솔루션피아

$$\begin{cases} m&= 78\ut{kg}\\ v&=64\ut{m/s}\\ g&=9.80665\ut{m/s^2} \end{cases}$$ $$\put \begin{cases} \KE : \text{Kinetic Energy}\\ \GE : \text{Gravitational Potential Energy}\\ \ME : \text{Mechanical Energy}\\ \end{cases}$$ $$\ab{a}$$ $$ \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..

$$\begin{cases} \theta&=40\degree\\ m&=52\ut{kg}\\ v&=\Cons\\ S&=3.0\ut{m}\\ \mu&=0.35\\ g&=9.80665\ut{m/s^2} \end{cases}$$ $$\put \begin{cases} \TE : \text{Thermal Energy}\\ \end{cases}$$ $$\begin{cases} \Sigma F_x&=0\\ \Sigma F_y&=0\\ \end{cases}$$ $$\begin{cases} F-f-mg\sin\theta&=0\\ N-mg\cos\theta&=0\\ \end{cases}$$ $$\ab{a}$$ $$ \begin{aligned} W&=FS\\ &=(mg\sin\theta+\mu mg\cos\th..

$$\begin{cases} m&=82\ut{kg}\\ v_i&=16\ut{m/s}\\ \Delta y &=4.2\ut{m}\\ g&=9.80665\ut{m/s^2} \end{cases}$$ $$\put \begin{cases} \KE : \text{Kinetic Energy}\\ \GE : \text{Gravitational Potential Energy}\\ \end{cases}$$ $$\Sigma \Delta E=0,$$ $$\Delta \KE+\Delta \GE=0$$ $$\begin{aligned} \Delta \KE&=-\Delta \GE\\ \KE_f-\KE_i&=-\Delta \GE\\ \end{aligned}$$ $$ \begin{aligned} \KE_f&=\KE_i-\Del..

$$\begin{cases} k&=4200\ut{N/m}\\ U_i&=1.10\ut{J}\\ \end{cases}$$ $$U=\frac{1}{2}kx^2,$$ $$x_i=\frac{1}{10}\sqrt{\frac{11}{210}}\ut{m}$$ $$x_a=x_i+\Delta x$$ $$\begin{aligned} \Delta U &= U_f-U_i\\ &=\frac{1}{2}k{x_a}^2-\frac{1}{2}k{x_i}^2\\ &=\frac{1}{2}k\Delta x(\Delta x+2x_i)\\ &=2\Delta x(\sqrt{2130}+1050\Delta x) \end{aligned}$$ $$\ab{a}$$ $$\Delta x=+2\ut{cm}$$ $$ \begin{aligned} \De..

$$\begin{cases} \Delta y &= -14\ut{m}\\ v_i&=-3.0\ut{m/s}\\ v_f&=-14\ut{m/s}\\ g&=9.80665\ut{m/s^2}\\ \end{cases}$$ $$\put \begin{cases} \KE : \text{Kinetic Energy}\\ \GE : \text{Gravitational Potential Energy}\\ \end{cases}$$ $$ \begin{aligned} \Ans&=-\frac{\Delta \KE}{\Delta \GE}\\ &=-\frac{\Delta \(\frac{1}{2}m{v}^2\)}{\Delta (mgy)}\\ &=\frac{\Delta \({v}^2\)}{2g(-\Delta y)}\\ &=\frac{{v_..