Physics I: Chapter 11

CHAPTER 11: DEFORMATION OF MATERIALS & ELASTICITY

KEY WORD LIST

Stress, Strain, Elastic, Elastic Limit, Hooke’s Law, Young’s Modulus, Ultimate Strength, Force Constant, Shear Deformation, Twisting Deformation, Pressure, Bulk Modulus, Compressibility

GLOSSARY

For details on the following concepts, please consult CHAPTER 11.

STRESS
Force needed for certain stretch is proportional to the cross-sectional area of the rod. If we define stress as the ratio of the force to the cross-sectional area, we have a quantity that measures the effectiveness of the force in accomplishing a given stretch, independent of the cross-sectional area of the rod. The dimensions of the stress are force per area (pascal = 1 N/m²). A given stress will give rise to a definite strain in a rod of a certain material irrespective of either the thickness or the length of the rod.

STRAIN
A given force will cause a stretch that is proportional to the length of the unstretched rod. We define strain as the ratio of the change in the length of the rod to the unstretched length of the rod. The strain due to a given force will be the same for any length of rod of the same material and cross-section. The strain is thus a measure of the stretch of the rod that is independent of the length of the rod. The strain is dimensionless.

ELASTIC
Any material that returns to its original shape after the distorting forces are removed is said to be elastic.

ELASTIC LIMIT
For a rod of any given material there is a stress beyond which the material will no longer return to its original length. This boundary stress is called the elastic limit.

HOOKE’S LAW
For stresses below the elastic limit it is found that, to a good approximation, the strain is proportional to the stress; for example, if we double the stress, the strain would double. This is called the Hooke’s Law.

YOUNG’S MODULUS
In the elastic region stress/strain = constant. The constant is called the Young’s modulus (Y). Its value depends on the material. Young’s modulus has dimensions of stress, and can be measured in pascals.

If a force tends to compress a rod rather than stretch it, the relationship of stress to strain still holds with the same Young’s modulus. In that case, the change in length represents a compression rather than stretch.

ULTIMATE STRENGTH
If one applies stress to a rod beyond the elastic limit, the rod will retain some permanent strain when the stress is removed. If the stress gets too great, the rod will break. The stress necessary to just reach the breaking point is called the ultimate strength of the material.

FORCE CONSTANT
For a rod of definite cross section (A) and length (L), the applied force (F) is proportional to the elongation ( L), and can therefore be expressed as F = kx, where k is the force constant of the system.