8.E: The Laplace Transform (Exercises)
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These are homework exercises to accompany Libl's " Differential Equations for Engineering " Textmap. This is a textbook targeted for a one semester first course on differential equations, aimed at engineering students. Prerequisite for the course is the basic calculus sequence.
6.1: The Laplace transform
Exercise \(\PageIndex{6.1.1}\)
Find the Laplace transform of \(3+ t^5 + \sin (\pi t)\).
Exercise \(\PageIndex{6.1.2}\)
Find the Laplace transform of \(a + bt +ct^2\) for some constants \(a\) , \(b\) , and \(c\) .
Exercise \(\PageIndex{6.1.3}\)
Find the Laplace transform of \(A \cos (\omega t) + B \sin (\omega t ) \).
Exercise \(\PageIndex{6.1.4}\)
Find the Laplace transform of \( \cos^2 (\omega t ) \).
Exercise \(\PageIndex{6.1.5}\)
Find the inverse Laplace transform of \(\dfrac{4}{s^2-9}\).
Exercise \(\PageIndex{6.1.6}\)
Find the inverse Laplace transform of \( \dfrac{2s}{s^2-1}\).
Exercise \(\PageIndex{6.1.7}\)
Find the inverse Laplace transform of \( \dfrac{1}{(s-1)^2(s+1)}\).
Exercise \(\PageIndex{6.1.8}\)
Find the Laplace transform of \(f(t)= \left\{ \begin{array}{cc} t & {\rm{if~}}t \geq 1, \\ 0 & {\rm{if~}}t < 1.\end{array} \right.\).
Exercise \(\PageIndex{6.1.9}\)
Find the inverse Laplace transform of \( \dfrac{s}{(s^2+s+2)(s+4)}\).
Exercise \(\PageIndex{6.1.10}\)
Find the Laplace transform of \(\sin \left( \omega (t-a) \right) \).
Exercise \(\PageIndex{6.1.11}\)
Find the Laplace transform of \( t \sin (\omega t) \) . Hint: Several integrations by parts.
Exercise \(\PageIndex{6.1.12}\)
Find the Laplace transform of \(4(t+1)^2\).
- Answer
-
\(\frac{8}{s^{3}}+\frac{8}{s^{2}}+\frac{4}{s}\)
Exercise \(\PageIndex{6.1.13}\)
Find the inverse Laplace transform of \(\dfrac{8}{s^3 (s+2)}\).
- Answer
-
\(2t^{2}-2t+1-e^{-2t}\)
Exercise \(\PageIndex{6.1.14}\)
Find the Laplace transform of \(te^{-t}\) (Hint: integrate by parts).
- Answer
-
\(\frac{1}{(s+1)^{2}}\)
Exercise \(\PageIndex{6.1.15}\)
Find the Laplace transform of \(\sin (t) e^{-t}\) (Hint: integrate by parts).
- Answer
-
\(\frac{1}{s^{2}+2s+2}\)
6.2: Transforms of Derivatives and ODEs
Exercise \(\PageIndex{6.2.1}\)
Verify Table 6.2.1 .
Exercise \(\PageIndex{6.2.2}\)
Using the Heaviside function write down the piecewise function that is \(0\) for \(t<0, t^2\) for \(t\) in \([0,1]\) and \(t\) for \(t>1\).
Exercise \(\PageIndex{6.2.3}\)
Using the Laplace transform solve
\[ mx'' + cx'+kx =0,\quad x(0)=a, \quad x'(0)=b.\]
where \(m>0,c>0,k>0\), and \(c^2-4km>0\) (system is overdamped).
Exercise \(\PageIndex{6.2.4}\)
Using the Laplace transform solve
\[ mx'' + cx'+kx =0,\quad x(0)=a, \quad x'(0)=b.\]
where \(m>0,c>0,k>0\), and \(c^2-4km<0\) (system is underdamped).
Exercise \(\PageIndex{6.2.5}\)
Using the Laplace transform solve
\[ mx'' + cx'+kx =0,\quad x(0)=a, \quad x'(0)=b.\]
where \(m>0,c>0,k>0\), and \(c^2=4km\) (system is critically damped).
Exercise \(\PageIndex{6.2.6}\)
Solve \(x''+x=u(t-1)\) for initial conditions \(x(0)=0\) and \(x'(0)=0\).
Exercise \(\PageIndex{6.2.7}\)
Show the differentiation of the transform property. Suppose \(\mathcal{L}\{f(t)\}=F(s)\), then show
\[ \mathcal{L}\{-tf(t)\}=F'(s).\]
Hint: Differentiate under the integral sign.
Exercise \(\PageIndex{6.2.8}\)
Solve \(x'''+x=t^3u(t-1)\) for initial conditions \(x(0)=1\) and \(x'(0)=0\), \(x''(0)=0\).
Exercise \(\PageIndex{6.2.9}\)
Show the second shifting property: \( \mathcal{L}\{f(t-a)u(t-a)\}=e^{-as}\mathcal{L}\{f(t)\} \).
Exercise \(\PageIndex{6.2.10}\)
Let us think of the mass-spring system with a rocket from Example 6.2.2. We noticed that the solution kept oscillating after the rocket stopped running. The amplitude of the oscillation depends on the time that the rocket was fired (for 4 seconds in the example).
- Find a formula for the amplitude of the resulting oscillation in terms of the amount of time the rocket is fired.
- Is there a nonzero time (if so what is it?) for which the rocket fires and the resulting oscillation has amplitude 0 (the mass is not moving)?
Exercise \(\PageIndex{6.2.11}\)
Define
\[ f(t)= \left\{ \begin{array}{ccc} (t-1)^2 & if~1 \leq t<2, \\ 3-t & if~2 \leq t<3, \\ 0 & otherwise. \end{array} \right. \]
- Sketch the graph of \(f(t)\).
- Write down \(f(t)\) using the Heaviside function.
- Solve \(x''+x=f(t), x(0)=0,x'(0)=0\) using Laplace transform.
Exercise \(\PageIndex{6.2.12}\)
Find the transfer function for \(mx'' + cx'+kx =f(t)\) (assuming the initial conditions are zero).
Exercise \(\PageIndex{6.2.13}\)
Using the Heaviside function \(u(t)\), write down the function
\[ f(t)= \left\{ \begin{array}{ccc} 0 & if~~~~~t<1, \\ t-1 & if~1 \leq t<2, \\ if~~~~~2 \leq t. \end{array} \right. \]
- Answer
-
\(f(t)=(t-1)(u(t-1)-u(t-2))+u(t-2)\)
Exercise \(\PageIndex{6.2.14}\)
Solve \(x''-x=(t^2-1)u(t-1)\) for initial conditions \(x(0)=1,x'(0)=2\) using the Laplace transform.
- Answer
-
\(x(t)=(2e^{t-1}-t^{2}-1)u(t-1)-\frac{1}{2}e^{-t}+\frac{3}{2}e^{t}\)
Exercise \(\PageIndex{6.2.15}\)
Find the transfer function for \(x'+x=f(t)\) (assuming the initial conditions are zero).
- Answer
-
\(H(s)=\frac{1}{s+1}\)
6.3: Convolution
Exercise \(\PageIndex{6.3.1}\)
Let \(f(t)=t^2\) for \(t \geq 0\), and \(g(t)=u(t-1)\). Compute \(f * g\).
Exercise \(\PageIndex{6.3.2}\)
Let \(f(t)=t\) for \(t \geq 0\), and \(g(t)=\sin t\) for \(t \geq 0\). Compute \(f * g\).
Exercise \(\PageIndex{6.3.3}\)
Find the solution to
\( mx''+cx'+kx=f(t),\quad x(0)=0,\quad x'(0)=0,\)
for an arbitrary function \(f(t)\), where \(m>0,c>0,k>0\), and \(c^2-4km>0\) (system is overdamped). Write the solution as a definite integral.
Exercise \(\PageIndex{6.3.4}\)
Find the solution to
\( mx''+cx'+kx=f(t),\quad x(0)=0,\quad x'(0)=0,\)
for an arbitrary function \(f(t)\), where \(m>0,c>0,k>0\), and \(c^2-4km<0\) (system is underdamped). Write the solution as a definite integral.
Exercise \(\PageIndex{6.3.5}\)
Find the solution to
\( mx''+cx'+kx=f(t),\quad x(0)=0,\quad x'(0)=0,\)
for an arbitrary function \(f(t)\), where \(m>0,c>0,k>0\), and \(c^2=4km\) (system is critically damped). Write the solution as a definite integral.
Exercise \(\PageIndex{6.3.6}\)
Solve
