Stress and strain — common mistakes

Always ensure you are using the correct SI units for all quantities (force in N, area in m$^2$, length in m). Pay close attention to distinguishing between force-extension graphs and stress-strain graphs, as their gradients represent different physical quantities ($k$ for force-extension and $E$ for stress-strain in the linear region).

Strain is calculated as a ratio of two lengths (extension divided by original length). Since the units of length cancel out, strain has no units, making it a pure number that represents a relative change.

The spring constant ($k$) describes the stiffness of a specific object (like a particular spring or wire), and it depends on that object's dimensions. The Young Modulus ($E$) is an intrinsic property of the material itself, independent of its shape or size, used to compare the stiffness of different substances.

No, Hooke's Law states that force is directly proportional to extension and is only valid up to the limit of proportionality, which typically occurs before or at the elastic limit. Beyond this point, the material no longer behaves elastically, and the relationship between force and extension becomes non-linear.