Elastic potential energy is a form of potential energy that is specifically stored when materials are stretched or compressed from their original shape, such as a stretched spring. The energy is "elastic" because it can be recovered when the object returns to its original form.
In our specific example, elastic potential energy is stored in the stretched spring. When the spring is released, it can convert this stored energy back into kinetic energy, possibly moving an attached object. The elastic potential energy \( E_{PE} \) in a spring can be calculated using the formula:
- \( E_{PE} = \frac{1}{2} k x^2 \)
Here, \( k \) is the spring constant, telling us how stiff the spring is, and \( x \) is how much the spring is stretched or compressed.
In our problem, substituting the given values, the elastic potential energy stored in the spring is \( 0.617 \mathrm{~J} \). This energy is ready to be unleashed as the spring returns to its normal length, returning to its state of rest.