What is Hooke's law?
The force a spring exerts is proportional to how far it is stretched or compressed: F = kx, where k is the spring constant in newtons per metre. A spring with k = 200 N/m pulls back with 20 N when stretched 10 cm. The minus sign often written in front reflects that the force opposes the displacement — a stretched spring pulls back, a compressed one pushes out.
What does the spring constant actually mean?
Stiffness. A high k means a stiff spring needing large force for small movement; a low k means a soft one. Car suspension springs are in the tens of thousands of N/m; a ballpoint pen spring is a few hundred. The constant depends on the material, wire thickness, coil diameter and number of turns — thicker wire and fewer coils both make a spring stiffer.
When does Hooke's law stop working?
Beyond the elastic limit. Up to that point a material returns to its original shape and the relationship stays linear. Past it, the material yields — it deforms permanently, and the graph of force against extension curves away from the straight line. Push further and it reaches ultimate tensile strength and fractures. Every real spring has this limit, which is why over-stretching one ruins it.
How do springs combine in series and parallel?
The opposite way round from resistors, which catches people out. Springs in parallel add their constants: two 100 N/m springs side by side give 200 N/m, stiffer. In series the reciprocals add: the same two end to end give 50 N/m, softer, because each stretches under the full load. Longer springs are softer for exactly this reason.
How is energy stored in a spring calculated?
Elastic potential energy is ½kx², the area under the force-extension graph. Because it depends on displacement squared, stretching twice as far stores four times the energy. A spring at 10 cm with k = 200 N/m stores 1 joule; at 20 cm it stores 4. This is what makes heavily compressed springs genuinely dangerous — the stored energy releases all at once.
Does Hooke's law apply beyond springs?
Yes, to any elastic deformation within limits — stretching a wire, bending a beam, compressing rubber. In materials science it is expressed as stress proportional to strain, with Young's modulus playing the role of k normalised for the material's dimensions. That generalisation is why the same idea underpins structural engineering, not just spring design.