Hooke's Law & Springs
Stretch springs, see F vs x.
You hang weights on a spring. With 1 kg, it stretches 5 cm. With 2 kg, it stretches 10 cm.
How far does it stretch with 3 kg?
15 cm! Hooke's Law is beautifully simple: F = kx. The force is proportional to the stretch. Double the force, double the stretch. Triple the force, triple the stretch. The spring constant k tells you how stiff the spring is.
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Drag the mass to stretch the spring. Watch the force grow linearly on the F vs x graph.
F = −kx
The minus sign is everything — it means the force always pulls BACK toward equilibrium. Push right, force pulls left. This is why springs oscillate.
Skyscrapers use steel frames that flex like springs during earthquakes. Hooke's Law governs how far they bend before structural failure.
A guitar string is a spring under tension. Pluck it and it oscillates according to Hooke's Law. The spring constant determines the pitch.
The Achilles tendon stores elastic energy like a spring when you walk. Kangaroos are masters of this — 70% of their hopping energy comes from tendon springs.
“Hooke's Law is the gateway to all oscillatory physics. Anything that vibrates — atoms, bridges, stars — follows this law near equilibrium. Simple, elegant, universal.”
Spring Lab
Connect springs in series and parallel. Adjust spring constants and see how the effective stiffness changes.
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Put two identical springs in parallel — the effective k doubles (stiffer). Now in series — the effective k halves (softer). This surprises most people!
Springs in parallel ADD their constants (k_eff = k₁ + k₂). Springs in series combine like resistors in parallel: 1/k_eff = 1/k₁ + 1/k₂.