\( x(t)=e^{-t} +\int_0^t\cos(t-\tau)x(\tau)~d\tau . \)
Exercise \(\PageIndex{6.3.7}\)
Solve
\( x(t)=\cos t +\int_0^t\cos(t-\tau)x(\tau)~d\tau . \)
Exercise \(\PageIndex{6.3.8}\)
Compute \(\mathcal{L}^{-1} \left\{ \frac{s}{(s^2+4)^2}\right\}\) using convolution.
Exercise \(\PageIndex{6.3.9}\)
Write down the solution to \(x''-2x=e^{-t^2},x(0)=0,x'(0)=0\) as a definite integral. Hint: Do not try to compute the Laplace transform of \(e^{-t^2}\).
Exercise \(\PageIndex{6.3.10}\)
Let \(f(t)=\cos t\) for \(t \geq 0\), and \(g(t)=e^{-t}\). Compute \(f * g\).
- Answer
-
\(\frac{1}{2}(\cos t+\sin t-e^{-t})\)
Exercise \(\PageIndex{6.3.11}\)
Compute \(\mathcal{L}^{-1} \left\{ \frac{5}{s^4+s^2}\right\}\) using convolution.
- Answer
-
\(5t-5\sin t\)
Exercise \(\PageIndex{6.3.12}\)
Solve \(x''+x=\sin t, x(0)=0, x'(0)=0\) using convolution.
- Answer
-
\(\frac{1}{2}(\sin t-t\cos t)\)
Exercise \(\PageIndex{6.3.13}\)
Solve \(x'''+x'=f(t), x(0)=0, x'(0)=0,x''(0)=0\) using convolution. Write the result as a definite integral.
- Answer
-
\(\int_{0}^{t} f(\tau )(1-\cos (t-\tau ))d\tau \)
6.4: Dirac delta and impulse response
Exercise \(\PageIndex{6.4.1}\)
Solve (find the impulse response) \( x'' + x' + x = \delta(t),x(0) = 0, x'(0)=0.\)
Exercise \(\PageIndex{6.4.2}\)
Solve (find the impulse response) \(x'' + 2 x' + x = \delta(t), x(0) = 0, x'(0)=0.\)
Exercise \(\PageIndex{6.4.3}\)
A pulse can come later and can be bigger. Solve \(x'' + 4 x = 4\delta(t-1), x(0) = 0, x'(0)=0.\)
Exercise \(\PageIndex{6.4.4}\)
Suppose that \(f(t)\) and \(g(t)\) are differentiable functions and suppose that \(f(t) = g(t) = 0\) for all \(t \leq 0\). Show that \[ (f * g)'(t) = (f' * g)(t) = (f * g')(t) .\]
Exercise \(\PageIndex{6.4.5}\)
Suppose that \(L x = \delta(t), x(0) = 0, x'(0) = 0\), has the solution \(x = e^{-t}\) for \(t>0\). Find the solution to \(Lx = t^2, x(0) = 0, x'(0) = 0\) for \(t > 0\).
Exercise \(\PageIndex{6.4.6}\)
Compute \(\mathcal{L}^{-1} \left\{ \frac{s^2+s+1}{s^2} \right\}\).
Exercise \(\PageIndex{6.4.7}\): (challenging)
Solve Example 6.4.3 via integrating 4 times in the \(x\) variable.
Exercise \(\PageIndex{6.4.8}\)
Suppose we have a beam of length \(1\) simply supported at the ends and suppose that force \(F=1\) is applied at \(x=\frac{3}{4}\) in the downward direction. Suppose that \(EI=1\) for simplicity. Find the beam deﬂection \(y(x)\).
Exercise \(\PageIndex{6.4.9}\)
Solve (find the impulse response) \(x'' = \delta(t),\: x(0) = 0,\: x'(0)=0\).
- Answer
-
\(x(t)=t\)
Exercise \(\PageIndex{6.4.10}\)
Solve (find the impulse response) \(x' + a x = \delta(t),\: x(0) = 0,\: x'(0)=0\).
- Answer
-
\(x(t)=e^{-at}\)
Exercise \(\PageIndex{6.4.11}\)
Suppose that \(L x = \delta(t), x(0) = 0, x'(0) = 0\), has the solution \(x(t) = \cos(t)\) for \(t>0\). Find (in closed form) the solution to \(Lx = \sin(t), x(0) = 0, x'(0) = 0 for t > 0\).
- Answer
-
\(x(t)=(\cos\ast\sin )(t)=\frac{1}{2}t\sin (t)\)
Exercise \(\PageIndex{6.4.12}\)
Compute \({\mathcal{L}}^{-1} \left\{ \frac{s^2}{s^2+1} \right\}\).
- Answer
-
\(\delta (t)-\sin (t)\)
Exercise \(\PageIndex{6.4.13}\)
Compute \({\mathcal{L}}^{-1} \left\{ \frac{3 s^2 e^{-s} + 2}{s^2} \right\}\).
- Answer
-
\(3\delta (t-1)+2t\)
6.5: Solving PDEs with the Laplace Transform
Exercise \(\PageIndex{6.5.1}\)
Solve \[\begin{aligned} & y_t + y_x = 1, \qquad 0 < x < \infty, \enspace t > 0, \\ & y(0,t) = 1, \quad y(x,0) = 0 .\end{aligned}\]
Exercise \(\PageIndex{6.5.2}\)
Solve \[\begin{aligned} & y_t + \alpha y_x = 0, \qquad 0 < x < \infty, \enspace t > 0, \\ & y(0,t) = t, \quad y(x,0) = 0 .\end{aligned}\]
Exercise \(\PageIndex{6.5.3}\)
Solve \[\begin{aligned} & y_t + 2 y_x = x+t, \qquad 0 < x < \infty, \enspace t > 0, \\ & y(0,t) = 0, \quad y(x,0) = 0 .\end{aligned}\]
Exercise \(\PageIndex{6.5.4}\)
For an \(\alpha > 0\) , solve \[\begin{aligned} & y_t + \alpha y_x + y = 0, \qquad 0 < x < \infty, \enspace t > 0, \\ & y(0,t) = \sin(t), \quad y(x,0) = 0 .\end{aligned}\]
Exercise \(\PageIndex{6.5.5}\)
Find the corresponding ODE problem for \(Y(x)\) , after transforming the \(t\) variable \[\begin{aligned} & y_{tt} + 3y_{xx} + y_{xt} + 3 y_x + y = \sin(x) + t, \qquad 0 < x < 1, \enspace t > 0, \\ & y(0,t) = 1, \quad y(1,t) = t, \quad y(x,0) = 1-x, \quad y_t(x,0) = 1 .\end{aligned}\] Do not solve the problem.
Exercise \(\PageIndex{6.5.6}\)
Write down a solution to \[\begin{aligned} & y_t = y_{xx}, \qquad 0 < x < \infty, \enspace t > 0,\\ & y_x(0,t) = e^{-t}, \quad y(x,0) = 0 ,\end{aligned}\] as an definite integral (convolution).
Exercise \(\PageIndex{6.5.7}\)
Use the Laplace transform in \(t\) to solve \[\begin{aligned} & y_{tt} = y_{xx}, \qquad -\infty < x < \infty, \enspace t > 0,\\ & y_t(x,0) = \sin(x), \quad y(x,0) = 0 .\end{aligned}\] Hint: Note that \(e^{sx}\) does not go to zero as \(s \to \infty\) for positive \(x\) , and \(e^{-sx}\) does not go to zero as \(s \to \infty\) for negative \(x\) .
Exercise \(\PageIndex{6.5.8}\)
Solve \[\begin{aligned} & y_t + y_x = 1, \qquad 0 < x < \infty, \enspace t > 0, \\ & y(0,t) = 0, \quad y(x,0) = 0 .\end{aligned}\]
- Answer
-
\(y=(x-t)u(t-x)+t\)
Exercise \(\PageIndex{6.5.9}\)
For a \(c > 0\) , solve \[\begin{aligned} & y_t + y_x + c y = 0, \qquad 0 < x < \infty, \enspace t > 0, \\ & y(0,t) = \sin(t), \quad y(x,0) = 0 .\end{aligned}\]
- Answer
-
\(y=e^{-cx}\sin (t-x)u(t-x)\)
Exercise \(\PageIndex{6.5.10}\)
Find the corresponding ODE problem for \(Y(x)\) , after transforming the \(t\) variable \[\begin{aligned} & y_{tt} + 3y_{xx} + y = x+t, \qquad -1 < x < 1, \enspace t > 0, \\ & y(-1,t) = 0, \quad y(1,t) = 0, \quad y(x,0) = (1-x^2) , \quad y_t(x,0) = 0.\end{aligned}\] Do not solve the problem.
- Answer
-
\(s^{2}Y(x)-s(1+x^{2})+3Y''(x)+Y(x)=\frac{x}{s}+\frac{1}{s^{2}},\quad Y(-1)=0,\quad Y(1)=0.\)
Exercise \(\PageIndex{6.5.11}\)
Use the Laplace transform in \(t\) to solve \[\begin{aligned} & y_{tt} = y_{xx}, \qquad -\infty < x < \infty, \enspace t > 0,\\ & y_t(x,0) = x^2, \quad y(x,0) = 0 .\end{aligned}\] Hint: Note that \(e^{sx}\) does not go to zero as \(s \to \infty\) for positive \(x\) , and \(e^{-sx}\) does not go to zero as \(s \to \infty\) for negative \(x\) .
- Answer
-
\(y=tx^{2}+\frac{t^{3}}{3}\)


