Hooke's Law
Restoring force of a spring.
Formula
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Example
A spring with k = 200 N/m stretched 0.1 m pulls back with 20 N.
How it works
Hooke’s Law says that many springs and other elastic objects push or pull back with a force proportional to how far they are displaced from their natural length. The minus sign means the force always points opposite the displacement, so it acts to restore the object toward equilibrium. This linear relationship works well for small deformations, before the material stops behaving elastically.
When to use it
Use this when analyzing springs, elastic bands, or any small stretch/compression problem in mechanics. It is especially useful for finding the force exerted by a spring or the extension/compression caused by a known force.
Worked example, step by step
A spring has a spring constant k = 150 N/m and is compressed by x = 0.04 m. Use Hooke’s Law: F = -kx Substitute the values: F = -(150)(0.04) Calculate: F = -6 N The negative sign means the spring’s force is opposite the compression, so the spring pushes back with a force of 6 N.
Common mistakes to avoid
- Using the wrong units for displacement, such as centimeters instead of meters
- Forgetting that the negative sign indicates direction, not a smaller magnitude
- Applying Hooke’s Law beyond the elastic limit, where the force is no longer proportional to displacement
Did You Know?
Hooke published his spring law as an anagram, "ceiiinosssttuv", to claim priority while keeping it secret.
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