Table of Contents
What Is Elastic Potential Energy?
Elastic potential energy is the energy stored in an elastic object, such as a spring or rubber band, when it is stretched or compressed from its natural rest position. This form of potential energy arises from the molecular bonds within the material being deformed and is fully recoverable when the object returns to its equilibrium state.
The concept is fundamental in physics and engineering, appearing in applications ranging from vehicle suspension systems and mechanical watches to trampolines and archery bows. Understanding elastic potential energy helps engineers design springs for specific force and energy storage requirements.
The Formula
Where PE is the elastic potential energy in joules (J), k is the spring constant in newtons per meter (N/m), and x is the displacement from equilibrium in meters (m). The spring constant k measures the stiffness of the spring: a higher value means a stiffer spring that stores more energy for the same displacement.
The restoring force exerted by the spring follows Hooke's Law:
Worked Examples
| Spring Constant (N/m) | Displacement (m) | Energy (J) |
|---|---|---|
| 100 | 0.1 | 0.50 |
| 200 | 0.5 | 25.00 |
| 500 | 0.2 | 10.00 |
| 1000 | 1.0 | 500.00 |
Spring Types & Constants
- Compression springs: Resist being compressed; common in pens, mattresses, and valves (k: 10-10,000 N/m).
- Extension springs: Resist being stretched; found in garage doors and trampolines (k: 50-5,000 N/m).
- Torsion springs: Resist twisting; used in clothespins and mousetraps.
- Leaf springs: Flat springs used in vehicle suspensions (k: 20,000-100,000 N/m).
Frequently Asked Questions
Does doubling the displacement double the energy?
No. Because energy depends on x squared, doubling the displacement quadruples the stored energy. For example, compressing a spring 0.2 m stores four times more energy than compressing it 0.1 m with the same spring constant.
What happens when a spring exceeds its elastic limit?
Beyond the elastic limit, the spring deforms permanently and Hooke's Law no longer applies. The material enters the plastic deformation region and the spring will not return to its original shape, losing its ability to store and release energy efficiently.
Can elastic potential energy be negative?
No. Since the formula uses x squared, the result is always positive regardless of whether the spring is stretched or compressed. Energy is a scalar quantity and elastic PE is always zero or positive.