdot(-4)+1\cdot(-1)\\ &=1\ut{J}\\ &=1.00\ut{J}\\ \end{aligned} $$ $$\ab{j}$$ $$ \begin{aligned} U_{13}&=U_5-\int_5^{13} F \dd x\\ &=0-\bra{3\cdot(-4)+1\cdot(-1)}\\ &=13\ut{J}\\ &=13.0\ut{J}\\ \end{aligned} $$ $$\ab{k}$$ $$ \begin{cases} \vec F_{0\rarr2.00\ut{m}}&=+3.00\i\ut{N}\\ \vec F_{2.00\rarr3.00\ut{m}}&=+5.00\i\ut{N}\\ \vec F_{3.00\rarr8.00\ut{m}}&=0\\ \vec F_{8.00\rarr11.0\ut{m}}&=-4.00\i\ut{N}\\ \vec F_{11.0\rarr12.0\ut{m}}&=-1.00\i\ut{N}\\ \vec F_{12.0\rarr15.0\ut{m}}&=0\\ \end{cases} $$ $$ \begin{cases} \int_0^2F\dd x&=3x\\ \int_2^3F\dd x&=5(x-2)\\ \int_3^8F\dd x&=0\\ \int_8^{11}F\dd x&=-4(x-8)\\ \int_{11}^{12}F\dd x&=-(x-11)\\ \int_{12}^{15}F\dd x&=0\\ \end{cases} $$ $$ \begin{aligned} U(x)&=U(i)-\int_i^x F\dd x,\\ \end{aligned} $$ $$ \begin{cases} U_{0\rarr2}&=U(0)-3x\\ U_{2\rarr3}&=U(2)-5(x-2)\\ U_{3\rarr8}&=U(3)-0\\ U_{8\rarr11}&=U(8)+4(x-8)\\ U_{11\rarr12}&=U(11)+(x-11)\\ U_{12\rarr15}&=U(12)-0\\ \end{cases} $$ $$ \begin{cases} U_{0\rarr2}&=11-3x\\ U_{2\rarr3}&=5-5(x-2)\\ U_{3\rarr8}&=0-0\\ U_{8\rarr11}&=0+4(x-8)\\ U_{11\rarr12}&=12+(x-11)\\ U_{12\rarr15}&=13-0\\ \end{cases} $$ $$ \begin{cases} U_{0\rarr2}&=11-3x\\ U_{2\rarr3}&=15-5x\\ U_{3\rarr8}&=0\\ U_{8\rarr11}&=4x-32\\ U_{11\rarr12}&=x+1\\ U_{12\rarr15}&=13\\ \end{cases} $$

$$\ab{l}$$ $$ \begin{aligned} K_{5}&=K_0+\int_0^{5} F \dd x\\ &=0+(2\cdot3+1\cdot5)\\ &=11\ut{J}\\ &=11.0\ut{J}\\ \end{aligned} $$ $$\ab{m}$$ $$ K_{x}=K_0+\int_0^x F \dd x $$ $$ \begin{aligned} 0&=\int_0^x F \dd x\\ &=11+(-4)\cdot(x-8)\\ \end{aligned} $$ $$ \begin{aligned} x&=\frac{43}{4}\ut{m}\\ &=10.75\ut{m}\\ &\approx 10.8\ut{m}\\ \end{aligned} $$ $$\ab{n}$$ $$\text{Move Back}$$