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Biomechanics

Biomechanics. May 5, 2005 Dr. Kelsey Jordahl. Bacterium ~0.3 m. Whale ~30 m. Size. Factor of 10 8 in size Factor of 10 24 in mass!. Scaling Surface Area to Volume ratio. V  l 3 Volume to length m  l 3 mass to length S  l 2 Surface to volume

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Biomechanics

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  1. Biomechanics May 5, 2005 Dr. Kelsey Jordahl

  2. Bacterium ~0.3m Whale ~30 m Size Factor of 108 in size Factor of 1024 in mass!

  3. Scaling Surface Area to Volume ratio V l3 Volume to length m l3 mass to length S  l2 Surface to volume so S/V  l  m1/3

  4. Example for cube

  5. Consequences of falling for organisms of difference sizes >100 kg: serious injury possible even at one’s own height (cows, horses, elephants, very large humans) 100 g – 100 kg: may be injured if fall from greater than own height (dogs, cats, squirrels, most humans) 100 mg – 100 g: no injury from any height (mice, insects, baby birds) <100 mg: never really fall at all; airborne (pollen, spores, very small animals)

  6. “You can drop a mouse down a 1000 yard mine shaft and, arriving at the bottom, it gets a slight shock and walks away. A rat is killed, a man is broken, and a horse splashes.”

  7. Scaling

  8. Shew ~6 g Elephant ~6000 kg Land Mammals Factor of 106 in mass (only 100 in size)

  9. Scaling factors for mammals y  la l=m1/3

  10. Example of isometry and its consequences

  11. Example of allometry: bone proportions in pelycosaurs

  12. Example of allometry: shape change in human ontogeny

  13. Dimensionless numbers Mechanical advantage MA=Fo/Fi Flatness index FI=S1.5/V Strain x/x0 Froude number Fr=v2/gl Walking on water /l2g

  14. Final ExamThursday, May 14(same time & location) Chapters 22, 25, & 29 (sections 26.7, 26.8, & 26.9 also helpful) S. Vogel, Life’s Devices, chapters 3 & 4, on reserve in library Handout from today

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