Changes in Length (one dimensional)

To stretch or compress something you must exert a force on it at either end.

Definitions:

• Tensile Stress is the force per unit cross-sectional area exerted on the ends. (Note the surface whose area we wish to measure is perpendicular to the force. See Fig.9.1)

  

Figure 9.1: Tensile Stress

• Tensile Strain is the fractional change in length.
• Young's Modulus ( Y ) is the ratio of tensile stress to tensile strain:

  $${\frac{{\:\rm tensile stress}}{{\:\rm tensile strain}}} {\frac{F/A}{\Delta L/L_{O}}} {\frac{FL_{O}}{A \Delta L}}$$ (2)

  where F is the applied force, L_O is the original length of the object, A is the cross-sectional area of the object, and $\Delta$L is the change in the length of the object. Notice that Y has S.I. units of N/m ².