Question

I need precise explanation for the qestion of galileo galili,as to
why mammals are as large as they are and not much larger?And why did
the scaling argument fail to support the results?

Answer 1

see this lecture: http://ocw.mit.edu/courses/physics/8-01-physics-i-classical-mechanics-fall-1999/video-lectures/lecture-1/ at time 11:12

Answer 2

Its all related to Units and Dimensions, I'll just tell you what was explained in the lecturby Walter Lewin. Assume the mass of animal as M , size as S(lenght of animal), diameter of femur bone(thigh bone) as D, and lenght of femur bone as L. So as its know to every one the lenght of femur increase as the size increases so \[L \alpha S \] here \[\alpha\] is the proportionality sign. So according to natural relativity of body structure \[M \alpha S ^{3} \alpha L ^{3}\]\['Pressure' \alpha 'weight \div cross section area of femur' \alpha 'M \div D^{2}\] I've put apostrophes to separate the equation for reading as space doesn't work in creating equations. So, suppose the mass of an animal increases so its D^2 also needs to increase to prevent its bones from breaking thus, we can argue that\[M \alpha D^{2}\]Now taking the above equations into consideration we can conclude\[D^{2} \alpha L^{3}\]\[D \alpha L^{3/2}\] Now you can take two animals like an elephant and a cat.
Suppose the elephant is 100 times larger than the cat, so its femur must also be 100 times longer than the cat's femur. But, the thickness of the femur of the elephant will be
1000 times the thickness of the cat's femur, of course this is just an assumption as elephants are not exactly 100 times larger than cats most of the time. But I hope you got the point of how Galileo Galilee was able to prove of how size changed with the mass of an animal and other many things.

Answer 3

actually my main question was as to why did the test fail to support the scaling argument?d/l ratio did not support the argument...