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4. Stress and Strain Fracture Hooke's Law Stress and Strain Waves and Vibrations: Simple Harmonic Motion an... > Stress and Strain Free to share, print, make copies and changes. Get yours at www.boundless.com www.boundless.com/physics?campaign_content=book_5818_section_100&campaign_term=Physics&utm_campaign=powerpoint&utm_medium= direct&utm_source=boundless

5. The ratio of force to area [Equation 1] is called stress and the ratio of change in length to length [Equation 2] is called the strain. Stress and Strain Waves and Vibrations: Simple Harmonic Motion an... > Stress and Strain Free to share, print, make copies and changes. Get yours at www.boundless.com www.boundless.com/physics/textbooks/alternative-to-physics-9th-john-d-cutnell-kenneth-w-johnson-1118129172-9781118129173/waves-and- vibrations-simple-harmonic-motion-and-elasticity-10/stress-and-strain-100/stress-and-strain-395- 6689?campaign_content=book_5818_section_100&campaign_term=Physics&utm_campaign=powerpoint&utm_medium=direct&utm_source=bou ndless Equation 1 View on Boundless.com Tension/Compression View on Boundless.com Equation 2 View on Boundless.com

6. Stress and strain are related to each other by a constant called Young's Modulus or the elastic modulus which varies depending on the material. Using Young's Modulus the relation between stress and strain is given by: [Equation 3]. Stress and Strain Waves and Vibrations: Simple Harmonic Motion an... > Stress and Strain Free to share, print, make copies and changes. Get yours at www.boundless.com www.boundless.com/physics/textbooks/alternative-to-physics-9th-john-d-cutnell-kenneth-w-johnson-1118129172-9781118129173/waves-and- vibrations-simple-harmonic-motion-and-elasticity-10/stress-and-strain-100/stress-and-strain-395- 6689?campaign_content=book_5818_section_100&campaign_term=Physics&utm_campaign=powerpoint&utm_medium=direct&utm_source=bou ndless Equation 3 View on Boundless.com Tension/Compression View on Boundless.com

7. A material with a high elastic modulus is said to have high tensile strength. Such materials are very resistant to being stretched and require a large amount of force to deform a small amount. Stress and Strain Free to share, print, make copies and changes. Get yours at www.boundless.com www.boundless.com/physics/textbooks/alternative-to-physics-9th-john-d-cutnell-kenneth-w-johnson-1118129172-9781118129173/waves-and- vibrations-simple-harmonic-motion-and-elasticity-10/stress-and-strain-100/stress-and-strain-395- 6689?campaign_content=book_5818_section_100&campaign_term=Physics&utm_campaign=powerpoint&utm_medium=direct&utm_source=bou ndless Tension/Compression View on Boundless.com Waves and Vibrations: Simple Harmonic Motion an... > Stress and Strain

8. Most objects behave elastically for small strains and return to their original shape after being bent. If the strain on an object is greater than the elastic limit of the object, it will permanently deform or eventually fracture. Fracture strength is a measure of the force needed to break an object. Fracture Free to share, print, make copies and changes. Get yours at www.boundless.com www.boundless.com/physics/textbooks/alternative-to-physics-9th-john-d-cutnell-kenneth-w-johnson-1118129172-9781118129173/waves-and- vibrations-simple-harmonic-motion-and-elasticity-10/stress-and-strain-100/fracture-396- 5629?campaign_content=book_5818_section_100&campaign_term=Physics&utm_campaign=powerpoint&utm_medium=direct&utm_source=bou ndless Fracture View on Boundless.com Waves and Vibrations: Simple Harmonic Motion an... > Stress and Strain

9. Mathematically, Hooke's Law can be written as F=-kx. Many materials obey this law as long as the load does not exceed the material's elastic limit. The rate or spring constant, k, relates the force to the extension in SI units: N/m or kg/s2. Hooke's Law Free to share, print, make copies and changes. Get yours at www.boundless.com www.boundless.com/physics/textbooks/alternative-to-physics-9th-john-d-cutnell-kenneth-w-johnson-1118129172-9781118129173/waves-and- vibrations-simple-harmonic-motion-and-elasticity-10/stress-and-strain-100/hooke-s-law-397- 5646?campaign_content=book_5818_section_100&campaign_term=Physics&utm_campaign=powerpoint&utm_medium=direct&utm_source=bou ndless Diagram of Hooke's Law View on Boundless.com Waves and Vibrations: Simple Harmonic Motion an... > Stress and Strain

