Elastic Potential Energy Calculator

Understanding Elastic Potential Energy Calculator

Elastic potential energy is stored when a spring is compressed or stretched. It can be converted to kinetic energy when the spring is released.

How to use this calculator

1. Enter the spring constant \(k\), usually in \(\text{N/m}\).
2. Enter the displacement \(x\), the distance the spring is stretched or compressed from its resting length.
3. Check that the units are consistent, because the result will be in joules \(\text{J}\).
4. Click calculate to find the elastic potential energy.

The formula explained

The formula \(PE = \frac{1}{2}kx^2\) computes the energy stored in a spring. It shows that energy depends on both the stiffness of the spring and the square of the stretch or compression.

• PE = elastic potential energy, measured in joules \(\text{J}\)
• k = spring constant, measured in newtons per meter \(\text{N/m}\)
• x = displacement from the spring's natural length, measured in meters \(\text{m}\)

Step by step method

1. Write down \(k\) and \(x\).
2. Square the displacement, \(x^2\).
3. Multiply by \(k\), then multiply by \(\frac{1}{2}\).

Worked example

Problem. A spring has a spring constant of \(200\,\text{N/m}\) and is stretched \(0.15\,\text{m}\). Find the elastic potential energy.

1. Use \(PE = \frac{1}{2}kx^2\).
2. Substitute the values, \(PE = \frac{1}{2}(200)(0.15)^2\).
3. Compute \(0.15^2 = 0.0225\), so \(PE = 100 \times 0.0225 = 2.25\,\text{J}\).

Tips and common mistakes

• Make sure \(x\) is in meters, not centimeters, before calculating.
• Because \(x\) is squared, doubling the stretch makes the energy four times larger.

Frequently asked questions