Question 1

A hockey puck (m=160 grams) is loaded in spring (k=525 N/m) and compressed 400 mm from equilibrium. a) how much energy is stored in the system at this point? b) how fast is the hockey puck moving once it is released horizontally? c) how many times faster would it be moving if the spring was compressed 800 mm instead?

Question 2

$\begin{gathered} m=160gr=0.16kg \\ K=525N/m \\ x=400mm=0.4m \\ a) \\ P_e=? \\ P_e=(Kx^2)/(2) \\ P_e=((525N/m)(0.4)^2)/(2) \\ P_e=42J \\ The\text{ energy stored in the system is 42J} \\ b) \\ v=? \\ P_e=K \\ K=(mv^2)/(2) \\ P_e=(mv^(2))/(2) \\ Solving\text{ v} \\ 2P_e=mv^2 \\ v^2=(2P_e)/(m) \\ v=\sqrt{(2P_e)/(m)} \\ v=\sqrt{(2(42J))/(0.16kg)} \\ v=22.91\text{ m/s} \\ The\text{ velocity is 22.91 m/s} \\ \\ c) \\ x=800mm=0.8m \\ v=? \\ P_(e)=K \\ (Kx^(2))/(2)=(mv^(2))/(2) \\ Kx^2=mv^2 \\ v=\sqrt{(Kx^2)/(m)} \\ v=\sqrt{((525N/m)(0.8m)^2)/(0.16kg)} \\ v=45.83m/s \\ The\text{ velocity is 45.82m/s} \end{gathered}$

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