Phys 0174 Summer 2018 his bonus will walk you through some \"back of the envelop

Question

Phys 0174 Summer 2018 his bonus will walk you through some "back of the envelope" calculations. Often we can gain insight and intuition into the world around us using only a pencil and Problem 1) Some bacteria (such as E. colk) swim around in their liquid environment to search out mutrients. These single celled creatures are actually quite proficient swim- mers that are capable of traveling up to 10 body-lengths per sccond How costly is this motion? If swirmming is very costly to the cell, then we might that searching only happens when cells have ro other choice. We may even imagine that the motors could shut down once food is found. The motivation for these cells to swim would be to find food and then stay put while growing. If on the other hand swimming is very cheap, we may expect that thes all of the time to endlessly search their environment. Cells that find food would continue swimming and growing in case something even better is near by. In this case we expect that populations of cells quickly disperse around their environment in an endless scarch. The goal here is to compare the energy requirement of swimming to the total energy consumption of an individual cell. A simple experiment can be performed to determine the total metabolic requirement of a cell: inoculate a test tube with a known concentration of food, and count the number of bacteria that can be supported by the food. We find that for eachc 6x1018 gluco a single glucose molecule is 30eV .. Assume that all (or the vast majorit consumed by the bacteria is for reproduction. Ilow much energy (in eV) is required to grow a cell*? e (cubic centimetcr) se molecules can grow 10s cells. The total amount of energy available from eV is a usefu! unit of measure when worling with very smal) amounts of energy "this is what we mean by "tatal metabolism g with very small amounts of energy. Pronounced "electron vole", one eV is the amount of energy gained by allowing an electron to fall through 1 v

Explanation / Answer

a)
6 x 1018 molecules of glucose can grow 108 cells
For growing one cell, number of glucose molecules required is (6 x 1018) / 108
= 6 x 1010
Energy available from a single glucose molecule = 30 eV
Energy available from 6 x 1010 glucose molecule = (6 x 1010) x 30 eV
= 1.8 x 1012 eV
So energy needed for a single cell = 1.8 x 1012 eV

b)
Power consumed by a single motor = 2000 eV/s
Power consumed by 5 motors = 2000 eV/s x 5 = 10000 eV/s
Energy consumed in 20 minutes = 10000 eV/s = 20 x 60
= 1.2 x 107 eV

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