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SWARTHMORE PHYS 120 - The Consequences of Being Big

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The Consequences of Being BigWhat do we mean by “big”?ExponentsGravity and FallingSlide 5Gravity and Structure: TreesSlide 7Gravity and Skeleton StructureSlide 9Elephants on LSD??Surface Area and VolumeSlide 12Metabolic RateConsequences…MusclesDinosaurs!Advantages / Disadvantages of Being BigThe Consequences of Being BigThe Consequences of Being BigWhat do we mean by “big”?What do we mean by “big”?•Life spans 8 orders of magnitude• 0.3 micrometers --> 30 meters•“Typical” organism 1 mm - 1 cm•We’re bigExponentsExponents•L = Length (1 dimension)•L2 = Area•L 3 = Volume •V  M•Exponents: •1/3 --> Scales with Length•2/3 --> Scales with Area•1 --> Scales with Volume or MassGravity and FallingGravity and Falling•Vf2 = V02 + 2 a h•Vf  h1/2•M  L3•MV  L3.5•Height x 2 --> Momentum on impact x 11Gravity and FallingGravity and Falling•“The taller they are, the harder they fall”•“You can drop a mouse down a thousand-yard mine shaft and, on arriving at the bottom, it gets a slight shock and walks away. A rat is killed, a man is broken, a horse splashes.”Gravity and Structure: TreesGravity and Structure: Trees•Structure stressed by twisting, bending, crushing relatively weaker at large scales•Weight trunk can bear  Cross-Sectional Area (W  L2)•If trees are isometric, weight borne increases as L3 (W  L3) •Trunk must get thicker to withstand weight (exponent = 1.33)Gravity and Structure: TreesGravity and Structure: TreesGravity and Skeleton StructureGravity and Skeleton Structure•Bones must get thicker to withstand weight (exponent = 1.33)• elephant’s skeleton should = 78% of mass•In reality, exponent = 1.08•Big animals must move differently, inc. speeds at gait transitionsGravity and Skeleton StructureGravity and Skeleton StructureElephants on LSD??Elephants on LSD??Surface Area and VolumeSurface Area and Volume•Surface Area --> Outside Interaction•Volume --> Internal Processes•SA = L2 , V = L3 , SA/V = L-1•As size increases, SA/V decreasesSurface Area and VolumeSurface Area and Volume•Big animals must increase surface area --> add more structures•Lungs: V = 6L, SA = 50-100 m2•Digestive Tract: L = 7 m, SA = 2,000 m2Metabolic RateMetabolic Rate•Metabolic Rate = Power Input to Animal = O2 consumed / time•Heat input = Heat loss•Heat loss  SA•Exp. = 0.67•Big animals,relativelyslowermetabolic rateConsequences…Consequences…•Need less food / can withstand longer periods without food•Can hibernate at normal temperatures•Trouble cooling off, need “heat vents”MusclesMuscles•Muscle strength scales with cross-sectional area (F  L2)•Smaller animals relatively stronger•Work = F x D, D  L --> W  L3•Muscles perform same relative work on all scales --> Same energy “cost”•Power / Work / Time•Smaller animals have faster muscles --> generate more powerDinosaurs!Dinosaurs!•How did their skeletons hold all that weight?•How did they pump blood to their brains?•How did they lift their heads?•How active were they?•How were they so awesome?Advantages / Disadvantages of Being BigAdvantages / Disadvantages of Being Big•Advantages•Harder, better, faster, stronger•More efficient•Disadvantages•Falling•Bulkier•Blood pressure issues•Heat issues•Less


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SWARTHMORE PHYS 120 - The Consequences of Being Big

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