KinexiaLEARN PHYSICS

Hooke's Law — Mattress Spring (Worked Example)

Easy
Problem

A mattress spring with spring constant 800 N/m is compressed by 0.12 m when someone sits on the bed. What restoring force does the spring exert?

Given

  • k = 800 N/m

  • x = 0.12 m

Find

The spring force F.

Principle

Hooke's law: the restoring force is proportional to the displacement from equilibrium, F = kx, always pointing back toward equilibrium.

Formula

Solution

  1. Write the law: F=kxF = kx

  2. Substitute: F=(800)(0.12)F = (800)(0.12)

  3. Multiply: F=96 NF = 96\ \mathrm{N}

96 N upward

Unit check

N/m × m = N — a force, correct.

What this means physically

96 N upward from this one spring — a mattress has dozens sharing your weight, which is why the total support feels firm rather than bouncy.

Common mistake

Using the spring's total length instead of its compression x. Hooke's law needs the change from natural length, not the length itself.