10. Free to share, print, make copies and changes. Get yours at www.boundless.com Appendix

11. Key terms elastic Capable of stretching; particularly, capable of stretching so as to return to an original shape or size when force is released. elasticity The property by virtue of which a material deformed under the load can regain its original dimensions when unloaded strain The amount by which a material deforms under stress or force, given as a ratio of the deformation to the initial dimension of the material and typically symbolized by ε is termed the engineering strain. The true strain is defined as the natural logarithm of the ratio of the final dimension to the initial dimension. stress The internal distribution of force per unit area (pressure) within a body reacting to applied forces which causes strain or deformation and is typically symbolized by σ. Free to share, print, make copies and changes. Get yours at www.boundless.com Waves and Vibrations: Simple Harmonic Motion an...

12. Springs and Hooke's Law A brief overview of springs, Hooke's Law, and elastic potential energy for algebra-based physics students. Free to share, print, make copies and changes. Get yours at www.boundless.com View on Boundless.com Waves and Vibrations: Simple Harmonic Motion an...

13. Tension/Compression Tension: The rod is stretched a length ΔL when a force is applied parallel to its length. (b) Compression: The same rod is compressed by forces with the same magnitude in the opposite direction. For very small deformations and uniform materials, ΔL is approximately the same for the same magnitude of tension or compression. For larger deformations, the cross-sectional area changes as the rod is compressed or stretched. Free to share, print, make copies and changes. Get yours at www.boundless.com Connexions. CC BY 3.0 http://cnx.org/content/m42081/latest/Figure_06_03_03a.jpg View on Boundless.comCC BY 3.0http://cnx.org/content/m42081/latest/Figure_06_03_03a.jpgView on Boundless.com Waves and Vibrations: Simple Harmonic Motion an...

14. Fracture This is a graph of deformation ΔL versus applied force F. The straight segment is the linear region where Hooke's law is obeyed. The slope of the straight region is 1k. For larger forces, the graph is curved but the deformation is still elastic—L will return to zero if the force is removed. Still greater forces permanently deform the object until it finally fractures. The shape of the curve near fracture depends on several factors, including how the force F is applied. Note that in this graph the slope increases just before fracture, indicating that a small increase in F is producing a large increase in L near the fracture. Free to share, print, make copies and changes. Get yours at www.boundless.com Connexions. CC BY 3.0 http://cnx.org/content/m42081/latest/Figure_06_03_01a.jpg View on Boundless.comCC BY 3.0http://cnx.org/content/m42081/latest/Figure_06_03_01a.jpgView on Boundless.com Waves and Vibrations: Simple Harmonic Motion an...

15. Hooke's Law This graph illustrates how force, F, varies with position. You can change the spring constant, k, to see how the equation responds. Free to share, print, make copies and changes. Get yours at www.boundless.com Boundless. "Boundless." GNU FDL http://www.boundless.com/ View on Boundless.comGNU FDLhttp://www.boundless.com/View on Boundless.com Waves and Vibrations: Simple Harmonic Motion an...

16. Diagram of Hooke's Law The extension of the spring is linearly proportional to the force. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikimedia. "Dinamometro." CC BY-SA http://commons.wikimedia.org/wiki/File:Dinamometro.jpg View on Boundless.comCC BY-SAhttp://commons.wikimedia.org/wiki/File:Dinamometro.jpgView on Boundless.com Waves and Vibrations: Simple Harmonic Motion an...

17. Free to share, print, make copies and changes. Get yours at www.boundless.com Waves and Vibrations: Simple Harmonic Motion an... How does Hooke's law explain small deformations? A) Small deformations show change in length and material constant are equal to the force on the object B) Small deformations determine that objects return to their original shape when the force is removed C) Small deformations are elastic D) Small deformations are equivalent to Y mulitiplied by strain

18. Free to share, print, make copies and changes. Get yours at www.boundless.comwww.boundless.com Boundless - LO. "Boundless." CC BY-SA 3.0 http://www.boundless.com/CC BY-SA 3.0http://www.boundless.com/ Waves and Vibrations: Simple Harmonic Motion an... How does Hooke's law explain small deformations? A) Small deformations show change in length and material constant are equal to the force on the object B) Small deformations determine that objects return to their original shape when the force is removed C) Small deformations are elastic D) Small deformations are equivalent to Y mulitiplied by strain