7.3: Consonance and Dissonance
- Consonance and dissonance are musical terms describing whether combinations of notes sound good together or not.
Notes that sound good together when played at the same time are called consonant. Chords built only of consonances sound pleasant and "stable"; you can listen to one for a long time without feeling that the music needs to change to a different chord. Notes that are dissonant can sound harsh or unpleasant when played at the same time. Or they may simply feel "unstable"; if you hear a chord with a dissonance in it, you may feel that the music is pulling you towards the chord that resolves the dissonance. Obviously, what seems pleasant or unpleasant is partly a matter of opinion. This discussion only covers consonance and dissonance in Western music.
For activities that introduce these concepts to young students, please see Consonance and Dissonance Activities
Of course, if there are problems with tuning, the notes will not sound good together, but this is not what consonance and dissonance are about. (Please note, though, that the choice of tuning system can greatly affect which intervals sound consonant and which sound dissonant! Please see Tuning Systems for more about this.)
Consonance and dissonance refer to intervals and chords . The interval between two notes is the number of half steps between them, and all intervals have a name that musicians commonly use, like major third (which is 4 half steps), perfect fifth (7 half steps), or octave . (See Interval to learn how to determine and name the interval between any two notes.)
An interval is measured between two notes. When there are more than two notes sounding at the same time, that's a chord. (See Triads , Naming Triads , and Beyond Triads for some basics on chords.) Of course, you can still talk about the interval between any two of the notes in a chord.
The simple intervals that are considered to be consonant are the minor third , major third , perfect fourth , perfect fifth , minor sixth , major sixth , and the octave .
Consonant Intervals
In modern Western Music , all of these intervals are considered to be pleasing to the ear. Chords that contain only these intervals are considered to be "stable", restful chords that don't need to be resolved . When we hear them, we don't feel a need for them to go to other chords.
The intervals that are considered to be dissonant are the minor second , the major second , the minor seventh , the major seventh , and particularly the tritone , which is the interval in between the perfect fourth and perfect fifth.
Dissonant Intervals
These intervals are all considered to be somewhat unpleasant or tension-producing. In tonal music , chords containing dissonances are considered "unstable"; when we hear them, we expect them to move on to a more stable chord. Moving from a dissonance to the consonance that is expected to follow it is called resolution, or resolving the dissonance. The pattern of tension and release created by resolved dissonances is part of what makes a piece of music exciting and interesting. Music that contains no dissonances can tend to seem simplistic or boring. On the other hand, music that contains a lot of dissonances that are never resolved (for example, much of twentieth-century "classical" or "art" music) can be difficult for some people to listen to, because of the unreleased tension.
Resolving Dissonances
Why are some note combinations consonant and some dissonant? Preferences for certain sounds is partly cultural; that's one of the reasons why the traditional musics of various cultures can sound so different from each other. Even within the tradition of Western music , opinions about what is unpleasantly dissonant have changed a great deal over the centuries. But consonance and dissonance do also have a strong physical basis in nature.
In simplest terms, the sound waves of consonant notes "fit" together much better than the sound waves of dissonant notes. For example, if two notes are an octave apart, there will be exactly two waves of one note for every one wave of the other note. If there are two and a tenth waves or eleven twelfths of a wave of one note for every wave of another note, they don't fit together as well. For much more about the physical basis of consonance and dissonance, see Acoustics for Music Theory , Harmonic Series , and Tuning Systems .


