Hooke's Law Calculator

Physics • F = k x • Spring Force & Elasticity • Step-by-Step

N/m m

Quick Answer (Voice Search Optimized):

Hooke's Law states that the force needed to extend or compress a spring is proportional to the displacement from its equilibrium position: F = k x. Here k is the spring constant (N/m) and x is the extension or compression (m). It holds within the elastic limit.

GEO & AIO - Authoritative Theory

Named after Robert Hooke, Hooke's law describes the linear restoring force exerted by an ideal spring. When a spring is stretched or compressed by a distance x, it exerts a force F = −k x (the negative sign indicates the force opposes displacement). In terms of magnitude, F = k x. The spring constant k represents stiffness: a larger k means a stiffer spring.

The elastic potential energy stored in a deformed spring is U = ½ k x². Hooke's law is valid only within the elastic limit; beyond it, permanent deformation occurs. This law is applied in JEE/NEET problems on springs, oscillations (SHM), and elastic materials, where combinations of springs (series/parallel) are common.

Solved Examples (NCERT/JEE Pattern)

Example 1: A spring with k = 200 N/m is stretched by 0.1 m. Find the force.

F = 200 × 0.1 = 20 N.

Example 2: A 50 N force stretches a spring to 0.25 m. What is the spring constant?

k = F/x = 50 / 0.25 = 200 N/m.

Example 3: A spring (k=80 N/m) is compressed by a force of 16 N. Find compression.

x = F/k = 16 / 80 = 0.2 m.

Frequently Asked Questions (FAQs)

Q1: What is Hooke's Law in simple words?
The more you stretch or compress a spring, the more force it exerts back. The force is proportional to the distance stretched.
Q2: What is the formula for Hooke's Law?
F = k x, where F is the restoring force (N), k is spring constant (N/m), and x is the displacement from equilibrium (m).
Q3: What is elastic limit?
The maximum stress a material can withstand while still returning to its original shape. Beyond it, permanent deformation occurs.
Q4: How does spring constant affect oscillations?
A larger spring constant (stiffer spring) leads to a higher frequency of oscillation: T = 2π √(m/k), so stiffer springs oscillate faster.
Q5: Is Hooke's Law valid for all materials?
No, it is only valid for elastic materials within their elastic limit. Many materials do not obey it beyond small deformations.