1. 333 Physics Scaling & Fluids (liquids and gases)

2. What would happen if we “scaled up” a normal sized gorilla to the size of King Kong?

3. In order to understand the physics of things growing large, we will look at area and volume. How does the area of a cube grow if the cube is increased in size in all dimensions?

4. 1cm 1) What is the total surface area for the entire cube? 2) What is the volume of the cube? Let’s double every dimension

5. 2cm What is the total surface area for the entire cube now? What is the new volume of the cube?

6. Another way to see how small things have MORE S.A. PER cm 3 of space. Look at ratio. 9 cubes stuck together1 cube by itself

7. S.A. grows as a square (x 2 ) Volume grows as a cube (x 3 ) It turns out that the S.A. of an object is directly related to its ___________. For exampIe, cross- sectional area of bones ~ strength of animal. The volume of an object is directly related to its ____________. Square–Cube Law (Galileo)

8. EXAMPLE: Scale up an average human up in all dimensions…10x larger. So, mythical giants…possible or not possible to exist? WHY? b) By what factor does their volume increase? a) By what factor does their S.A. increase? c) How much heavier would they be?

9. An ant can carry 50x its bodyweight, very strong per pound!

10. This does NOT mean that an ANT is stronger than an ELEPHANT. It means that the ant can lift more per pound of bodyweight. Think of weight lifting and the bench press. It is not how much you can bench, but more what you can lift per lb of bodyweight.

11. Almost all life is made up of cells which have quite similar oxygen requirements. As larger creatures evolved, the surface area decreased relative to the volume, so it became more difficult to absorb enough oxygen. Physics and Evolution of animals The evolutionary breakthrough for larger size animals came with the development of blood circulation as a means of distributing oxygen. This was achieved by the development of lungs—the lungs of an adult human have a surface area of ~100m 2.

12. The intestine for larger animals to asbsorb food As animals got larger, they needed to be able to absorb nutrients. This problem is handled by replacing the straight tube gut (like in a worm) by one with many convolutions, in which also the smooth surface is replaced by one with many tiny folds to increase surface area so nutrients can be absorbed.

13. A cell’s surface area to volume ratio decreases as the cell grows. This decreasing ratio slows down the diffusion rate (oxygen) and along with this the metabolism of the cell thus causing a larger cell to be less efficient than a smaller cell. Cells are the basic building blocks for life. Why then, do cells divide? Why not have a few large cells? To keep an overall high efficiency throughout the body the larger cells will divide rather than continue growing. Thus multi-cell animals grow by increasing the number of cells rather than increasing the size of the cells.

14. If two objects are heated to the same temperature (billiard ball vs bowling ball) and then allowed to cool, which object will cool off faster? Heating and Cooling

15. Which is better for keeping warm?

16. Which is better for chilling a drink faster: 10lbs of crushed ice or 10lbs of ice cubes?

17. Which has more skin, a pound of grapes or a pound of grapefruit?

18. For the smaller mammals, a higher surface area to weight ratio, the constant consumption of food to maintain the required elevated body temperature is a primary concern of survival. Mice, Bats, and Humming birds have a high rate of heat loss relative to their total body weight. None of these animals exists in extreme cold habitats. To replace the thermal energy that they lose so quickly these small animals are committed to a life of being constantly on the move for the purpose of finding and consuming as much food as possible. Their daily intake of food can be more than one third of the animal’s total weight. Humans only consume a couple of lbs a day. Warm-blooded animals: Maintaining a constant body temperature

19. At the other end of the spectrum, elephants have a much lower surface-to-mass ratio so they have the opposite sizing problem in that they need a way to remove excess heat from their interior. The evolutionary solution is large earflaps whose purpose is more geared towards the radiation of heat rather than improvements in hearing. Elephants pump warm blood to the skin of their earflaps where through convection and radiation the excess heat is removed.

20. Notice that the shape of the mouse is as close as it can be to that of a sphere, a shape that produces the minimum amount of surface area. Now notice that the elephant’s skin is covered with wrinkles thus increasing the elephant’s surface area. Also notice that the mouse is like nearly all mammals in being covered with a thick fur coat while the elephant is nearly void of all hair. The small mouse is trying to maintain heat while the large elephant is trying to lose it.

21. Due to its low surface area to mass ratio, turkey requires more time for the heat to penetrate through to the interior. In contrast to a thanksgiving turkey that requires three to four hours in the oven, a pizza has a large surface area to mass ratio and so it only needs about 14 minutes to cook. Cooking

22. Which cooks faster? Why? If cupcakes were baked for the same time a cake was (of equal batter amount), what would happen? Why?