11.1: Developing Your Sense of Logic
By the end of this section, you will be able to:
- Identify key rhetorical concepts and thought patterns in a variety of texts.
- Explain how patterns of thought function for different audiences, purposes, and situations.
For the purposes of this course, logic means “reasoning based on thought and evidence.” In practical terms, logic is the ability to analyze and evaluate persuasive or argument writing for effectiveness. By extension, it also means that you can learn to use logic in your own argumentative writing. Like any other new skill, you are likely to learn best when you have a starting point. Here are some suggestions for how to begin thinking and writing logically:
- Approach a topic with an open mind.
- Consider what you already know about the topic.
- Consider what you want to know about the topic.
- Find credible information about the topic.
- Base your judgments of the topic on sound reasoning and evidence.
Once you have formed your opinions on a particular debatable subject, you must decide on the best way to organize them to share with others. Developing your skills in six widely used reasoning strategies , or patterns for thinking and writing, can help you determine the most logical and effective means of organizing information to make your points.
In this chapter, you will examine these six reasoning strategies—analogy, cause and effect, classification and division, comparison and contrast, problem and solution, and definition—that are often used in college classes. In addition, you will consider how writers’ personal views, cultural backgrounds, and purposes for writing help determine
- which reasoning strategy suits their needs; and
- what they decide to include in their writing.
As you progress in your college classes and beyond, you will find these reasoning strategies used in all genres of writing, both nonfiction (e.g., textbooks, how-to books) and fiction (e.g., novels, short stories). Understanding how these strategies work can help you recognize their common formats and analyze what you read; likewise, as a writer, understanding how these strategies work to reflect your thinking can help you determine the strategy you need to use.
Analogy
Writers frequently use analogy as a strategy to compare two unlike subjects—one subject is familiar to readers, whereas the other is not. To explain or clarify the unfamiliar subject, the writer emphasizes the way or ways in which the two subjects are similar, even though they are dissimilar and unrelated in all other ways.
Analogies are basically long forms of similes (short comparisons of unlike elements, based on the word like or as ) or metaphors (short comparisons without signal words). In the example paragraph, the writer explains unfamiliar aspects of the COVID-19 pandemic by comparing it with the more familiar concept of a robbery spree.
Model Paragraph
Examining COVID-19 is like examining a robbery case in this way: both require a great deal of investigation. Those investigating the causes behind the pandemic look for the history of how the virus spread, and those investigating a crime look for the backstory that might connect the victims and criminals. In addition, the two groups of investigators look at the reasons behind the focus of their study. Medical investigators look at why the virus spread throughout the world; police investigators look at why the crime spree took place in a particular area. Also, both types of investigators are trying to stop whatever or whoever is the focus of their investigation. Medical investigators want to stop the virus; police investigators want to stop the crimes.
Cause and Effect
Cause-and-effect writing identifies and examines the reasons (causes) for and consequences (effects) of an action, event, or idea. Cause-and-effect writing often answers the question “Why?” and helps readers understand the connections between what happens because of—or as a result of—something else.
Model Paragraph
Ray’s grocery, Artie’s Hardware store, and Cradle and Teen department store all went out of business because a well-known superstore opened in Springdale. Customers who frequented Ray’s, an establishment that had been run by the same family for four generations, used to drive many miles to take advantage of the high quality of items in the meat and deli departments. After the opening of the superstore, however, those same customers found they could get similar items at a savings, even if the quality was not as high as the products at Ray’s. Customers at Artie’s Hardware often talked with owner Artie Shoeman about their hardware needs, but the store did not offer the same variety of items they could find in the superstore. The same was true for those who shopped at Cradle and Teen. The superstore featured lower prices and more variety, even if the items did not match the quality of the items at Cradle and Teen.
Figure \(11.2\) Small retailers often lose out to superstores. (credit: “Fort Bragg CA Storefront” by Ellin Beltz/ Wikimedia Commons, Public Domain)
Classification and Division
Classification and division are actually two closely related strategies, generally discussed together because of their similarity. When using the strategy of division, the writer identifies a single subject or group and explains categories within that subject or group. In other words, the writer divides the larger unit into component parts. When using the strategy of classification, writers do the opposite. They group various elements and place them into larger, more comprehensive categories rather than divide the whole into parts. In general, the reasoning strategy of classification and division looks at smaller elements as parts of a larger element and thus helps readers understand a general concept and the elements that it comprises.
Model Paragraphs
Extra material in the textbook can be divided into photographs, quotations, and tables. The photographs were all taken by the author and focus on various parts of the life cycle of the plants highlighted in the chapter. In addition, to add color and more information about the subject matter of each chapter, the author has inserted sidebar quotations from both famous and non-famous people. The tables the author has included help readers see more details about the progression of the plants’ spread across the country.
After three months of training, the young dogs were placed into three categories: those who would go directly to permanent homes, those who would repeat the course, and those who would advance to the next level. The dogs that would be homed immediately were those who were far too social or far too active to be service dogs. The dogs that would repeat the course had possibilities as service dogs but needed more discipline and instruction. Their futures were yet to be decided. Those that advanced to the next level were obedient and focused and learned quickly. They displayed great promise as service dogs.
Comparison and Contrast
Compare and contrast , one of the most frequently used reasoning strategies, analyzes two (sometimes more) subjects, examining the similarities (comparisons) and differences (contrasts) between them. Nearly everything you can think of can be a subject for comparison and contrast: objects, people, concepts, places, movies, literature, and styles, to name a few. To elaborate on the separate points, writers provide details about each element being compared or contrasted. Comparison and contrast helps readers analyze and evaluate subjects.
This strategy is helpful when the similarities or differences are not obvious and when a significant common thread exists between the subjects. For example, a contrast between an expensive, elegant restaurant and a fast-food restaurant would be useless because the differences are clearly obvious, despite the common thread—both are restaurants. However, not so obvious might be some similarities.
When subjects have no common thread or have obvious shared characteristics, any comparison or contrast makes little sense—like contrasting a fish and a shoe (no common thread) or comparing two fast-food restaurants (obvious similarities). However, a writer actually might find a common thread between a fish and a shoe (perhaps shine or texture or color), and a valid topic of contrast might be differences between the two fast-food restaurants.
Model Paragraph
Although they seem different on the surface, one way in which Romantic-period poetry and 1980s rap music are alike is the desire the writers had to create a new approach to their art. They wanted to represent simpler values that were more connected to the natural world, values to which a general audience could relate. For example, in William Wordsworth’s “Daffodils,” the speaker can escape the depressing, industrialized urban world to find peace in nature by contemplating a field of flowers. Similarly, in the Sugarhill Gang’s 1979 “Rapper’s Delight,” the band sings of how their beats can lift spirits and cause listeners to dance and forget their woes. However, Romantic-period poetry and 1980s rap music are different in the delivery style and form of the art; “Rapper’s Delight” is set to music, which is an integral part of the piece, but “Daffodils” is not.
Problem and Solution
When using this reasoning strategy, writers introduce a predicament or challenging issue (the problem) and offer information about what was done or what should be done to remedy the predicament or issue (the solution). Problem-and-solution writing helps readers understand the complexities of some predicaments and the actions that can improve or eliminate them.
Model Paragraph
The issue of combating the spread of hate speech and misinformation on social media can be addressed if more social media providers improve their monitoring services. Aside from creating more algorithms that search for linked key words and phrases, social media providers should increase the number of professional monitors conducting active searches. Additionally, while many platforms such as Twitter and Facebook respond within a few days to reports of posts that violate their policies, more monitors could lessen the amount of time these posts are available. According to Facebook, inappropriate posts are investigated and removed within 24 to 48 hours (Facebook “Community Standards”). Some offenders have been reported multiple times for their platform violations, and social media sponsors should increase their monitoring of those offenders. Although such surveillance would increase the burden on the social media providers, it would help solve the growing challenge of online hate speech and misinformation.
Figure \(11.3\) Social Media Icons (credit: “Social Media Mixed Icons – Banner” by Blogtrepreneur/Wikimedia Commons, Creative Commons, CC BY 2.0)
Definition
When using the reasoning strategy of definition , writers elaborate on the meaning of an idea, a word, or an expression, usually one that is controversial or that can be viewed in multiple ways. Beginning writers tend to think that definition writing looks only at the denotation , or dictionary definition. However, definition writing entails much more than relaying a dictionary definition. It also explains and elaborates on the connotations , the emotions and implications the topic evokes. Definition writing is especially useful for explaining and interpreting terms, ideas, or concepts that are easily or often confused or that have meanings beyond their denotations. Sometimes these meanings are personal interpretations and thus reflect a writer’s particular viewpoint. Additionally, this strategy is beneficial when writers want to explain or reinforce a term before making an argument about a larger concept.
Model Paragraph
In everyday speech, the word critical is often used to highlight negative aspects of a topic. If someone says a friend was critical of a new haircut, the implication is that the friend did not like the cut. However, when used in college classes, critical has an expanded meaning: noting both the negative and positive aspects of a topic, examining those aspects in depth, and then making decisions about the discoveries. Students directed to use critical thinking, critical reading, or critical writing should know they are expected to examine all sides of a topic fully, evaluate the validity of those sides, and then make sound judgments on the basis of their evaluation.
In this chapter, you have learned about various reasoning strategies that you may use in academic and professional writing. Utilizing these strategies when you write can help you both evaluate and analyze text that you read and create more logical and persuasive arguments.


