솔루션피아

$$ \put \begin{cases} \KE : \text{Kinetic Energy}\\ \GE : \text{Gravitational Potential Energy}\\ \TE : \text{Thermal Energy}\\ \end{cases} $$ $$ \begin{cases} S&=6.00\ut{m}\\ F&=2.00\ut{N}\\ f&=10.0\ut{N}\\ \Delta \KE&=+40.0\ut{J} \end{cases} $$ $$\Sigma \Delta E=W_F,$$ $$\Delta \KE+\Delta \GE+\Delta \TE=W_F$$ $$ \begin{aligned} W_G&=-\Delta \GE\\ &=\Delta \KE+\Delta \TE- W_F\\ &=\Delta \KE+fS-..

$$ \begin{cases} R&=18.0\ut{m}\\ \theta_i&=0\\ y_i&=R\\ v_i&=0\\ \end{cases} $$ $$ \begin{aligned} \Delta y &= -(R-R\cos\theta_f)\\ \end{aligned} $$ $$\Sigma \Delta E=0,$$ $$\Delta \KE+\Delta \GE=0$$ $$ \begin{aligned} \Delta \KE&=-\Delta \GE\\ \Delta \(\frac{1}{2}m{v}^2\)&=-\Delta (mgy)\\ \Delta \({v}^2\)&=2g(-\Delta y)\\ \end{aligned} $$ $$ \begin{aligned} {v_f}^2&={v_i}^2+2gh\\ &=2g(-\Delta y..

$$ \put \begin{cases} K : \text{Kinetic Energy}\\ U : \text{Potential Energy}\\ \end{cases} $$ $$ \begin{cases} U_A&=15.0\ut{J}\\ U_B&=35.0\ut{J}\\ U_C&=45.0\ut{J}\\ \end{cases} $$ $$ \begin{cases} U_{0\rarr2}&=35\\ U_{2\rarr4}&=35-10(x-2)=55-10x\\ U_{4\rarr5}&=15\\ U_{5\rarr6}&=15+30(x-5)=30 x-135 \\ U_{6\rarr\infin}&=45\\ \end{cases} $$ $$ \begin{aligned} \Delta U&=-\int F\dd x,\\ F&=-\dyx{U} ..

$$ \begin{cases} m&=12.0\ut{kg}\\ x_1&=10.0\ut{cm}=0.1\ut{m}\\ \Delta x&=30.0\ut{cm}=0.3\ut{m}\\ g&=9.80665\ut{m/s^2}\\ \end{cases} $$ $$x_2=x_1+\Delta x=0.4\ut{m}$$ $$ \put \begin{cases} \KE : \text{Kinetic Energy}\\ \GE : \text{Gravitational Potential Energy}\\ \LE : \text{Elastic Potential Energy}\\ \end{cases} $$ $$\ab{a}$$ $$F=kx,$$ $$ \begin{aligned} k&=\frac{F}{x}\\ &=\frac{mg}{x_1}\\ &=1..

$$ \begin{cases} m&= 78\ut{kg}\\ v&=64\ut{m/s}\\ g&=9.80665\ut{m/s^2} \end{cases} $$ $$ \put \begin{cases} \KE : \text{Kinetic Energy}\\ \GE : \text{Gravitational Potential Energy}\\ \ME : \text{Mechanical Energy}\\ \end{cases} $$ $$\ab{a}$$ $$ \begin{aligned} \dyt{\GE}&=\dyt{mgy}\\ &=mg\dyt{y}\\ &=mgv\\ &=4992g\\ &=48954.7968\ut{W}\\ &\approx 4.9\times10^4\ut{W}\\ &\approx 49\ut{kW}\\ \end{alig..

$$ \begin{cases} v&=0.200\ut{m/s}\\ f&=98.0\ut{N}\\ \end{cases} $$ $$ \begin{aligned} P&=fv\\ &=\frac{98}{5}\ut{W}\\ &=19.6\ut{W} \end{aligned} $$

$$ \begin{cases} m&=2.12\ut{kg}\\ v_0&=2.50\ut{m/s}\\ h&=3.80\ut{m}\\ g&=9.80665\ut{m/s^2} \end{cases} $$ $$ \put \begin{cases} \KE : \text{Kinetic Energy}\\ \GE : \text{Gravitational Potential Energy}\\ \end{cases} $$ $$\ab{a,b}$$ $$\Sigma \Delta E=0,$$ $$\Delta \KE+\Delta \GE=0$$ $$ \begin{aligned} \Delta \KE&=-\Delta \GE\\ \KE_f-\KE_i&=-\Delta (mgy)\\ \end{aligned} $$ $$ \begin{aligned} \KE_f..

$$ \put \begin{cases} \KE : \text{Kinetic Energy}\\ \GE : \text{Gravitational Potential Energy}\\ \TE : \text{Thermal Energy}\\ \ME : \text{Mechanical Energy}\\ \end{cases} $$ $$ \begin{cases} m&=8.10\ut{kg}\\ \Delta \ME&=-72.0\ut{kJ}=-72000\ut{J}\\ g&=9.80665\ut{m/s^2} \end{cases} $$ $$\Delta \TE=-\Delta \ME,$$ $$\Sigma \Delta E=\Delta \KE_1+\Delta \GE_1+\Delta \TE_1=0,$$ $$ \begin{aligned} \De..

(풀이자 주 : 문제의 데이터가 부족하여 풀 수 없습니다. 아마 모터에 공급되는 에너지가 누락된것 같습니다. 풀이자 임의로 두고 풀겠습니다.) $$ \begin{cases} N&=212\ut{N}\\ R&=20.0\ut{cm}=\frac{1}{5}\ut{m}\\ f&=2.50\ut{rev/s}\\ \mu&=0.390\\ \end{cases} $$ $$ \put \begin{cases} \KE : \text{Kinetic Energy}\\ \TE : \text{Thermal Energy}\\ \EE : \text{Electric Energy} \end{cases} $$ $$ \begin{cases} \frac{\KE}{t}&=P_K\\ \frac{\TE}{t}&=P_T\\ \frac{\EE}{t}&=P_E..

$$ \begin{cases} m&=65.0\ut{kg}\\ v_0&=0\\ v_2&=0\\ g&= \end{cases} $$ $$ \begin{cases} y_0&=0\\ y_1&=-10.0\ut{m}\\ \Delta y_{1\rarr2}&=-1.20\ut{m}\\ \end{cases} $$ $$ \put \begin{cases} \KE : \text{Kinetic Energy}\\ \GE : \text{Gravitational Potential Energy}\\ \LE : \text{Elastic Potential Energy}\\ \end{cases} $$ $$\Sigma \Delta E=0,$$ $$\Delta \KE+\Delta \GE+\Delta \LE=0$$ $$\Delta \GE+\Delt..