솔루션피아

$$\begin{cases} L&=0.80\ut{m}\\ m&=0.12\ut{kg}\\ g&=9.80665\ut{m/s^2}\\ \end{cases}$$ $$\put \begin{cases} \KE : \text{Kinetic Energy}\\ \GE : \text{Gravitational Potential Energy}\\ \end{cases}$$ $$\put \begin{cases} 0 : \text{Vertical Peak Point}\\ 1 : \text{Horizontal Point}\\ 2 : \text{Lowest Point}\\ \end{cases}$$ $$\ab{a}$$ $$\begin{cases} v_0&=0 \end{cases}$$ $$\Sigma E_0=\Sigma E..

$$\begin{cases} v_0 &= 0\\ m &= 5.0\ut{kg}\\ k &= 640\ut{N/m}\\ \mu &= 0.25\\ D&=8.5\ut{m}\\ v_2&=0\\ g&=9.80665\ut{m/s^2} \end{cases}$$ $$\put \begin{cases} \KE : \text{Kinetic Energy}\\ \LE : \text{Elastic Potential Energy}\\ \TE : \text{Thermal Energy}\\ \end{cases}$$ $$\ab{a}$$ $$ \begin{aligned} \Delta \TE &= fD\\ &=\mu m g D\\ &=\frac{85g}{8}\\ &=104.19565625\ut{J}\\ &=1.0\times10^2\ut..

$$\begin{cases} L&=1.50\ut{m}\\ m&=4.00\ut{kg}\\ \theta_0&=30.0\degree\\ \vec v_0&=0\\ g&=9.80665\ut{m/s^2} \end{cases}$$ $$\put \begin{cases} 0 : \text{Start}\\ 1 : \text{Lowest Point} \end{cases}$$ $$\put \begin{cases} \KE : \text{Kinetic Energy}\\ \GE : \text{Gravitational Potential Energy}\\ \end{cases}$$ $$ \begin{aligned} -\Delta h_{0\rarr1}&=L-L\cos\theta_0\\ &=L(1-\cos\theta_0)\\ \..

$$\begin{cases} L&=1.50\ut{m}\\ m&=4.00\ut{kg}\\ \theta_0&=30.0\degree\\ \vec v_0&=0\\ g&=9.80665\ut{m/s^2} \end{cases}$$ $$\put \begin{cases} 0 : \text{Start}\\ 1 : \text{Lowest Point} \end{cases}$$ $$\put \begin{cases} \GE : \text{Gravitational Potential Energy}\\ \end{cases}$$ $$\begin{aligned} -\Delta h_{0\rarr1}&=L-L\cos\theta_0\\ &=L(1-\cos\theta_0)\\ \end{aligned}$$ $$\ab{a}$$ $$W..

$$\begin{cases} m&=0.040\ut{kg}\\ R&=14\ut{cm}=0.14\ut{m}\\ h&=5.0R\\ \end{cases}$$ $$\put \begin{cases} \KE : \text{Kinetic Energy}\\ \GE : \text{Gravitational Potential Energy}\\ \end{cases}$$ $$\put \begin{cases} P : \text{P Point}\\ L : \text{Lowest Point}\\ Q : \text{Q Point}\\ H : \text{Highest Point}\\ \end{cases}$$ $$ \begin{cases} h_P&=h=5R\\ h_L&=0\\ h_Q&=R\\ h_H&=2R\\ \end{cases..

$$\begin{cases} m&=0.040\ut{kg}\\ R&=14\ut{cm}=0.14\ut{m}\\ h&=5.0R\\ \end{cases}$$ $$\put \begin{cases} \KE : \text{Kinetic Energy}\\ \GE : \text{Gravitational Potential Energy}\\ \end{cases}$$ $$\put \begin{cases} P : \text{P Point}\\ L : \text{Lowest Point}\\ Q : \text{Q Point}\\ H : \text{Highest Point}\\ \end{cases}$$ $$ \begin{cases} h_P&=h=5R\\ h_L&=0\\ h_Q&=R\\ h_H&=2R\\ \end{cases..

$$\begin{cases} k &= 120\ut{N/m}\\ m &= 4.0\ut{kg}\\ \theta &= 40.0\degree\\ g&=9.80665\ut{m/s^2}\\ \end{cases}$$ $$\put \begin{cases} \KE : \text{Kinetic Energy}\\ \GE : \text{Gravitational Potential Energy}\\ \LE : \text{Elastic Potential Energy}\\ \end{cases}$$ $$\begin{aligned} -\Delta h &= \Delta x\sin\theta \end{aligned}$$ $$\Sigma E_i=\Sigma E_f,$$ $$\KE_i+\GE_i+\LE_i=\KE_f+\GE_f+\L..

$$\begin{cases} L&=140\ut{cm}=1.40\ut{m}\\ d&=80.0\ut{cm}=0.800\ut{m}\\ g&=9.80665\ut{m/s^2} \end{cases}$$ $$\put \begin{cases} \KE : \text{Kinetic Energy}\\ \GE : \text{Gravitational Potential Energy}\\ \end{cases}$$ $$\Sigma E_i=\Sigma E_f,$$ $$ \begin{aligned} \GE_i&=\KE_f+\GE_f\\ \KE_f&=-\Delta \GE\\ \frac{1}{2}m{v_f}^2&=-\Delta (mg h)_{i\rarr f}\\ {v_f}^2&=2g(-\Delta h_{i\rarr f})\\ {v_..

$$\put \begin{cases} \KE : \text{Kinetic Energy}\\ \GE : \text{Gravitational Potential Energy}\\ \EE : \text{Electric Energy}\\ \end{cases}$$ $$\begin{cases} \Delta h&=-120\ut{m}\\ \frac{V}{t}&=1500\ut{m^3/s}\\ \EE&=\frac{3}{4}\KE\\ \rho_{w}&=1000\ut{kg/m^3}\\ g&=9.80665\ut{m/s^2} \end{cases}$$ $$\rho=\frac{m}{V},$$ $$ \begin{aligned} \frac{m}{t}&=\rho\cdot\frac{V}{t}\\ &=1000\ut{kg/m^3}\cdo..

$$\begin{cases} R&=L\\ v_A&=v_0\\ v_D&=0 \end{cases}$$ $$\put \begin{cases} \KE : \text{Kinetic Energy}\\ \GE : \text{Gravitational Potential Energy}\\ \ME : \text{Mechanical Energy} \end{cases}$$ $$\ab{a}$$ $$\Sigma E_A=\Sigma E_D,$$ $$\begin{aligned} \KE_A+\GE_A&=\KE_D+\GE_D\\ \KE_A&=\Delta \GE_{A\rarr D}~~~(\because v_D=0)\\ \end{aligned}$$ $$ \begin{aligned} \frac{1}{2}m{v_A}^2&=mg\Del..