1.3: Introduction to Staying Connected
What you’ll learn to do: Discuss the importance of staying connected with colleagues, other professionals and customers in the digital age
Now that we understand the tools and the processes by which we connect with other human beings—that is, the social communication model and the methods of communication—we can look at them in terms of this crazy, technological world we live in. Our coworkers, colleagues, and customers are out there waiting to communicate and be communicated with, and they’re doing it in a variety of ways that are vastly different than they were twenty years ago.
More times than not, you don’t even get to choose the tool you’re using to communicate your message, so in this section, we’re going to look at the ways you can digitally communicate with colleagues and customers, the strengths and weaknesses of those tools, and how to best leverage them to be understood.
Contributors and Attributions
- Introduction to Staying Connected. Authored by : Freedom Learning Group. Provided by : Lumen Learning. License : CC BY: Attribution


7.E: Other Worlds - An Introduction to the Solar System (Exercises)
For Further Exploration
Articles
Davidson, K. “Carl Sagan’s Coming of Age.” Astronomy. (November 1999): 40. About the noted popularizer of science and how he developed his interest in astronomy.
Garget, J. “Mysterious Microworlds.” Astronomy. (July 2005): 32. A quick tour of a number of the moons in the solar system.
Hartmann, W. “The Great Solar System Revision.” Astronomy . (August 1998): 40. How our views have changed over the past 25 years.
Kross, J. “What’s in a Name?” Sky & Telescope . (May 1995): 28. How worlds are named.
Rubin, A. “Secrets of Primitive Meteorites.” Scientific American . (February 2013): 36. What meteorites can teach us about the environment in which the solar system formed.
Soter, S. “What Is a Planet?” Scientific American . (January 2007): 34. The IAU’s new definition of a planet in our solar system, and what happened to Pluto as a result.
Talcott, R. “How the Solar System Came to Be.” Astronomy . (November 2012): 24. On the formation period of the Sun and the planets.
Wood, J. “Forging the Planets: The Origin of our Solar System.” Sky & Telescope . (January 1999): 36. Good overview.
Websites
Gazetteer of Planetary Nomenclature: http://planetarynames.wr.usgs.gov/ . Outlines the rules for naming bodies and features in the solar system.
Planetary Photojournal: http://photojournal.jpl.nasa.gov/index.html . This NASA site features thousands of the best images from planetary exploration, with detailed captions and excellent indexing. You can find images by world, feature name, or mission, and download them in a number of formats. And the images are copyright-free because your tax dollars paid for them.
The following sites present introductory information and pictures about each of the worlds of our solar system:
- NASA/JPL Solar System Exploration pages: http://solarsystem.nasa.gov/index.cfm .
- National Space Science Data Center Lunar and Planetary Science pages: http://nssdc.gsfc.nasa.gov/planetary/ .
- Nine [now 8] Planets Solar System Tour: www.nineplanets.org/.
- Planetary Society solar system pages: www.planetary.org/explore/spa...opics/compare/.
- Views of the Solar System by Calvin J. Hamilton: http://www.solarviews.com/eng/homepage.htm .
Videos
Brown Dwarfs and Free Floating Planets: When You Are Just Too Small to Be a Star: https://www.youtube.com/watch?v=zXCDsb4n4KU . A nontechnical talk by Gibor Basri of the University of California at Berkeley, discussing some of the controversies about the meaning of the word “planet” (1:32:52).
In the Land of Enchantment: The Epic Story of the Cassini Mission to Saturn: https://www.youtube.com/watch?v=Vx135n8VFxY . A public lecture by Dr. Carolyn Porco that focuses mainly on the exploration of Saturn and its moons, but also presents an eloquent explanation of why we explore the solar system (1:37:52).
Origins of the Solar System: www.pbs.org/wgbh/nova/space/o...ar-system.html. A video from PBS that focuses on the evidence from meteorites, narrated by Neil deGrasse Tyson (13:02).
To Scale: The Solar System: https://www.youtube.com/watch?t=84&v=zR3Igc3Rhfg . Constructing a scale model of the solar system in the Nevada desert (7:06).
Collaborative Group Activities
- Discuss and make a list of the reasons why we humans might want to explore the other worlds in the solar system. Does your group think such missions of exploration are worth the investment? Why?
- Your instructor will assign each group a world. Your task is to think about what it would be like to be there. (Feel free to look ahead in the book to the relevant chapters.) Discuss where on or around your world we would establish a foothold and what we would need to survive there.
- In the There’s No Place Like Home feature in Section 7.2, we discuss briefly how human activity is transforming our planet’s overall environment. Can you think of other ways that this is happening?
- Some scientists criticized Carl Sagan for “wasting his research time” popularizing astronomy. To what extent do you think scientists should spend their time interpreting their field of research for the public? Why or why not? Are there ways that scientists who are not as eloquent or charismatic as Carl Sagan or Neil deGrasse Tyson can still contribute to the public understanding of science?
- Your group has been named to a special committee by the International Astronomical Union to suggest names of features (such as craters, trenches, and so on) on a newly explored asteroid. Given the restriction that any people after whom features are named must no longer be alive, what names or types of names would you suggest? (Keep in mind that you are not restricted to names of people, by the way.)
- A member of your group has been kidnapped by a little-known religious cult that worships the planets. They will release him only if your group can tell which of the planets are currently visible in the sky during the evening and morning. You are forbidden from getting your instructor involved. How and where else could you find out the information you need? (Be as specific as you can. If your instructor says it’s okay, feel free to answer this question using online or library resources.)
- In the Carl Sagan: Solar System Advocate feature in Section 7.1, you learned that science fiction helped spark and sustain his interest in astronomy. Did any of the members of your group get interested in astronomy as a result of a science fiction story, movie, or TV show? Did any of the stories or films you or your group members saw take place on the planets of our solar system? Can you remember any specific ones that inspired you? If no one in the group is into science fiction, perhaps you can interview some friends or classmates who are and report back to the group.
- A list of NASA solar system spacecraft missions can be found at http://www.nasa.gov/content/solar-missions-list . Your instructor will assign each group a mission. Look up when the mission was launched and executed, and describe the mission goals, the basic characteristics of the spacecraft (type of instruments, propellant, size, and so on), and what was learned from the mission. If time allows, each group should present its findings to the rest of the class.
- What would be some of the costs or risks of developing a human colony or base on another planetary body? What technologies would need to be developed? What would people need to give up to live on a different world in our solar system?
Review Questions
- Venus rotates backward and Uranus and Pluto spin about an axis tipped nearly on its side. Based on what you learned about the motion of small bodies in the solar system and the surfaces of the planets, what might be the cause of these strange rotations?
- What is the difference between a differentiated body and an undifferentiated body, and how might that influence a body’s ability to retain heat for the age of the solar system?
- What does a planet need in order to retain an atmosphere? How does an atmosphere affect the surface of a planet and the ability of life to exist?
- Which type of planets have the most moons? Where did these moons likely originate?
- What is the difference between a meteor and a meteorite?
- Explain our ideas about why the terrestrial planets are rocky and have less gas than the giant planets.
- Do all planetary systems look the same as our own?
- What is comparative planetology and why is it useful to astronomers?
- What changed in our understanding of the Moon and Moon-Earth system as a result of humans landing on the Moon’s surface?
- If Earth was to be hit by an extraterrestrial object, where in the solar system could it come from and how would we know its source region?
- List some reasons that the study of the planets has progressed more in the past few decades than any other branch of astronomy.
-
Imagine you are a travel agent in the next century. An eccentric billionaire asks you to arrange a “Guinness Book of Solar System Records” kind of tour. Where would you direct him to find the following (use this chapter and Appendix F and Appendix G):
- the least-dense planet
- the densest planet
- the largest moon in the solar system
- excluding the jovian planets, the planet where you would weigh the most on its surface (Hint: Weight is directly proportional to surface gravity.)
- the smallest planet
- the planet that takes the longest time to rotate
- the planet that takes the shortest time to rotate
- the planet with a diameter closest to Earth’s
- the moon with the thickest atmosphere
- the densest moon
- the most massive moon
- What characteristics do the worlds in our solar system have in common that lead astronomers to believe that they all formed from the same “mother cloud” (solar nebula)?
- How do terrestrial and giant planets differ? List as many ways as you can think of.
- Why are there so many craters on the Moon and so few on Earth?
- How do asteroids and comets differ?
- How and why is Earth’s Moon different from the larger moons of the giant planets?
- Where would you look for some “original” planetesimals left over from the formation of our solar system?
- Describe how we use radioactive elements and their decay products to find the age of a rock sample. Is this necessarily the age of the entire world from which the sample comes? Explain.
- What was the solar nebula like? Why did the Sun form at its center?
Thought Questions
- What can we learn about the formation of our solar system by studying other stars? Explain.
- Earlier in this chapter, we modeled the solar system with Earth at a distance of about one city block from the Sun. If you were to make a model of the distances in the solar system to match your height, with the Sun at the top of your head and Pluto at your feet, which planet would be near your waist? How far down would the zone of the terrestrial planets reach?
- Seasons are a result of the inclination of a planet’s axial tilt being inclined from the normal of the planet’s orbital plane. For example, Earth has an axis tilt of 23.4° (Appendix F). Using information about just the inclination alone, which planets might you expect to have seasonal cycles similar to Earth, although different in duration because orbital periods around the Sun are different?
- Again using Appendix F, which planet(s) might you expect not to have significant seasonal activity? Why?
- Again using Appendix F, which planets might you expect to have extreme seasons? Why?
- Using some of the astronomical resources in your college library or the Internet, find five names of features on each of three other worlds that are named after real people. In a sentence or two, describe each of these people and what contributions they made to the progress of science or human thought.
- Explain why the planet Venus is differentiated, but asteroid Fraknoi, a very boring and small member of the asteroid belt, is not.
- Would you expect as many impact craters per unit area on the surface of Venus as on the surface of Mars? Why or why not?
- Interview a sample of 20 people who are not taking an astronomy class and ask them if they can name a living astronomer. What percentage of those interviewed were able to name one? Typically, the two living astronomers the public knows these days are Stephen Hawking and Neil deGrasse Tyson. Why are they better known than most astronomers? How would your result have differed if you had asked the same people to name a movie star or a professional basketball player?
- Using Appendix G, complete the following table that describes the characteristics of the Galilean moons of Jupiter, starting from Jupiter and moving outward in distance.
| Moon | Semimajor Axis (km 3 ) | Diameter | Density (g/cm 3 ) |
|---|---|---|---|
| Io | |||
| Europa | |||
| Ganymede | |||
| Callisto |
This system has often been described as a mini solar system. Why might this be so? If Jupiter were to represent the Sun and the Galilean moons represented planets, which moons could be considered more terrestrial in nature and which ones more like gas/ice giants? Why? (Hint: Use the values in your table to help explain your categorization.)
Figuring for Yourself
- Calculate the density of Jupiter. Show your work. Is it more or less dense than Earth? Why?
- Calculate the density of Saturn. Show your work. How does it compare with the density of water? Explain how this can be.
- What is the density of Jupiter’s moon Europa (see Appendix G for data on moons)? Show your work.
- Look at Appendix F and Appendix G and indicate the moon with a diameter that is the largest fraction of the diameter of the planet or dwarf planet it orbits.
- Barnard’s Star, the second closest star to us, is about 56 trillion (5.6 × 10 12 ) km away. Calculate how far it would be using the scale model of the solar system given in Overview of Our Planetary System.
- A radioactive nucleus has a half-life of 5 × 10 8 years. Assuming that a sample of rock (say, in an asteroid) solidified right after the solar system formed, approximately what fraction of the radioactive element should be left in the rock today?


