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Muscle Mysteries
Super Bugs and Weak Dinosaurs
http://www.zin.ru/Animalia/Siphonaptera/jump_!.gif
Ants can lift 50
times their body weight, and fleas can jump over 100 times their
height!!!
While
the prior statement sounds amazing, it does not mean the insects would
be able to do this feat if they were as large as a human.
This is because muscle force is proportional to the cross sectional area of the muscle. ( F~L2
At maximum force, muscles can produce a force of about ~ 4-5 N/cm2 , this holds true for insects as well as humans.
This is because muscle force is proportional to the cross sectional area of the muscle. ( F~L2
At maximum force, muscles can produce a force of about ~ 4-5 N/cm2 , this holds true for insects as well as humans.
So why can't humans lift 50 times
their weight?
The answer is because of
proportionality. While muscle force relies on cross sectional area, L2, weight relies on
volume, or L3.
The ratio of force to weight is equal to L2/L3, or L-1. For small animals this ratio is much larger than for larger animals, such as humans.
The ratio of force to weight is equal to L2/L3, or L-1. For small animals this ratio is much larger than for larger animals, such as humans.
Therefore
if an ant was as large as a human, it would definitely not be able to
lift 50 times its weight,
and a human sized flea would not be able to leap 600 feet in the air.
and a human sized flea would not be able to leap 600 feet in the air.
Weak, Slow T-Rex?
This ratio continues to apply for larger
and larger animals.
The Tyrannosaurus rex has a stride that could allow him estimated speeds of 20 miles per hour, but many physicists have argued that the T-rex did not have enough muscle mass to produce the forces necessary to reach those speeds, because a large dinosaur would need an exponentially larger muscle mass to accelerate its overall larger mass. The dinosaur's bones would also have to be extremely strong to support the large stresses running produces.
http://www.physicstoday.org/vol-55/iss-4/images/p18fig2.jpg
The greatest stress in a running stride occurs when the animal is at
it's lowest point and is using its muscles to accelerate upwards. The
normal force, or the ground reaction force, for running bipeds has been
shown to be about 2.5 times size.
This normal force corresponds to the height the animal can rise, or its potential energy. The forward velocity of an animal can be found by using this normal force and by using the animals "Froude number," Fr = v2/gh, where v is the forward velocity, g the acceleration due to gravity, and h the hip height. as described in Physics Today,
"Animals moving with the same Froude number should have similar gaits and exert similar relative forces. A fast-running ostrich experiences a GRF of 2.7 times its body weight at Fr = 16; a T. rex with a similar relative GRF should have a similar Froude number, which corresponds to about [speeds of] 20 m/s..."
However, these estimates do not take into account the large amount of muscle a T-rex would need, and since there is no T-rex muscle to study, the debate on the T-rex's speed continues.
The Tyrannosaurus rex has a stride that could allow him estimated speeds of 20 miles per hour, but many physicists have argued that the T-rex did not have enough muscle mass to produce the forces necessary to reach those speeds, because a large dinosaur would need an exponentially larger muscle mass to accelerate its overall larger mass. The dinosaur's bones would also have to be extremely strong to support the large stresses running produces.
http://www.physicstoday.org/vol-55/iss-4/images/p18fig2.jpg
This normal force corresponds to the height the animal can rise, or its potential energy. The forward velocity of an animal can be found by using this normal force and by using the animals "Froude number," Fr = v2/gh, where v is the forward velocity, g the acceleration due to gravity, and h the hip height. as described in Physics Today,
"Animals moving with the same Froude number should have similar gaits and exert similar relative forces. A fast-running ostrich experiences a GRF of 2.7 times its body weight at Fr = 16; a T. rex with a similar relative GRF should have a similar Froude number, which corresponds to about [speeds of] 20 m/s..."
However, these estimates do not take into account the large amount of muscle a T-rex would need, and since there is no T-rex muscle to study, the debate on the T-rex's speed continues.