Elastic Potential Energy Calculator
Calculate the energy stored in compressed or stretched springs using Hooke's Law
Did You Know? Elastic potential energy is used in everything from trampolines to mechanical watches!
Measure of spring stiffness
Positive for stretch, negative for compression
For calculating work done between two positions
Calculation Results
Elastic Potential Energy (U):
Spring Force (F):
Work Done (W):
0.00 J
0.00 N
0.00 J
Formula Used: U = ½kx²
Understanding Elastic Potential Energy
Hooke's Law
The foundation of spring physics states that the force (F) needed to extend or compress a spring is proportional to the displacement (x): F = -kx where k is the spring constant (stiffness).
Energy Storage
The potential energy (U) stored in a spring is given by: U = ½kx² This energy equals the work done to displace the spring and can be completely converted to kinetic energy when released.
Practical Applications of Spring Energy
Mechanical Systems
Springs are fundamental in mechanical watches, vehicle suspensions, and industrial machinery. The precise storage and release of elastic potential energy enables controlled motion and vibration absorption.
Sports Equipment
From pole vaulting poles to archery bows, elastic potential energy conversion is key to performance. Understanding these principles helps athletes optimize their equipment for maximum energy transfer.
Energy Storage
Large-scale spring systems are being developed for renewable energy storage, offering an alternative to batteries by storing mechanical energy that can be converted back to electricity when needed.
Frequently Asked Questions
Why is there a ½ in the elastic potential energy formula?
The ½ factor comes from the work-energy principle. As you stretch a spring, the force required increases linearly from 0 to kx. The average force during displacement is ½kx, and work (energy) equals average force × displacement (½kx × x = ½kx²).
Can elastic potential energy be negative?
The energy value itself is always non-negative because the displacement is squared in the formula (U = ½kx²). However, the work done can be positive or negative depending on whether the spring is doing work on its surroundings or work is being done on the spring.
How does spring constant affect energy storage?
A higher spring constant (stiffer spring) stores more energy for the same displacement. However, stiffer springs require more force to achieve that displacement. The relationship is linear - double the spring constant doubles the energy stored at the same displacement.
What's the difference between compression and stretching?
Physically, both compression and stretching store energy similarly. The formulas are identical, with compression typically represented as negative displacement. The main practical difference is in the spring's mechanical design to handle each type of deformation.
When does Hooke's Law not apply?
Hooke's Law is only valid within the elastic limit of the material. If stretched too far, springs undergo plastic deformation and won't return to their original shape. The law also doesn't account for factors like spring mass or damping effects in dynamic systems.