솔루션피아

$$ \begin{cases} \vec F(x\ut{m})&=(cx-3.00x^2)\i\ut{N}\\ K(0)&=26.0\ut{J}\\ K(3.00\ut{m})&=11.0\ut{J} \end{cases} $$ $$W=\Delta K,$$ $$ \begin{aligned} W&=K(3)-K(0)\\ -15&=\int_{0}^{3} F \cdot \dd x\\ &=\int_{0}^{3} (cx-3x^2) \cdot \dd x\\ &=\[\frac{c}{2}x^2-x^3\]_{0}^{3}\\ &=\frac{9c}{2}-27\\ \end{aligned} $$ $$ \begin{aligned} c&=\frac{8}{3}\\ &\approx 2.6666666666666665\\ &\approx 2.67\\ \end..

$$ \begin{cases} m_A&=5700\ut{kg}\\ m_B&=2020\ut{kg}\\ v&=2.0\ut{m/s}\\ g&=9.80665\ut{m/s^2}\\ \end{cases} $$ $$P=\vec F \cdot \vec v,$$ $$ \begin{aligned} P&=\Sigma m gv\\ &=15440g\\ &=151414.676\ut{W}\\ &\approx 1.5\times10^5\ut{W}\\ &\approx 0.15\ut{MW} \end{aligned} $$

$$ \begin{cases} k&=15.0\ut{N/cm}=1.5\times10^3\ut{N/m}\\ x&=6.20\ut{mm}=6.2\times10^{-3}\ut{m}\\ \Delta x &= 7.60\ut{mm}=7.6\times10^{-3}\ut{m}\\ \end{cases} $$ $$\ab{a}$$ $$W_S=\frac{1}{2}kx^2,$$ $$ \begin{aligned} W_S&=\frac{1}{2}\(1.5\times10^3\)\(6.2\times10^{-3}\)^2\\ &=\frac{2883}{10^5}\ut{J}\\ &=0.02883\ut{J}\\ &\approx 2.88\times10^{-2}\ut{J}\\ &\approx 28.8\ut{mJ}\\ \end{aligned} $$ $$..

$$ \begin{cases} v_0&=0\\ m&=4.0\ut{kg}\\ t&=3.0\ut{s}\\ v&=12\ut{m/s}\\ \end{cases} $$ $$\ab{a}$$ $$K=\frac{1}{2}mv^2,$$ $$ \begin{aligned} W&=\Delta K=K~~(\because v_0=0)\\ &=\frac{1}{2}mv^2\\ &=288\ut{J}\\ &\approx 2.9\times10^2\ut{J} \end{aligned} $$ $$\ab{b}$$ $$v=v_0+at,$$ $$ \begin{aligned} a&=\frac{v-v_0}{t}\\ &=\frac{v}{t}\\ &=4\ut{m/s^2} \end{aligned} $$ $$ \begin{aligned} F&=ma\\ &=16..

(풀이자 주: 그래프의 면적으로 구하라는 것이 어림으로 구하라는 뜻으로 생각되는데, 정확한 적분이 가능하므로 생략하겠습니다.) $$ \begin{cases} F&=\cfrac{a}{x^2}\\ a&=7.0\ut{N\cdot m^2}\\ x_i&=1.0\ut{m}\\ x_f&=2.5\ut{m}\\ \end{cases} $$ $$\ab{a}$$ $$\ab{b}$$ $$W_{i\rarr f}=\int_{i}^{f} \vec F \cdot \dd \vec S,$$ $$ \begin{aligned} W&=\int_{i}^{f} \frac{a}{x^2} \cdot \dd x\\ &=\[\frac{-a}{x}\]_{i}^{f}\\ &=-a\(\frac{1}{x_f}-\frac{1}{x_i}\)\\ &=\frac{21..

$$ \begin{cases} m&=3.20\ut{kg}\\ k&=650\ut{N/m}\\ x_i&=0.400\ut{m} \end{cases} $$ $$\ab{a}$$ $$K=\frac{1}{2}mv^2,W_s=\frac{1}{2}kx^2,$$ $$ \begin{aligned} K&=W_s\\ \frac{1}{2}mv^2&=\frac{1}{2}kx^2\\ \end{aligned} $$ $$ \begin{aligned} v&=x\sqrt{\frac{k}{m}}\\ &=\sqrt{\frac{65}{2}}\ut{m/s}\\ &\approx 5.70087712549569\ut{m/s}\\ &\approx 5.70\ut{m/s}\\ \end{aligned} $$ $$\ab{b}$$ $$ \begin{aligned..

$$ \begin{cases} F&=120\ut{N}\\ S&=1.8\ut{m}\\ \Delta K_a &= 42\ut{J}\\ \end{cases} $$ $$\ab{a}$$ $$ \begin{aligned} \Delta K_a &= \Sigma W =W_F+W_{mg}\\ W_{mg}&=\Delta K - W_F\\ &=42-(-120\cdot1.8)\\ &=258\ut{J}\\ &\approx 2.6\times10^2\ut{J}\\ \end{aligned} $$ $$\ab{b}$$ $$ \begin{aligned} \Delta K_b&=W_{mg}\\ &=258\ut{J}\\ &\approx 2.6\times10^2\ut{J}\\ \end{aligned} $$

$$ \begin{cases} m&=31.0\ut{kg}\\ \theta&=25.0\degree\\ F&=350\ut{N}\\ S&=2.30\ut{m}\\ g&=9.80665\ut{m/s^2}\\ \end{cases} $$ $$\ab{a}$$ $$W=\vec F \cdot \vec S,$$ $$ \begin{aligned} W_F&=350\cdot2.30\\ &=805\ut{J} \end{aligned} $$ $$\ab{b}$$ $$ \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{alig..

$$ \begin{cases} t&=70.0\ut{s}\\ h&=220\ut{m}\\ mg&=660\ut{N}\\ N&=100 \end{cases} $$ $$ \begin{aligned} P&=\dxt{W}\\ &=\dxt{N\cdot mg\cdot h}\\ &=Nmg\dxt{h}\\ &=\frac{1452000}{7}\ut{W}\\ &\approx 207428.57142857142\ut{W}\\ &\approx 2.07\times10^5\ut{W}\\ &\approx 207\ut{kW}\\ \end{aligned} $$

(풀이자주:풀이에 테일러급수가 필요합니다. 관련한 내용은 별도의 링크로 분리했습니다. 테일러 급수 자체에 대한 이해는 현재과정에서의 필수는 아니니 결론만 보고 건너뛰어도 무방합니다.) https://solutionpia.tistory.com/624 테일러 급수 $$\title{About Taylor Series}$$ $$ \put \begin{cases} f(x)&=\text{Any Function}\\ g(x)&=c_0+c_1x+c_2x^2+\cdots+c_nx^n+\cdots \end{cases} $$ $$ \put \begin{cases} f(0)&=g(0)\\ f'(0)&=g'(0)\\ f''(0)&=g''(0)\\ &\vdots\\ f^{(n)}(0)&=g^{(n)}(0)\\ &\vdots\\ ..