1. INCOMPLETE DRAFT XI. Elasticity W. Pezzaglia Updated: 2014Feb22

2. Springs & Elasticity A. Springs B. Stress C. Strain & Modulus 2

3. A. Springs 1.Hooke’s law 2.Springs in Parallel 3.Springs in Series 3

4. 1. Hooke’s Law This idea was first stated by Robert Hooke in 1675 as a Latin anagram "ceiiinossssttuu" whose solution he published in 1678 as "Ut tensio, sic vis" which means "As the extension, so the force." 4 Spring compressed by “x” will push back with force “F” Spring constant “k” (units of N/m) describes the stiffness of the spring

5. B. Stress 1.x 2.x 3.x 5

6. 1. Stress Types of stress -> Units: Pascals (i.e. force/area) Breaking stress or “ultimate strength” is the maximum stress at which material fails 6

7. 2. Ultimate Strengths Ultimate strengths in table are in MPa (million Pascals) Carbon nanotubes are very strong! Concrete is rather poor (must use steel reinforcement) 7 SubstanceMPa Nanotubes30000 Spider Silk1000 Steel250 Granite100-250 Bone130 Concrete3

8. 3. Self Stress A tall enough column will crumble under its own weight For granite, this maximum height would be about 3750 meters for a cylindrical mountain. For pyramid shaped mountain the limit would be 3x bigger: 11,250 meters Mauna Kea is 10,200 meters tall 8

9. Biggest Mountain on Venus Maxwell Montes Gravity: 0.904 g Mountain height 11 km Consistent with our estimate!

10. Biggest Mountain on Mars Gravity 2.66x smaller, so increase maximum height by that factor to 29.9 km Olympus Mons height 24 km consistent!

11. C. Strain & Modulus 1.x 2.x 3.x 11

12. 12 1. Strain Most substances deform linearly following Hooke’s law up to a point (i.e. will spring back to original shape). Past that point they irreversibly deform (plastic)