Measurements - relation between mass and size

[Angelsharma]

Homework Statement

Why are mammals as large as they are and not much larger?

Homework Equations

Two figures are given. One of the mammal with size S and mass M. Femur is the thigh bone of the mammal with l being the length of the femur, d being the thickness of the femur and A being the cross sectional area:
i)l ∞ s - length of the femur is proportional to the size
ii) m∞s³∞l³
iii) pressure ∞ weight/Area ∞ m/d²
iv) m ∞d²
v) d²∞l³
Therefore, d ∞ l ^3/2

The Attempt at a Solution

These have been worked out, but I am confused at how length is proportional to the size. Is volume the size? In fact, I don't understand the whole thing. Please help. I have looked at the MIT video three times and still confused. Sorry for being so dumb but I don't hesitate to ask.

 

[member 553083]

The relationship between length and size is that as the size of the mammal grows, so does the length of its femur. This is because the mass of a mammal increases with its size cubed, so the longer its femur is, the greater its mass and thus size will be. This is due to the fact that the pressure exerted by the mammal's weight on its femur depends on its mass divided by its cross-sectional area, which in turn is proportional to the square of the femur's thickness. So, as the mass of the mammal increases, the thickness of the femur must increase (since m∞d2) and thus its length (since d2∞l3). As the length of the femur increases, so too does the size of the mammal.This relationship is limited, however, as the thickness of the femur can only increase so much before it becomes too thick to support the weight of the mammal. Therefore, the size of mammals is limited by the strength of their bones and the pressure they are able to withstand.