Use adaptive quiz-based learning to study this topic faster and more effectively.

# 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.