3. Objectives  Understand how elasticity is related to Hooke’s Law for springs.  Know that the change in length of an object is proportional to the force placed on the object, but only to the proportional limit.  Understand the meaning of the terms elastic region, proportional limit, elastic limit, plastic region, and breaking point.

4. Objectives  Know that the elastic modulus, or Young’s modulus, is a ratio of the stress on an object to the strain of the object.  Differentiate between tensile stress, compressive stress, and shear stress.  Solve problems using elastic modulus, shear modulus, and bulk modulus.

5. Introductory Video

6. Reading Activity Questions?

7. Hooke’s Law  The change in length of an object is directly proportional to the amount of force placed on it  Normally thought of in terms of springs where k is the spring constant  The same is true for any material – but only to a certain point

8. Elasticity  Hooke’s Law holds true for all materials up to the material’s proportional limit  Beyond the proportional limit, the change in length per force applied increases

9. Elasticity  The material will return to its original shape when the force is removed, provided the elastic limit is not exceeded  Once the elastic limit is exceeded, permanent deformation, or permanent set, occurs

10. Elasticity  Deformation continues until the breaking point  Breaking, or fracture, is the subject of Lesson 9-7  The maximum force that can be applied to a material without breaking is its ultimate strength

11. Elasticity  When force is applied to a material, it is said to undergo stress  Stress is defined as force per unit cross-sectional area  The ratio of the change in length to the original length is called strain

12. Elasticity  Cross-Sectional Area  Cylindrical rod – πr 2  Rectangular rod – l x w  Triangular prism – ½ bh

13. Elasticity  Experimentation has found that the change in length of an object is directly proportional to force place on in, but inversely proportional to the object’s cross-sectional area  This value is specific to the material the object is made of  The elastic modulus, E, replaces the spring constant in Hooke’s Law  The elastic modulus, or Young’s modulus, is the ratio of stress to strain

14. Elasticity

15.  Rearranging, we find a formula for the change in length, ΔL, of a material with an elastic modulus E, cross-sectional area A, original length L 0, subjected to a force F

16. Elasticity  This formula applies equally to tensile stress and compressive stress  Values for elastic moduli are found in Table 9-1 on page 254 in your textbook and in the data guide

17. Shear Modulus  A similar formula applies to shear stress using the shear modulus, G  In tensile or compressive stress, the applied force is perpendicular to the cross-sectional area  In shear stress, the applied force is parallel to the cross-sectional area

18. Bulk Modulus  A third situation arises when an object is subjected to forces from all sides  Like a submarine at the bottom of the ocean  This creates a change in volume instead of just length

19. Bulk Modulus  The proportionality constant for this situation is called bulk modulus, B  ΔP is the change in pressure  Pressure is defined as force per area and is thus the equivalent of stress  ΔP is the change in pressure and V 0 is the original volume  The minus sign indicates volume decreases with applied force

20. Summary Review  Do you understand how elasticity is related to Hooke’s Law for springs?  Do you know that the change in length of an object is proportional to the force placed on the object, but only to the proportional limit?  Do you understand the meaning of the terms elastic region, proportional limit, elastic limit, plastic region, and breaking point?

21. Summary Review  Do you know that the elastic modulus, or Young’s modulus, is a ratio of the stress on an object to the strain of the object?  Can you differentiate between tensile stress, compressive stress, and shear stress?  Can you solve problems using elastic modulus, shear modulus, and bulk modulus?

23. #44-52 Homework