Answer:
The elastic potential energy stored in a spring is given by the formula:
\[ U = \frac{1}{2} k x^2 \]
where:
- \( U \) is the elastic potential energy (0.25 J in this case),
- \( k \) is the spring constant (200 N/m),
- \( x \) is the displacement from the equilibrium position.
In this scenario, the spring's total length is relevant to find the displacement. The displacement (\( x \)) is the difference between the stretched length and the unstretched length.
Let \( L \) be the unstretched length of the spring, and \( L_{\text{total}} \) be the total length (20 cm or 0.2 m). The displacement (\( x \)) is \( L_{\text{total}} - L \).
Now, plug these values into the elastic potential energy formula:
\[ 0.25 = \frac{1}{2} \times 200 \times (L_{\text{total}} - L)^2 \]
Solve for \( L \) to find the unstretched length of the spring.
