*Reference:** Beginning Physics I*

**CHAPTER 11: DEFORMATION OF MATERIALS & ELASTICITY**

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**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**

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## 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/m^{2}). 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.

**SHEAR DEFORMATION**

**TWISTING DEFORMATION**

**PRESSURE**

**BULK MODULUS**

**COMPRESSIBILITY**

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