솔루션피아

$$ \begin{cases} 0:\text{Start}\\ 1:x_{1}=2.0\ut{m}\\ 2:x_{2}=14\ut{m}\\ \end{cases} $$ $$ \begin{cases} v_0&=0\\ v_1&=4.2\ut{m/s}\\ v_2&=0\\ \end{cases} $$ $$ \begin{cases} m&=0.69\ut{kg}\\ a_{0\rarr1}&=\Cons\\ a_{1\rarr2}&=0\\ f_{0\rarr2}&=\Cons\\ \end{cases} $$ $$ \put \begin{cases} \KE : \text{Kinetic Energy}\\ \TE : \text{Thermal Energy}\\ \end{cases} $$ $$\ab{a}$$ $$\Sigma \Delta E=0,$$ $$..

(풀이자 주: 문제의 의미가 강수량을 해발0m 바다로 보내는 동안 전체를 수력발전 한다는 의미로 보입니다. 다른 의미라면 답은 달라질 수 있습니다.) $$ \begin{cases} A&= 8\times10^6\ut{km^2}=8\times10^{12}\ut{m^2}\\ y&=500\ut{m}\\ \frac{h}{t}&=75\ut{cm/year}=\frac{1}{42076800}\ut{m/s}\\ k&=\frac{1}{3}\\ \rho&=1000\ut{kg/m^3}\\ \end{cases} $$ $$ \begin{aligned} P&=k\frac{\Delta \PE}{t}\\ &=k\frac{\Delta (mgy)}{t}\\ &=\frac{kmg\Delta y}{t}\\ &=\frac{k\rho Vg\De..

$$ \put \begin{cases} \KE : \text{Kinetic Energy}\\ \PE : \text{Potential Energy}\\ \end{cases} $$ $$ \begin{cases} m&=1\ut{kg}\\ F(x)&=-3.0x-5.0x^2\ut{N}\\ \PE_0&=0\\ \end{cases} $$ $$\ab{a}$$ $$ \begin{aligned} \PE(x)&=\PE(0)+\Delta \PE\\ &=\PE(0)+ \int_0^xF\dd x\\ &=0+\int_0^x(-3x-5x^2)\dd x\\ &=-\frac{3}{2}x^2-\frac{5}{3}x^3\\ \end{aligned} $$ $$ \begin{aligned} \PE(2.0\ut{m})&=-\frac{3}{2}(..

$$ \begin{cases} v_i&=610\ut{m/s}\\ m&=40\ut{g}=0.04\ut{kg}\\ d&=12\ut{cm}=0.12\ut{m}\\ v_f&=0 \end{cases} $$ $$ \put \begin{cases} \KE : \text{Kinetic Energy}\\ \TE : \text{Thermal Energy}\\ \ME : \text{Mechanical Energy}\\ \end{cases} $$ $$\ab{a}$$ $$ \begin{aligned} \Delta \ME&=\Delta \KE\\ &=\Delta \(\frac{1}{2}mv^2\)\\ &=\frac{1}{2}m\Delta \(v^2\)\\ &=\frac{1}{2}m \({0}^2-{v_i}^2\)\\ &=-\fr..

$$ \begin{cases} mg&=14720\ut{N}\\ v_i&=92.0\ut{km/h}=\frac{230}{9}\ut{m/s}\\ v_f&=0\\ f&=7022\ut{N}\\ g&=9.80665\ut{m/s^2} \end{cases} $$ $$ \put \begin{cases} \KE : \text{Kinetic Energy}\\ \TE : \text{Thermal Energy}\\ \end{cases} $$$$\Sigma \Delta E=0,$$ $$\Delta \KE+\Delta \TE=0$$ $$ \begin{aligned} \Delta \TE&=-\Delta \KE\\ fd&=-\Delta\(\frac{1}{2}mv^2\)\\ \end{aligned} $$ $$ \begin{aligned..

$$ \begin{cases} H&=443\ut{m}\\ g&=9.80665\ut{m/s^2}\\ \end{cases} $$ $$ \put \begin{cases} \GE : \text{Gravitational Potential Energy}\\ {B\mkern{-0.1 em}E} : \text{Bio Energy}\\ \end{cases} $$ $$\put m= 80.0\ut{kg}$$ $$\ab{a}$$ $$\Sigma \Delta E=0,$$ $$\Delta {B\mkern{-0.1 em}E}+\Delta \GE=0$$ $$ \begin{aligned} -\Delta {B\mkern{-0.1 em}E}_a&=\Delta(mgh)\\ &=mg\Delta h\\ &=mgH\\ &=35440g\\ &=3..

$$ \put \begin{cases} 0 : \text{Start}\\ 1 : \text{2cm move}\\ 2 : \text{Spring Neutral Point}\\ \end{cases} $$ $$ \begin{cases} m&=20\ut{kg}\\ k&=6.0\ut{kN/m}=6.0\times10^3\ut{N/m}\\ x_0&=10\ut{cm}=0.1\ut{m}\\ f&=80\ut{N}\\ \Delta x_{0\rarr 1}&=2\ut{cm}=2\times10^{-2}\ut{m} \end{cases} $$ $$ d=-\Delta x $$ $$ \put \begin{cases} \KE : \text{Kinetic Energy}\\ \LE : \text{Elastic Potential Energy}..

$$ \begin{cases} v_0&=0\\ m&=70\ut{kg}\\ \Delta y &= -6.0\ut{m}\\ \Delta d&=-\Delta y \end{cases} $$ $$ \put \begin{cases} \KE : \text{Kinetic Energy}\\ \GE : \text{Gravitational Potential Energy}\\ \TE : \text{Thermal Energy}\\ \end{cases} $$ $$\Sigma E_i=\Sigma E_f,$$ $$\KE_i+\GE_i+\TE_i=\KE_f+\GE_f+\TE_f$$ $$ \begin{aligned} \KE_f&=-\Delta \TE-\Delta \GE\\ \frac{1}{2}mv^2&=-\Delta (fd)-\Delta..

$$ \begin{cases} H&=820\ut{m}\\ h&=750\ut{m}\\ \Sigma S&=3.2\ut{km}=3.2\times10^3\ut{m}\\ \theta &= 30\degree\\ g&=9.80665\ut{m/s^2} \end{cases} $$ $$ \put \begin{cases} \KE : \text{Kinetic Energy}\\ \GE : \text{Gravitational Potential Energy}\\ \TE : \text{Thermal Energy}\\ \ME : \text{Mechanical Energy}\\ \end{cases} $$ $$\ab{a}$$ $$\Sigma E_i=\Sigma E_f,$$ $$ \begin{aligned} \KE_i+\GE_i&=\KE_..

$$ \put \begin{cases} \KE : \text{Kinetic Energy}\\ \GE : \text{Gravitational Potential Energy}\\ \end{cases} $$ $$ \put \begin{cases} 0 : \text{Start}\\ 1 : v_y=65\ut{m/s}\\ 2 : \text{Highest Point} \end{cases} $$ $$ \begin{cases} m&=0.650\ut{kg}\\ \KE_0 &= 1700\ut{J}\\ \Delta h_{0\rarr2}&=+180\ut{m}\\ g&=9.80665\ut{m/s^2}\\ \end{cases} $$ $$\ab{a}$$ $$\vec v_2 = v_x\i+0\j,$$ $$ \therefore v_2=..