19. Free to share, print, make copies and changes. Get yours at www.boundless.com Waves and Vibrations: Simple Harmonic Motion an... How are stress and strain related to each other via Young's Modulus? A) Young's Modulus divided by strain is equivalent to stress B) Young's Modulus multiplied by strain is equivalent to stress C) Strain is equivalent to stress D) Young's Modulus is equivalent to stress multiplied by strain

20. Free to share, print, make copies and changes. Get yours at www.boundless.comwww.boundless.com Boundless - LO. "Boundless." CC BY-SA 3.0 http://www.boundless.com/CC BY-SA 3.0http://www.boundless.com/ Waves and Vibrations: Simple Harmonic Motion an... How are stress and strain related to each other via Young's Modulus? A) Young's Modulus divided by strain is equivalent to stress B) Young's Modulus multiplied by strain is equivalent to stress C) Strain is equivalent to stress D) Young's Modulus is equivalent to stress multiplied by strain

21. Free to share, print, make copies and changes. Get yours at www.boundless.com Waves and Vibrations: Simple Harmonic Motion an... Fracture strength is usually determined for a given specimen by a A) indentation test B) conductivity test C) tensile test D) resistance test

22. Free to share, print, make copies and changes. Get yours at www.boundless.comwww.boundless.com Boundless - LO. "Boundless." CC BY-SA 3.0 http://www.boundless.com/CC BY-SA 3.0http://www.boundless.com/ Waves and Vibrations: Simple Harmonic Motion an... Fracture strength is usually determined for a given specimen by a A) indentation test B) conductivity test C) tensile test D) resistance test

23. Free to share, print, make copies and changes. Get yours at www.boundless.com Waves and Vibrations: Simple Harmonic Motion an... Strain placed on an object such that it deforms beyond its elastic limit will cause object to A) bend and then return to its original shape when the force is abated B) deform elastically C) deform inelastically D) permanently deform and eventually fracture

24. Free to share, print, make copies and changes. Get yours at www.boundless.comwww.boundless.com Boundless - LO. "Boundless." CC BY-SA 3.0 http://www.boundless.com/CC BY-SA 3.0http://www.boundless.com/ Waves and Vibrations: Simple Harmonic Motion an... Strain placed on an object such that it deforms beyond its elastic limit will cause object to A) bend and then return to its original shape when the force is abated B) deform elastically C) deform inelastically D) permanently deform and eventually fracture

25. Attribution Wikipedia. "Fracture." CC BY-SA 3.0 http://en.wikipedia.org/wiki/FractureCC BY-SA 3.0http://en.wikipedia.org/wiki/Fracture Wiktionary. "elastic." CC BY-SA 3.0 http://en.wiktionary.org/wiki/elasticCC BY-SA 3.0http://en.wiktionary.org/wiki/elastic Wiktionary. "strain." CC BY-SA 3.0 http://en.wiktionary.org/wiki/strainCC BY-SA 3.0http://en.wiktionary.org/wiki/strain Connexions. "Mechanical Properties of Matter: deformation of materials." CC BY 3.0 http://cnx.org/content/m39533/latest/CC BY 3.0http://cnx.org/content/m39533/latest/ Wikipedia. "Hooke's law." CC BY-SA 3.0 http://en.wikipedia.org/wiki/Hooke%2527s_lawCC BY-SA 3.0http://en.wikipedia.org/wiki/Hooke%2527s_law Wiktionary. "elasticity." CC BY-SA 3.0 http://en.wiktionary.org/wiki/elasticityCC BY-SA 3.0http://en.wiktionary.org/wiki/elasticity Wikipedia. "Deformation (engineering)." CC BY-SA 3.0 http://en.wikipedia.org/wiki/Deformation_(engineering)CC BY-SA 3.0http://en.wikipedia.org/wiki/Deformation_(engineering) Connexions. "Elasticity: Stress and Strain." CC BY 3.0 http://cnx.org/content/m42081/latest/CC BY 3.0http://cnx.org/content/m42081/latest/ Wiktionary. "strain." CC BY-SA 3.0 http://en.wiktionary.org/wiki/strainCC BY-SA 3.0http://en.wiktionary.org/wiki/strain Wiktionary. "stress." CC BY-SA 3.0 http://en.wiktionary.org/wiki/stressCC BY-SA 3.0http://en.wiktionary.org/wiki/stress Free to share, print, make copies and changes. Get yours at www.boundless.com Waves and Vibrations: Simple Harmonic Motion an...