Hooke's Law

When you stretch a spring by pulling on it, the spring pulls back. The more you stretch it, the harder it pulls. Robert Hooke first described this behaviour in 1676 and it remains one of the most useful relationships in physics.

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Hooke's Law

Hooke's law states that the extension of a spring is directly proportional to the applied force, provided the limit of proportionality is not exceeded:

$F = kx$F=kx

where:

• F is the applied force in N (newtons)
• k is the spring constant (also called stiffness constant) in N m⁻¹
• x is the extension (or compression) in m — this is the change in length from the natural (unstretched) length

The spring constant k tells you how stiff the spring is. A large k means you need a large force to produce a small extension — the spring is stiff. A small k means the spring extends easily — it is compliant.

Worked example: A spring has a natural length of 15.0 cm. When a force of 4.0 N is applied, the spring extends to 21.0 cm. What is the spring constant?