The Minus Sign Is the Physics

You'll learnto read the sign of a spring's displacement and force from F=−kΔx, always restoring toward equilibrium.

Stretch a spring and it pulls back in; compress it and it pushes back out. Hooke’s law writes that one rule as F = −k·Δx, and the minus sign is the whole point — it is “back toward equilibrium” in algebra. Watch the force flip sign at the natural length, hang a mass to find the settle point, then combine springs without swapping the series and parallel rules.

8 STEPS · 6 QUICK CHECKS · v3

Before you start

What you're looking at

A block on a frictionless track tied to a wall by a spring (k = 100 N/m), pulled 0.20 m right then pushed 0.15 m left.

The question

Each time, which way does the spring force on the block point, and how strong is it?

Watch for

The force does not follow the displacement; the emerald arrow always aims back toward the natural length.

What the symbols mean

Emerald arrow = spring force; Δx = displacement from natural length; Δx and Fs always carry opposite signs.

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