Exercise 01

FYS7206 Biological Physics
Exercise 1 (Wednesday 10.09.2014)

Maximum points from this exercise class are 6 points for the 3 cr version of the course and 10 points
for the 5 cr version.
The assignments are ordered so that the rst ones are intended for the 3 cr version, however, you
may choose whichever assignments you wish to complete. Naturally, the level of difculty and/or the
workload of the assignment is reected in the number of points given.
Assignment 1. (1 p)
During the lectures we used Benjamin Franklins experiment to estimate the value of Avogadros
number. Now, let us consider the same experiment but in the opposite direction.
Let us assume that Avogadros number were known, that is N
A
6 10
23
. Imagine a tanker to leave
from St. Petersburg to Denmark. The Danes love sh, therefore the tanker is lled with sh oil known
as omega-3 fatty acids they are very good for your health!. Unfortunately, the ship drives aground
and starts to leak. The amount of sh oil that makes it to leak out of the ship before repair is about
75 000 kg.
Assume the density of sh oil to be 1000 kg/m
3
. Also assume the oil to spread on water such that
it forms a one-molecule thick monolayer whose thickness is 1.5 nm. Estimate the area of sea level
covered by oil.
The above amount of 10
4
kg is pretty small. Use e.g. google to nd what is the average amount of oil
usually lost when a ship is being agrounded.
Assignment 2. (2 p)
Metabolism is a generic term for all of the chemical reactions that break down and burn food,
thereby releasing energy. Here are some data for metabolism and gas exchange in humans.
food kcal/g liters O
2
/g liters CO
2
/g
carbohydrate 4.1 0.81 0.81
fat 9.3 1.96 1.39
protein 4.0 0.94 0.75
alcohol 7.1 1.46 0.97
The table gives you the energy released, the oxygen consumed, and the carbon dioxide released upon
metabolizing the given food, per gram of food.
Calculate the energy yield per liter of oxygen consumed for each food type and note that it is
roughly constant. Thus, we can determine a persons metabolic rate simply be measuring her
rate of oxygen consumption. In contrast, the CO
2
/O
2
ratios are different for the different food
groups; this circumstance allows us to estimate what is actually being used as the energy source,
by comparing oxygen intake to carbon dioxide output.
An average adult at rest uses 16 liters of O
2
per hour. The corresponding heat release is called
the basal metabolic rate (BMR). Find it, in kcal/hour and in kcal/day.
What power output does this correspond to in watts?
1
Typically, the CO
2
output rate might be 13.4 liters per hour. What, if anything, can you say
about the type of food materials being consumed?
During exercise, the metabolic rate increases. Someone performing hard labor for 10 hours a
day might need about 3500 kcal of food per day. Suppose the person does mechanical work
at a steady rate of 50 W over 10 hours. We can dene the bodys efciency as the ratio of
mechanical work done to excess energy intake (beyond the BMR calculated in (b)). Find this
efciency.
Assignment 3. (3 p)
A typical small animal, say a microscopic worm, has a smooth skin through which it can absorb
all the oxygen it needs. If the worm gets 10 times bigger (meaning its dimensions would be
increased tenfold in every direction), how much more oxygen would it need?
Use your result to explain why bigger animals do not get their oxygen simply through their
skin.
Describe strategies that bigger animals use to get enough oxygen to their tissues.
Now, since we talked so much about oxygen, what do we need it for anyway?
Assignment 4. (4 p)
A bicycle rider in Tour de France eats a lot. If his total daily food intake were burned, it would liberate
about 8000 kcal of heat. Over the three or four weeks of the race, his weight change is negligible, less
than 1%. Thus, his energy input and output must balance.
Lets rst look at the mechanical work done by the racer. A bicycle is incredibly efcient. The energy
lost to internal friction, even including the tires, is negligible. The expenditure against air drag is,
however, signicant, amounting to 10 MJ per day. Each day, the rider races for 6 hours.
a. Compare the 8000 kcal input to the 10 MJ of work done. Somethings missing! Could the
missing energy be accounted for by the altitude change in a hard days racing?
Regardless of how you answered (a), next suppose that on one particular day of the racing theres no
net altitude change, so that we must look elsewhere to see where the missing energy went. We have
so far neglected another part of the energy equation: the rider gives off heat. Some of this is radiated.
Some goes to warm up the air he breathes in. But by far the greatest share goes somewhere else.
b. How much water would the rider have to drink for the energy budget to balance? Is this reason-
able?
Next lets go back to the 10 MJ of mechanical work done by the rider each day.
c. The wind drag for a situation like this is a backward force of magnitude f = Bv
2
, where B is
some constant. We measure B in a wind-tunnel to be 1.5 kg m
1
. If we simplify by supposing
a days racing to be at constant speed, what is that speed? Is your answer reasonable?
2

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FYS7206 Biological Physics

Exercise 1 (Wednesday 10.09.2014)

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