솔루션피아

$$\begin{cases} F&=750\ut{N}\\ k&=2.5\times10^5\ut{N/m}\\ \end{cases}$$ $$\ab{a}$$ $$F=kx,$$ $$\begin{aligned} x&=\frac{F}{k}\\ &=3.0\times10^{-3}\ut{m}\\ &=3.0\ut{mm}\\ \end{aligned}$$ $$\ab{b}$$ $$\begin{aligned} W&=\frac{1}{2}kx^2\\ &=\frac{1}{2}k\(\frac{F}{k}\)^2\\ &=\frac{F^2}{2k}\\ &=\frac{9}{8}\ut{J}\\ &=1.125\ut{J}\\ &\approx 1.1\ut{J} \end{aligned}$$ $$\ab{c}$$ $$F=kx,$$ $$\ab{d}$..

$$\begin{cases} v_{A1}&=2.00\ut{m/s}\\ v_{B1}&=2.60\ut{m/s}\\ v_{A2}&=6.00\ut{m/s}\\ \end{cases}$$ $$\Sigma \Delta E=0,$$ $$\Delta \KE+\Delta \GE=0$$ $$\begin{aligned} \Delta \(\frac{1}{2}m{v}^2\)&=-\Delta (mgy)\\ \Delta \({v}^2\)&=2g(-\Delta y)\\ {v_f}^2-{v_i}^2&=2g(-\Delta y)\\ &=\Cons\\ \end{aligned}$$ $${v_{B2}}^2-{v_{A2}}^2={v_{B1}}^2-{v_{A1}}^2$$ $$ \begin{aligned} v_{B2}&=\sqrt{{v_{A2..

$$\begin{cases} L&=230\ut{cm}\\ g&=9.80665\ut{m/s^2} \end{cases}$$ $$\put \begin{cases} 0:\text{Start}\\ 1:\text{Lowest Point}\\ 2:\text{Over P Highest Point} \end{cases}$$ $$\begin{cases} y_0&=L\\ y_1&=0\\ y_2&=2r\\ \end{cases}$$ $$\Sigma \Delta E=0,$$ $$\Delta \KE+\Delta \GE=0$$ $$ \begin{aligned} \Delta \KE&=-\Delta \GE\\ \Delta \(\frac{1}{2}m{v}^2\)&=-\Delta (mgy)\\ \Delta \({v}^2\)&=2..

$$\begin{cases} m&=3.6\ut{kg}\\ y&=3.8\ut{m}\\ g&=9.80665\ut{m/s^2}\\ \end{cases}$$ $$\put \begin{cases} \KE : \text{Kinetic Energy}\\ \GE : \text{Gravitational Potential Energy}\\ \end{cases}$$ $$\ab{a}$$ $$\begin{aligned} \GE&=mgy\\ &=\frac{342g}{25}\\ &=134.154972\ut{J}\\ &\approx 1.3\times10^2\ut{J}\\ \end{aligned}$$ $$\ab{b}$$ $$\Sigma \Delta E=0,$$ $$ \begin{aligned} \KE&=\GE\\ &=134..

$$\begin{cases} v_i&=7.0\ut{m/s}\\ h&=2.0\ut{m}\\ \mu&=0.50\\ \end{cases}$$ $$\put \begin{cases} \KE : \text{Kinetic Energy}\\ \GE : \text{Gravitational Potential Energy}\\ \TE : \text{Thermal Energy}\\ \end{cases}$$ $$\Sigma \Delta E=0,$$ $$\Delta \KE+\Delta \GE+\Delta \TE=0$$ $$ \begin{aligned} \Delta \TE&=-\Delta \KE-\Delta \GE\\ fd&=-\Delta\(\frac{1}{2}mv^2\)-\Delta (mgy)\\ \mu m g d&=-\..

$$\begin{cases} m&=5.0\ut{kg}\\ k&=425\ut{N/m}\\ x&=6.0\ut{cm}=0.06\ut{m}\\ \mu&=0.25\\ g&=9.80665\ut{m/s^2} \end{cases}$$ $$\put \begin{cases} \KE : \text{Kinetic Energy}\\ \LE : \text{Elastic Potential Energy}\\ \TE : \text{Thermal Energy}\\ \end{cases}$$ $$\ab{a}$$ $$ \begin{aligned} W_s&=-\Delta \LE\\ &=\LE_i-\LE_f\\ &=-\LE_f\\ &=-\frac{1}{2}kx^2\\ &=-\frac{153}{200}\ut{J}\\ &=-0.765\ut{..

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