Elastic potential energy is the energy stored in an elastic object, such as a spring, when it is stretched or compressed from its equilibrium position. This energy is the result of the work done to deform the object and can be released when the object returns to its original shape.

The formula for elastic potential energy is:

\[ E = \frac{1}{2}kx^2 \]

Where:

- \(E\) is the elastic potential energy (measured in joules, J)
- \(k\) is the spring constant (measured in newtons per meter, N/m)
- \(x\) is the displacement from the equilibrium position (measured in meters, m)

Let's calculate the elastic potential energy of a spring with a spring constant of 100 N/m that is stretched 0.2 meters from its equilibrium position:

- Identify the known values:
- Spring constant, \(k = 100\) N/m
- Displacement, \(x = 0.2\) m

- Apply the elastic potential energy formula: \[ E = \frac{1}{2}kx^2 \]
- Substitute the known values: \[ E = \frac{1}{2} \times 100 \text{ N/m} \times (0.2 \text{ m})^2 \]
- Perform the calculation: \[ E = \frac{1}{2} \times 100 \times 0.04 = 2 \text{ J} \]

Let's visualize the elastic potential energy in our example:

This visual representation shows:

- The spring in its stretched position
- The spring constant (k = 100 N/m)
- The displacement from equilibrium (x = 0.2 m)
- The resulting elastic potential energy (E = 2 J)

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