Name LAB HW: FORCE, MASS, AND ACCELERATION Why are biological cells only so big?
ID: 1582549 • Letter: N
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Name LAB HW: FORCE, MASS, AND ACCELERATION Why are biological cells only so big? Section ave you ever wondered why biological cells happen to be around 0.01 mm in size? Why can't they be 0.10 some other phenomena like why cats usually survive long falls, why elephants have extra-thick legs, and wh mm or 1.0 mm? Some fundamental math is behind it. We'll find that the same reasoning explains y hippos have to spend a lot of time in the water. (Now is a good time to address this question, because we l use some of the mathematical modeling ideas that came up in our study of acceleration and mass.) A little biology first: A cell needs oxygen, which it takes in through its surface. Oxygen diffuses into the cell at a rate proportional to the surface area of the cell. The rate at which a cell uses oxygen is proportional to its volume. So let's reason out what happens as a cell gets bigger and bigger, like these spherical cells with diameters of Do, 2Do, and 3Do: RD 1. Calculate the surface area of each the cells (in terms of Do) and fill in the table. In the last column, enter e surface area in terms of the surface area of a sphere of diameter Do. For example, ifi's 6 times more, enter 6. Surface area A Surface area in terms of surface area of sphere of diameter Do Diameter D Do 2Do 3Do 2. 2. So for a cell of double the size (diameter), what can you say about the cell's capacity to take in oxygen? (lt increases by a factor of 1/2..) And for a cell of triple the size, the cell's capacity to take in oxygen increases by a factor of Note: As the formula for the surface area of a sphere suggests, and your calculations support, we can say in general that the surface area of a sphere increases as the square of the size (diameter).Explanation / Answer
a) SA = 4pi r^2= 4pi ( D/2)^2= 4pi D^2/4 = piD^2= Do
SA= 4pi ( 2D/2)^2= 4piD^2= 4Do
SA= 4pi (3D/2)^2= 9piD^2= 9Do
b)It increases by 4 times ( oxygen capacity of double size)
Increases by 9 times ( oxygen capacity of triple size)
c)Volume = 4/3 pi ( D/2)^3= piD^3/ 6 = 1
volume= 4/3 pi ( 2D/2)^3= ( 4/3 pi D^3) =8
volume= 4/3 pi ( 3D/2)^3= ( 9/2) pi D^3= 27
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