#digipen/phy250 Physics Quiz $ k = 2(4.5)^2= 40.5 $ $ PE = \frac{1}{2} \cdot 40.5 \cdot 13 + 2 \cdot 9.8 \cdot 13 $ $\huge \begin{align} k &= 50 \pu{ N/m } \\ m &= 115 \pu{ kg } \\ -\frac{k}{2} x &= mg \\ x &= \frac{2mg}{k} \\ &= 2\frac{ 115 * 9.81}{50} \end{align} $ When the oscillation takes the opera singer back up to the top, Bugs Bunny hands them an anvil to hold onto for just a moment, with a mass of 1000 kg.  What is the new maximum extension of the spring below equilibrium? $\huge \begin{align} x &= 2\frac{(115+1000)*9.81}{50} \end{align}$ $\huge \begin{align} \frac{1}{2}kx^2 - mgx &= m\frac{1}{2 }v^2\\ \frac{kx^2}{m}-2gx &= v^2 \\ \sqrt{ \frac{kx^2}{m}-2gx }&= v \\ v&= \sqrt{ \frac{50 * 437^2}{115} - 2*9.81 *437 }\\ &\approx 272 \end{align}$