Lecture 4: Physics of the Skeleton1. Skull2. Mandible3. Hyoid Bone4. Cervical Vertebra5. Clavicle6. Sternum7. Costal Cartilage8. Ribs9. Scapula10. Humerus11. Radius12. Ulna13. Carpal Bones14. Metacarpal Bones15. Phalanges of Fingers16. Thoracic Vertebra17. Lumbar Vertebra18. Sacrum19. Os Coxa20. Femur21. Patella22. Tibia23. Fibula24. Tarsal Bones25. Metatarsal Bones26. Phalanges of Toes
Kinds of Bones• Tubular support bones (limbs, digits)
• Cylindrical bones protect soft tissue (spine)
• Plate-like bones (skull)
• Hip and shoulder bones
• Ribs• Wrist/ankle• Teeth• Inner Ear
Bones• Support the body• Protect organs
– Rib cage (lungs, heart, thoracic organs)– Skull (Brain, eyes, ears)– Vertebrae (Spinal chord)
• Walking, lifting, manipulation• Chemical storage (Ca)• Hearing
Composition of BoneCollagen, Mineral Ca10(PO4)6(OH!)2,
water
• Collagen makes bones flexible (elastic)• Mineral makes bones rigid• Water in interstitial spaces stores nutrients
Compact BoneSpongy Bone
(Trabelcular)
Strength of Bones
Compact Y = 1.8x1010 N/m2
Trabecular Y = 7.6x107 N/m2
Tensile Strength (Stress) Compact T = 1.2x108 N/m2
Compressive StrengthCompact C = 1.7x1010 N/m2
Trabecular C = 2.2x106 N/m2
Viscoelasticity: Short duration:increased Strength
120x106
100
80
60
40
20
0
Stre
ss (
N/m
2 )
0.0120.0080.0040Strain
Yield Point
Hookes Law
Tensile Strength
F=kDL F/A = YDL/L Y is Stress/Strain k = Y A/L
Elastic (Young’s) Modulus
Too Much Stress(or what’s wrong with this picture?)
How Bones Break• Compression
• Tension
• Shear
• Bending
• Torsion
Oblique - a fracture which goes at an angle to the axisComminuted - a fracture of many relatively small fragmentsSpiral - a fracture which runs around the axis of the boneCompound - a fracture (also called open) which breaks the skinGreenstick - an incomplete fracture in which the bone bendsTransverse - a fracture that goes across the bone's axisSimple - a fracture which does not break the skin
Deceleration
Kinetic Energy = 1/2 mv2
Work done by force = F.d
Deceleration Force F = 1/2 mv2/d
Bungee Jumping: mg(h+d) = F.d or F = mg (h/d+1) (if h=d, a = “2 g’s”)
Lethal Force: 150-200 g
