1.) The femur of an elephant is about 90 cm long and 15 cm indiameter. This is a scaling problem. The largest dinosaur probablyweighed about 10 times as much as a large elephant. In this problemwe will be discussing scaling. For reference, areas scale as lengthsquared(A=L^2 for a square and A=3.14*r^2 for a circle) and volumescales as length cubed. To describe the size of a dinosaur's femurcompared to that of an elephant's, the dinosaur's femur appears tobe 3 times as wide and one and a half times as tall.
a.) How do you expect the mass of an animal to scale with thelength of typical bone? Use this to estimate the length of thedinosaur's femur.
b.) How do you expect the strength of a bone to scale with itswidth?(We want a uniform strain (delta L/L) for all animals.) Usethis to estimate the width of the dinosaur's femur.
c.) Are your answers to a and b consistent with the descriptionof the size of a dinosaur's femur stated above? Why or why not?
d.) Based on this, briefly argue why whales (2.5 times largerthan the largest dinosaurs) are not land animals.