3.14: Apostrophe Errors
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Apostrophes give many writers a lot of trouble. Sometimes, you might be tempted to put an apostrophe where it does not belong, such as when you are simply making a word plural. Other times, you need to make a word possessive, but you might forget to use the apostrophe.
Then, of course, there is that whole its / it’s thing that confuses most everyone.
Remember, the rule is to use an apostrophe when you need to show possession or ownership. The exception is with its .
Its shows ownership because it’s means it is . So, it’s like it’s is already taken, so its gets to be an ownership exception. To make sure you are using It’s correctly, just say it is when you read it. If it makes sense, you’re fine. However, if you’re trying to show ownership, and it is would not work in the sentence, you need to make the change to its .
For more information on the apostrophe, be sure to check out the Apostrophe section in the Punctuation area of Grammar Essentials (or if you just need to brush up your skills, visit the Apostrophe Refresher ). Otherwise, you might end up with a sentence like this:
And, you would want a sentence like this:


12.17: Discussion- Selecting Primary Key Tips
There are many ways to make a primary key or have one automatically generated in Microsoft Access. For additional information about selecting or creating a primary key watch this video which walks through a few examples and discusses various ways to create a custom key for your Access table.
After watching the video ask yourself a few questions and discuss your answers to them.
A link to an interactive elements can be found at the bottom of this page.
Discussion Questions
- Why is it important to choose a memorable primary key?
- Is adding a description important for a primary key? Why or why not?
- In what types of scenarios would you use this information?
Share your opinions below and respond to two of your classmates’ thoughts.
Contributors and Attributions
CC licensed content, Original
- Discussion: Selecting Primary Key Tips. Authored by : Sherri Pendleton. Provided by : Lumen Learning. License : CC BY: Attribution
All rights reserved content
- How To Select and Make PRIMARY KEYS in Microsoft Access. Authored by : Leon Marsden. Located at : https://youtu.be/jpARwLelAek . License : All Rights Reserved . License Terms : Standard YouTube License


8.8: Paleomagnetic Evidence for Plate Tectonics
Although Alfred Wegener would not live to see it, his ideas about continental drift would gradually gain acceptance within the scientific community after other scientists adjusted and molded it to form the Theory of Plate Tectonics. With the continued research within the scientific community more evidence began to accumulate. Some of the most important evidence came from the study of paleomagnetism , or changes in Earth’s magnetic field over millions of years.
Earth’s magnetic field is defined by the North and South Poles that align generally with the axis of rotation (Figure \(\PageIndex{1}\)). The lines of magnetic force flow into Earth in the Northern Hemisphere and out of Earth in the Southern Hemisphere. Because of the shape of the field lines, the magnetic force trends at different angles to the surface in different locations (red arrows of Figure \(\PageIndex{1}\)). At the North and South Poles, the force is vertical. Anywhere on the equator the force is horizontal, and everywhere in between, the magnetic force is at some intermediate angle to the surface.
In its fluid form, the minerals that make up magma are free to move in any direction and take on any orientation. But as the magma cools and solidifies, movement ceases and the mineral orientation and position become fixed. As the mineral magnetite (Fe 3 O 4 ) crystallizes from magma, it becomes magnetized with an orientation parallel to that of Earth’s magnetic field at that time, similar to the way a compass needle aligns with the magnetic field to point north. This magnetic record in the rock is called remnant magnetism . Rocks like basalt, which cool from a high temperature and commonly have relatively high levels of magnetite, are particularly susceptible to being magnetized in this way, but even sediments and sedimentary rocks, as long as they have small amounts of magnetite, will take on remnant magnetism because the magnetite grains gradually become reoriented following deposition. By studying both the horizontal and vertical components of the remnant magnetism, one can tell not only the direction to magnetic north at the time of the rock’s formation, but also the latitude where the rock formed relative to magnetic north.
In the early 1950s, a group of geologists from Cambridge University, including Keith Runcorn , Edward Irving and several others, started looking at the remnant magnetism of Phanerozoic British and European volcanic rocks, and collecting paleomagnetic data. They found that rocks of different ages sampled from generally the same area showed quite different apparent magnetic pole positions (green line, Figure \(\PageIndex{2}\)). They initially assumed that this meant that Earth’s magnetic field had, over time, departed significantly from its present position, which is close to the rotational pole.
The curve defined by the paleomagnetic data was called a polar wandering path because Runcorn and his colleagues initially thought that their data represented actual movement of the magnetic poles (since geophysical models of the time suggested that the magnetic poles did not need to be aligned with the rotational poles). We now know that the magnetic data define movement of continents, and not of the magnetic poles, so we call it an apparent polar wandering path (APWP). Runcorn and colleagues soon extended their work to North America, and this also showed apparent polar wandering, but the results were not consistent with those from Europe (Figure \(\PageIndex{2}\)). For example, the 200 Ma pole for North America placed somewhere in China, while the 200 Ma pole for Europe placed in the Pacific Ocean. Since there could only have been one pole position at 200 Ma, this evidence strongly supported the idea that North America and Europe had moved relative to each other since 200 Ma. Subsequent paleomagnetic work showed that South America, Africa, India, and Australia also have unique polar wandering curves. Rearranging the continents based on their positions in Pangaea caused these wandering curves to overlap, showing that the continents had moved over time.
Additional evidence for movement of the continents came from analysis of magnetic dip . Recall from Figure \(\PageIndex{1}\) that the angle of the magnetic field changes as a function of latitude, with the field directed vertically downwards at the north pole, upwards at the south pole, and horizontal at the equator. Every latitude between the equator and the poles will have a corresponding angle between horizontal and vertical (red arrows, Figure \(\PageIndex{1}\)). By looking at the dip angle in rocks, we can determine the latitude at which those rocks were formed. Combining that with the age of the rocks, we can trace the movements of the continents over time. For example, at around 500 Ma, what we now call Europe was south of the equator, and so European rocks formed then would have acquired an upward-pointing magnetic field orientation (Figure \(\PageIndex{3}\)). Between then and now, Europe gradually moved north, and the rocks forming at various times acquired steeper and steeper downward-pointing magnetic orientations.
This paleomagnetic work of the 1950s was the first new evidence in favor of continental drift, and it led a number of geologists to start thinking that the idea might have some merit.
*”Physical Geology” by Steven Earle used under a CC-BY 4.0 international license. Download this book for free at http://open.bccampus.ca


