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Hooke's law

Hooke's law states that the displacement of one end of an elastic material is negatively proportional to the restoring force . This means that the restoring force points in the opposite direction to the displacement.

The magnitude of the restoring force is directly proportional to the magnitude of displacement: $$$\Tred{\vecphy{F}}=-\Tblue{k}\Tviolet{\vecphy{x}} \quad \Rightarrow \quad \Tred{F}=\Tblue{k}\Tviolet{x}$$$

A spring pulls back against any force that stretches it. The further the spring is stretched, the greater the force.

  • $$\Tred{\vecphy{F}}$$ is the restoring force . The right-hand side of the equation is negative because the force points in the opposite direction to the extension and the load.

  • $$\Tblue{k}$$ is the spring constant , which depends on the material that the elastic material is made of. The value of $$\Tblue{k}$$ for a particular material is determined empirically. The unit of the spring constant is newton per metre $$(\text{N m}^{-1})$$.

  • $$\Tviolet{\vecphy{x}}$$ is the displacement of the spring's end from its equilibrium position.

  • $$\Tviolet{\vecphy{x}}$$ can be negative, such as in the case where the spring is contracted. The directions of the restoring and load forces thus have to be reversed.

The spring in a weighing scale obeys Hooke's law. The linear relationship between load and extension makes it simple to convert the extension into a measurement of the load.