F = kx Formula – Hooke’s Law Practice
F = kx — Hooke’s law for an ideal spring (magnitude)
For an ideal spring, restoring force magnitude is F = k x, where x is stretch or compression from equilibrium. Energy stored is U = ½kx² — don’t mix the two.
Guide — how to use this formula
- 1. Convert stretch to metres if k is in N/m.
- 2. Use F = kx, k = F/x, or x = F/k.
- 3. At equilibrium hanging: kx = mg → x = mg/k.
- 4. Energy is ½kx², not Fx.
Derivation
Hooke’s law models a linear spring:
- Force law (magnitude):
F = kx - Elastic potential energy:
U = \tfrac{1}{2}kx^{2}
Convert cm → m before using k in N/m.
Examples
Example: k = 200, x = 0.1 m
F = 20 N.
Example: find k
F = 40 N, x = 0.2 m → k = 200 N/m.