Download PHYS 1001 General Physics I

Biomechanics
May 5, 2005
Dr. Kelsey Jordahl
Size
Bacterium
~0.3m
Whale
~30 m
Factor of 108 in size
Factor of 1024 in mass!
Scaling Surface Area to
Volume ratio
so
V  l3
m  l3
Volume to length
mass to length
S  l2
S/V  l  m1/3
Surface to volume
Example for cube
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)
“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.”
Scaling
Land Mammals
Shew
~6 g
Elephant ~6000 kg
Factor of 106 in mass
(only 100 in size)
Scaling factors for
mammals
y
a
Surface area
1.95
Skeletal mass (terrestrial)
3.25
Skeletal mass (cetacean)
3.07
Muscle mass
3.00
Metabolic rate
2.25
Effective lung volume
3.09
Frequency of breathing
-0.78
Heart mass
2.94
Frequency of heartbeat
-0.75
Kidney mass
2.55
Liver mass
2.61
Brain mass (nonprimates)
2.10
Brain mass (humans)
1.98
y  la
l=m1/3
Example of isometry and its consequences
Example of allometry:
bone proportions in pelycosaurs
Example of allometry:
shape change in human ontogeny
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
Final Exam
Thursday, 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