5.8C: Fermentation Without Substrate-Level Phosphorylation
- Give examples of various types of fermentation: homolactic, heterolactic and alcoholic
Fermentation is the process of extracting energy from the oxidation of organic compounds, such as carbohydrates, using an endogenous electron acceptor, which is usually an organic compound. In contrast, respiration is where electrons are donated to an exogenous electron acceptor, such as oxygen, via an electron transport chain. Fermentation is important in anaerobic conditions when there is no oxidative phosphorylation to maintain the production of ATP (adenosine triphosphate) by glycolysis.
During fermentation, pyruvate is metabolised to various compounds. Homolactic fermentation is the production of lactic acid from pyruvate; alcoholic fermentation is the conversion of pyruvate into ethanol and carbon dioxide; and heterolactic fermentation is the production of lactic acid as well as other acids and alcohols. Fermentation does not necessarily have to be carried out in an anaerobic environment. For example, even in the presence of abundant oxygen, yeast cells greatly prefer fermentation to oxidative phosphorylation, as long as sugars are readily available for consumption (a phenomenon known as the Crabtree effect). The antibiotic activity of Hops also inhibits aerobic metabolism in Yeast.
Sugars are the most common substrate of fermentation, and typical examples of fermentation products are ethanol, lactic acid, lactose, and hydrogen. However, more exotic compounds can be produced by fermentation, such as butyric acid and acetone. Yeast carries out fermentation in the production of ethanol in beers, wines, and other alcoholic drinks, along with the production of large quantities of carbon dioxide. Fermentation occurs in mammalian muscle during periods of intense exercise where oxygen supply becomes limited, resulting in the creation of lactic acid.
Key Points
- Fermentation without substrate level phosphorylation uses an endogenous electron acceptor, which is usually an organic compound.
- Fermentation is important in anaerobic conditions when there is no oxidative phosphorylation to maintain the production of ATP (adenosine triphosphate) by glycolysis.
- During fermentation, pyruvate is metabolised to various compounds such as lactic acid, ethanol and carbon dioxide or other acids.
Key Terms
- fermentation : Any of many anaerobic biochemical reactions in which an enzyme (or several enzymes produced by a microorganism) catalyses the conversion of one substance into another; especially the conversion (using yeast) of sugars to alcohol or acetic acid with the evolution of carbon dioxide.
- substrate : a surface on which an organism grows or to which it is attached
- oxidative phosphorylation : Oxidative phosphorylation (or OXPHOS in short) is a metabolic pathway that uses energy released by the oxidation of nutrients to produce adenosine triphosphate (ATP).
- electron acceptor : An electron acceptor is a chemical entity that accepts electrons transferred to it from another compound. It is an oxidizing agent that, by virtue of its accepting electrons, is itself reduced in the process.


<IP_ADDRESS>: Putting It All Together
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In this section of Grammar Essentials, you have learned about the 20 most common errors students make and how you can avoid them. Hopefully, you have also learned that, if you have had these errors marked on your papers, you aren’t alone. The key is having awareness, as this can help you when you edit.
To help you review, check out the video below, which provides a basic overview of what you have learned about the 20 most common errors students in the United States make.
NOTE: Because the use of the singular "they" is new, you may find some people who disagree, but most academics now agree that the singular "they" is correct. Please always refer to your style guide, as some style guides still recommend not using the singular "they".


15.6: International Banking
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5. What roles do U.S. banks play in the international marketplace?
The financial marketplace spans the globe, with money routinely flowing across international borders. U.S. banks play an important role in global business by providing loans to foreign governments and businesses. Multinational corporations need many special banking services, such as foreign-currency exchange and funding for overseas investments. U.S. banks also offer trade-related services, such as global cash management, that help firms manage their cash flows, improve their payment efficiency, and reduce their exposure to operational risks. Sometimes consumers in other nations have a need for banking services that banks in their own countries don’t provide. Therefore, large banks often look beyond their national borders for profitable banking opportunities.
Many U.S. banks have expanded into overseas markets by opening offices in Europe, Latin America, and Asia. They often provide better customer service than local banks and have access to more sources of funding. Citibank, for example, was the first bank to offer banking by phone and 24-hour-a-day ATM service in Japan.
For U.S. banks, expanding internationally can be difficult. Banks in other nations are often subject to fewer regulations than U.S. banks, making it easier for them to undercut American banks on the pricing of loans and services. Some governments also protect their banks against foreign competition. For example, the Chinese government imposes high fees and limits the amount of deposits that foreign banks can accept from customers. It also controls foreign-bank deposit and loan interest rates, limiting the ability of foreign banks to compete with government-owned Chinese banks. Despite the banking restrictions for foreign banks in China, many of the large U.S. banking institutions continue to do business there. 15
International banks operating within the United States also have a substantial impact on the economy through job creation—they employ thousands of people in the United States, and most workers are U.S. citizens—operating and capital expenditures, taxes, and other contributions. According to March 2017 Federal Reserve data, the combined banking and nonbanking assets of the U.S. operations of foreign banks total more than $24 trillion. 16
| The World’s Biggest Banks, 2017 |
|---|
| Industrial and Commercial Bank of China |
| China Construction Bank |
| JPMorgan Chase & Co. (USA) |
| Wells Fargo & Co. (USA) |
| Agricultural Bank of China |
| Bank of America Corp. (USA) |
| Bank of China Ltd. |
| Citigroup (USA) |
| BNP Paribas (France) |
| Mitsubishi UFJ Financial Group (Japan) |
Table 15.7 Source: “The World’s Biggest Banks in 2017: The American Bull Market Strengthens,” Forbes, http://www.forbes.com , May 24, 2017.
The United States has four banks listed in the top 10 world’s biggest banks, as shown in Table 15.7 .
Political and economic uncertainty in other countries can make international banking a high-risk venture. European and Asian banks were not immune to the financial crisis of 2007–2009. In fact, several countries, including Greece, Portugal, Spain, and Ireland, continue to rebound slowly from the near-collapse of their economic and financial systems they experienced a decade ago. Financial bailouts spearheaded by the European Union and the International Monetary Fund have helped stabilize the European and global economy. It is unclear at this writing, however, whether the impending “Brexit” move by the United Kingdom (leaving the European Union) will impact international banking, as many of the world’s top financial institutions seek to move their global operations out of London and shift them to other financial capitals within the eurozone. 17
CONCEPT CHECK
- What is the role of U.S. banks in international banking?
- What challenges do U.S. banks face in foreign markets?


