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How It Works
Hooke's Law states that the force needed to stretch or compress a spring is proportional to the displacement: F = −k(x − x₀). The spring constant k measures stiffness — a higher k means a stiffer spring. The stored potential energy is U = ½kx².
This law applies to any elastic material within its proportional limit, including rubber bands, metal beams, and biological tissues.
Example Problem
A spring with k = 200 N/m is stretched 0.15 m from its natural length. What force is required?
- F = k · x = 200 × 0.15 = 30 N
- Potential energy stored: U = ½ × 200 × 0.15² = 2.25 J
Frequently Asked Questions
What is a spring constant?
The spring constant k (in N/m) measures how stiff a spring is. A k of 500 N/m means you need 500 N of force to stretch the spring by 1 meter.
Does Hooke's Law work for all materials?
Only within the elastic (proportional) limit. Beyond that point the material deforms permanently and the linear relationship breaks down. Metals, for example, follow Hooke's Law up to their yield strength.
How is spring potential energy used?
Spring potential energy (U = ½kx²) is stored when a spring is compressed or stretched and released as kinetic energy. It powers mechanical watches, vehicle suspension systems, and spring-loaded mechanisms.
Related Calculators
- Potential Energy Calculator — calculate gravitational potential energy.
- Stress & Strain Calculator — analyze elastic deformation in materials.
- Pendulum Calculator — explore another system with restoring forces.
- Work Calculator — compute the work done in stretching or compressing a spring.
- Kinetic Energy Calculator — find kinetic energy when a spring releases its stored energy.
- Force Unit Converter — convert between newtons, pounds-force, and other force units.
Reference: Tipler, Paul A. 1995. Physics For Scientists and Engineers. Worth Publishers. 3rd ed.