Chapter 8/10: Self assembly/Machines
PHSCS 313R: The Physics of Life
Homework 16:
Do problem 8.5 in the text
Solution:
Let A denote the dissociated form of the acid. Let x = [H+ ] and y = [A ]. Then we can nd [OH ] by charge
neutrality: [H+ ] = [OH ] + [A

Chapter 5: Reynolds Numbers in Biology
PHSCS 313R: The Physics of Life
Homework 08:
Do problem 5.4 in the text
Solution:
Part (a)
Recall Newtons second law
F = ma =
dv
m
dt
The only force is friction so
m
d
= Ffrict = vdi = v(6r)
dt
(for a spherical bacte

Chapter 5: Reynolds Numbers in Biology
PHSCS 313R: The Physics of Life
Homework 08:
Do problem 5.8 in the text
Solution:
First, remember that the volume fraction of the solid is small. That justies some of our mathematical and
physical assumptions later.

Chapter 6: Open systems
PHSCS 313R: The Physics of Life
Homework 11:
Do problem 6.4 in the text
Solution:
Part (a) The spring moves a distance (f f1 )/k. So, the work done against the load is W = F d = f1 (f f1 )/k).
1
Part (b) We can maximize this work b

Chapter 6: Entropy and Temperature
PHSCS 313R: The Physics of Life
Homework 10:
Do problem 6.2 in the text
Solution:
Part (a)
The two boxes will come to the same temperature as each other when they are in thermal equilibrium. So, the
nal temperature is an

Chapter 4.6: Biological diusion
PHSCS 313R: The Physics of Life
Homework 06:
A1. Nernst-Planck Behavior
Write a random walker simulation (you can use one of the previous solutions as a starting point) that includes
the eects of electric force assuming tha

Chapter 6: Microscopic systems
PHSCS 313R: The Physics of Life
Homework 12:
Do problem 6.5 in the text
Solution:
Part (a) Let x = e E/kB T . Using Equation (6.25), we have
P1 =
1
1+x
and
P1 =
x
1+x
Use mean =
n
i=1 Pi Ei ,
where Ei = +1 or Ei = 1
mean = P

Chapter 7: Osmosis
PHSCS 313R: The Physics of Life
Homework 13:
Do problem 7.1 in the text
Solution:
Part (a) It didnt come from the airit came from within the strawberries. Introducing the sugar (dissolving in
the water on the surface of the berries) cau

Chapter 8: Chemical forces and self assembly
PHSCS 313R: The Physics of Life
Homework 15:
Do problem 8.1 in the text
Solution:
Part (a) Salt dissociated into charged ions. According to Idea 7.28, the presence of these ions reduces electrostatic
repulsion

Chapter 8/10: Self assembly/Machines
PHSCS 313R: The Physics of Life
Homework 16:
Do problem 8.5 in the text
Solution:
Let A denote the dissociated form of the acid. Let x = [H+ ] and y = [A ]. Then we can nd [OH ] by charge
neutrality: [H+ ] = [OH ] + [A

Chapter 10: Molecular Machines
PHSCS 313R: The Physics of Life
Homework 17:
Do problem 10.1 in the text
Solution:
Lets make the hypothesis that the process contains one rate-limiting (bottleneck) step controlled by an Arrhenius rate law, rate eG/kB T . We

Chapter 5: Reynolds Numbers
PHSCS 313R: The Physics of Life
Homework 07:
Do problem 4.7 in the text
AP
d(c)
=(
)c. This
dt
v
assumes that the concentration of the reservoir doesnt change. The volume of blood outside the capillaries is
Recall the example o

Solutions
PHSCS 313R: The Physics of Life
Homework 04: Solutions
A1. Use some program like Mathematica, Maple, or Matlab to make a plot like Fig. 4.3(c) in your text.
Repeat your plot several times. (You have 36 coins, so use 36 bins in your histogram.)

Chapter 8: Chemical forces and self assembly
PHSCS 313R: The Physics of Life
Homework 15:
Do problem 8.1 in the text
Solution:
Part (a) Salt dissociated into charged ions. According to Idea 7.28, the presence of these ions reduces electrostatic
repulsion

Chapter 7: Osmosis
PHSCS 313R: The Physics of Life
Homework 13:
Do problem 7.1 in the text
Solution:
Part (a) It didnt come from the airit came from within the strawberries. Introducing the sugar (dissolving in
the water on the surface of the berries) cau

Chapter 6: Microscopic systems
PHSCS 313R: The Physics of Life
Homework 12:
Do problem 6.5 in the text
Solution:
Part (a) Let x = e E/kB T . Using Equation (6.25), we have
P1 =
1
1+x
and
P1 =
x
1+x
Use mean =
n
i=1 Pi Ei ,
where Ei = +1 or Ei = 1
mean = P

Chapter 6: Open systems
PHSCS 313R: The Physics of Life
Homework 11:
Do problem 6.4 in the text
Solution:
Part (a) The spring moves a distance (f f1 )/k . So, the work done against the load is W = F d = f1 (f f1 )/k ).
1
Part (b) We can maximize this work

Chapter 6: Entropy and Temperature
PHSCS 313R: The Physics of Life
Homework 10:
Do problem 6.2 in the text
Solution:
Part (a)
The two boxes will come to the same temperature as each other when they are in thermal equilibrium. So, the
nal temperature is an

Chapter 5: Reynolds Numbers in Biology
PHSCS 313R: The Physics of Life
Homework 08:
Do problem 5.8 in the text
Solution:
First, remember that the volume fraction of the solid is small. That justies some of our mathematical and
physical assumptions later.

Chapter 5: Reynolds Numbers in Biology
PHSCS 313R: The Physics of Life
Homework 08:
Do problem 5.4 in the text
Solution:
Part (a)
Recall Newtons second law
F = ma =
dv
m
dt
The only force is friction so
m
d
= Ffrict = vdi = v (6r)
dt
(for a spherical bact

Chapter 5: Reynolds Numbers
PHSCS 313R: The Physics of Life
Homework 07:
Do problem 4.7 in the text
AP
d(c)
=(
)c. This
dt
v
assumes that the concentration of the reservoir doesnt change. The volume of blood outside the capillaries is
Recall the example o

Chapter 4.6: Biological diusion
PHSCS 313R: The Physics of Life
Homework 06:
A1. Nernst-Planck Behavior
Write a random walker simulation (you can use one of the previous solutions as a starting point) that includes
the eects of electric force assuming tha