솔루션피아

$$\begin{cases} mg&=560\ut{N}\\ R&=20\ut{m}\\ v_B&=7.0\ut{m/s}\\ \theta&=20\degree\\ g&=9.80665\ut{m/s^2}\\ \end{cases}$$ $$\put \begin{cases} \KE : \text{Kinetic Energy}\\ \GE : \text{Gravitational Potential Energy}\\ \end{cases}$$ $$\begin{aligned} \Delta h &= R-R\cos\theta\\ &=R(1-\cos\theta) \end{aligned}$$ $$\ab{a}$$ $$\Sigma \Delta E=0,$$ $$\Delta \KE+\Delta \GE=0$$ $$ \begin{aligned..

$$\begin{cases} m&=1200\ut{kg}\\ v&=1.34\ut{m/s}\\ d_1&=\Delta x = 60\ut{m}\\ d_2&=\Delta y=30\ut{m}\\ \mu&=0.40\\ g&=9.80665\ut{m/s^2} \end{cases}$$ $$\tan\theta=\frac{d_2}{d_1}=\frac{1}{2}$$ $$\Sigma \vec F = 0\Harr \Delta \vec v=0,$$ $$\begin{cases} \Sigma F_x&=0\\ \Sigma F_y&=0\\ \end{cases}$$ $$\begin{cases} F-\mu N - mg\sin\theta&=0\\ N-mg\cos\theta&=0\\ \end{cases}$$ $$ \begin{align..

$$\begin{cases} \theta &= 30\degree\\ m&= 42.0\ut{kg}\\ d&=5.20\ut{m}\\ \mu &= 0.170 \end{cases}$$ $$\Sigma \vec F =0\Harr \Delta \vec v=0$$ $$\begin{cases} \Sigma F_x &=0\\ \Sigma F_y &=0\\ \end{cases}$$ $$\begin{cases} F-\mu N-mg\sin\theta &=0\\ N-mg\cos\theta &=0\\ \end{cases}$$ $$\therefore F=mg(\mu \cos\theta+\sin\theta)$$ $$\ab{a}$$ $$ \begin{aligned} W&=Fd\\ &=mgd(\mu \cos\theta+\si..

$$\begin{cases} m&=82\ut{kg}\\ v_i&=12\ut{m/s} \end{cases}$$ $$\put \begin{cases} \KE : \text{Kinetic Energy}\\ \TE : \text{Thermal Energy}\\ \end{cases}$$ $$\ab{a}$$ $$\begin{aligned} -\Delta \KE&=-\Delta \(\frac{1}{2}mv^2\)\\ &=-\frac{1}{2}m\Delta \(v^2\)\\ &=\frac{1}{2}m\({v_i}^2-{v_f}^2\)\\ &=\frac{1}{2}m{v_i}^2\\ &=5904\ut{J}\\ &=5.9\times10^3\ut{J}\\ &=5.9\ut{kJ}\\ \end{aligned}$$ $$..

$$\begin{cases} \theta&=8.0\degree\\ S&=815\ut{m} \end{cases}$$ $$\Delta h = S\sin\theta$$ $$\Sigma \Delta E=0,$$ $$\Delta \KE+\Delta \GE=0$$ $$\begin{aligned} \Delta \KE&=-\Delta \GE\\ \Delta \(\frac{1}{2}mv^2\)&=-\Delta(mgh)\\ \Delta \(v^2\)&=-2g\Delta h\\ {v_f}^2-{v_i}^2&=-2g(S\sin\theta)\\ \end{aligned}$$ $$ \begin{aligned} v_i&=\sqrt{2gS\sin\theta}\\ &=1630g\sin8\degree\\ &\approx 2224...

$$\put \begin{cases} i : \text{Start}\\ f : \text{Highest Point} \end{cases}$$ $$\begin{cases} m&=0.750\ut{kg}\\ \vec v_i&=2.75\j\ut{m/s}\\ g&=9.80665\ut{m/s^2}\\ \end{cases}$$ $$\put \begin{cases} \KE : \text{Kinetic Energy}\\ \GE : \text{Gravitational Potential Energy}\\ \end{cases}$$ $$\ab{a}$$ $$ \begin{aligned} \KE &= \frac{1}{2}mv^2\\ &=\frac{363}{128}\ut{J}\\ &=2.8359375\ut{J}\\ &\a..

$$\begin{cases} m&=17.0\ut{kg}\\ a&=2.50\ut{m/s^2}\\ v_i&=14.0\ut{m/s}\\ v_f&=34.0\ut{m/s}\\ \end{cases}$$ $$\put \begin{cases} \KE : \text{Kinetic Energy}\\ \GE : \text{Gravitational Potential Energy}\\ \ME : \text{Mechanical Energy}\\ \end{cases}$$ $$\ab{a}$$ $$ \begin{aligned} \Delta \ME&=\Delta \KE+\Delta \GE\\ &=\Delta \KE\\ &=\Delta \(\frac{1}{2}mv^2\)\\ &=\frac{1}{2}m\Delta \(v^2\)\\ ..

$$\put \begin{cases} \GE : \text{Gravitational Potential Energy}\\ \LE : \text{Elastic Potential Energy}\\ \end{cases}$$ $$\begin{cases} x_i&=0\\ kx_f&=mg\\ \Delta x&=\abs{\Delta h}=-\Delta h \end{cases}$$ $$\begin{aligned} -\Delta \GE &= -\Delta (mgh)\\ &=-mg\Delta h\\ &=mg(-\Delta h)\\ &=mg\Delta x\\ &=mg(x_f-x_i)\\ &=mgx_f\\ &=mg\(\frac{mg}{k}\)\\ &=\frac{(mg)^2}{k}\\ \end{aligned}$$ $$..

(풀이자 주 : 그래프의 함수가 정확히 주어지지 않아 풀이자가 임의로 그래프의 함수를 추정했습니다. 추정함수가 다를 경우 결과는 달라질 수 있습니다.) $$\put \exp(x)=\e^x,$$ $$\put U(x)=\begin{cases} (x-2)^2&\cdots(x\le2)\\ \exp\(\cfrac{3x-6}{10}\)-1&\cdots(x\ge2)\\ \end{cases}$$ $$\ab{a}$$ $$\begin{aligned} W_{i\rarr f}&=-\Delta U_{i\rarr f},\\ \int_2^{x} F\dd x&=U_2-U_x\\ \dx\(\int_2^x F\dd x\)&=\dx\(U_2-U_x\)\\ F(x)&=-\dyx{U(x)}, \end{aligned}$$ $$ U(x)..

$$\put \begin{cases} U : \text{Potential Energy}\\ \end{cases}$$ $$\begin{cases} F(x)&=G\cfrac{m_1m_2}{x^2}\\ U(\infin)&=0\\ \end{cases}$$ $$\begin{cases} x&\gt0\\ x_1&=x_1\\ x_2&=x_1+d \end{cases}$$ $$\ab{a}$$ $$ \begin{aligned} U(x)&=U(\infin)+\int_{\infin}^xF(x)\dd x\\ &=0+\int_{\infin}^x G\frac{m_1m_2}{x^2}\dd x\\ &=Gm_1m_2\int_{\infin}^x \frac{1}{x^2}\dd x\\ &=-Gm_1m_2\[\frac{1}{x}\]_..