8.6: Outcome- Implementing Positioning Strategy
What you’ll learn to do: describe the process of implementing a positioning strategy
With your new positioning strategy and a well-formulated positioning statement, you are poised to take action.
But . . . how exactly?
What comes next is more familiar than you might think: You head back to the fundamentals of the marketing mix. The positioning strategy helps guide your adjustments to product, price, place (distribution), and promotion, so that you can effectively reach and shape the perceptions of your target market segment(s). In this section you’ll learn how to do this.
The specific things you’ll learn in this section include:
- Adjust the marketing mix to deliver on positioning strategy
- Develop promotion strategy based on new positioning
- Measure effectiveness
Learning Activities
The learning activities for this section include the following:
- Reading: Implementing Positioning Strategy
- Self Check: Implementing Positioning Strategy
Contributors and Attributions
- Outcome: Implementing Positioning Strategy. Provided by : Lumen Learning. License : CC BY: Attribution


4.7: Communication Study Today and Tomorrow
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Today, many colleges and universities have Communication as part of their curriculum with departments titled with names like Speech, Speech Communication, and Communication. Likewise, our professional organizations are still active in growing and strengthening the field through teaching and research. Even with the increased recognition, there is still considerable growth, change, and movement taking place in communication study. Those involved in the field actively and openly debate and discuss various theoretical and methodological approaches for studying human communication. The study of human communication continues to be a wide and diverse field, with each area increasing our understanding of how humans communicate.
As history explains, changes in the world will continue to guide our approaches for understanding and researching communication. We have moved from an industrial age to an information age and have yet to fully understand the communicative implications of this shift. Advances in communication and information technologies are forever changing the ways we research and teach communication in our colleges and universities. While it is difficult to predict the specific areas and phenomena of study for future communication research, it is safe to assume that continued global and social changes will shape the development of our field.


9.7: Running the Hypothesis Test in Practice
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At this point some of you might be wondering if this is a “real” hypothesis test, or just a toy example that I made up. It’s real. In the previous discussion I built the test from first principles, thinking that it was the simplest possible problem that you might ever encounter in real life. However, this test already exists: it’s called the
binomial test
, and it’s implemented by an R function called
binom.test()
. To test the null hypothesis that the response probability is one-half
p = .5
,
164
using data in which
x = 62
of
n = 100
people made the correct response, here’s how to do it in R:
binom.test( x=62, n=100, p=.5 )
##
## Exact binomial test
##
## data: 62 and 100
## number of successes = 62, number of trials = 100, p-value =
## 0.02098
## alternative hypothesis: true probability of success is not equal to 0.5
## 95 percent confidence interval:
## 0.5174607 0.7152325
## sample estimates:
## probability of success
## 0.62
Right now, this output looks pretty unfamiliar to you, but you can see that it’s telling you more or less the right things. Specifically, the p-value of 0.02 is less than the usual choice of α=.05, so you can reject the null. We’ll talk a lot more about how to read this sort of output as we go along; and after a while you’ll hopefully find it quite easy to read and understand. For now, however, I just wanted to make the point that R contains a whole lot of functions corresponding to different kinds of hypothesis test. And while I’ll usually spend quite a lot of time explaining the logic behind how the tests are built, every time I discuss a hypothesis test the discussion will end with me showing you a fairly simple R command that you can use to run the test in practice.


2.10: In the Spotlight
In February 2005, Amazon launched Amazon Prime , which offered unlimited two-day delivery for millions of items (Brown, 2023). At a time when consumers were accustomed to paying high shipping fees and experiencing slow service, the membership service—$79 per year—offered a new alternative. It was a first-of-its-kind pricing structure that has sparked many companies to do the same. Today’s subscription services cover everything from toilet paper to dog toys. Amazon Prime is still arguably the most prevalent subscription service in history. In 2021, Amazon reported its Amazon Prime members had reached 200 million worldwide (Tatevosian, 2021).
The membership, according to a public letter from Jeff Bezos, executive chair of the Amazon board, “takes the effort out of ordering; no minimum purchase and no consolidating orders. Two-day shipping becomes an everyday experience rather than an occasional indulgence” (Trap Nation, 2014).
Since its first offering in 2005, Amazon has raised its prices only three times—in 2014 to $99 a year, in 2018 to $119, and most recently to $139/year (Sekar & Tindall, 2022). While rumbles in the market suggested that these price increases might drive away customers, Amazon has proven this was not true. The price increases through the years also included new benefits—Amazon Prime Video, Prime Pantry, Prime Reading, and many others. The company demonstrates that consumers are, in fact, willing to pay higher prices—so long as they can perceive value that is added to the increase in price.


7: Microbial Biochemistry
The earth is estimated to be 4.6 billion years old, but for the first 2 billion years, the atmosphere lacked oxygen, without which the earth could not support life as we know it. One hypothesis about how life emerged on earth involves the concept of a “primordial soup.” This idea proposes that life began in a body of water when metals and gases from the atmosphere combined with a source of energy, such as lightning or ultraviolet light, to form the carbon compounds that are the chemical building blocks of life. In 1952, Stanley Miller (1930–2007), a graduate student at the University of Chicago, and his professor Harold Urey (1893–1981), set out to confirm this hypothesis in a now-famous experiment. Miller and Urey combined what they believed to be the major components of the earth’s early atmosphere—water (H 2 O), methane (CH 4 ), hydrogen (H 2 ), and ammonia (NH 3 )—and sealed them in a sterile flask. Next, they heated the flask to produce water vapor and passed electric sparks through the mixture to mimic lightning in the atmosphere (Figure \(\PageIndex{1}\)). When they analyzed the contents of the flask a week later, they found amino acids, the structural units of proteins—molecules essential to the function of all organisms.
-
- 7.1: Organic Molecules
- Biochemistry is the discipline that studies the chemistry of life, and its objective is to explain form and function based on chemical principles. Organic chemistry is the discipline devoted to the study of carbon-based chemistry, which is the foundation for the study of biomolecules and the discipline of biochemistry. Both biochemistry and organic chemistry are based on the concepts of general chemistry.
-
- 7.2: Carbohydrates
- The most abundant biomolecules on earth are carbohydrates. From a chemical viewpoint, carbohydrates are primarily a combination of carbon and water, and many of them have the empirical formula (CH₂O)ₙ, where n is the number of repeated units. This view represents these molecules simply as “hydrated” carbon atom chains in which water molecules attach to each carbon atom, leading to the term “carbohydrates.”
-
- 7.3: Lipids
- Although they are composed primarily of carbon and hydrogen, lipid molecules may also contain oxygen, nitrogen, sulfur, and phosphorous. Lipids serve numerous and diverse purposes in the structure and functions of organisms. They can be a source of nutrients, a storage form for carbon, energy-storage molecules, or structural components of membranes and hormones. Lipids comprise a broad class of many chemically distinct compounds, the most common of which are discussed in this section.
-
- 7.4: Proteins
- Amino acids are capable of bonding together in essentially any number, yielding molecules of essentially any size that possess a wide array of physical and chemical properties and perform numerous functions vital to all organisms. The molecules derived from amino acids can function as structural components of cells and subcellular entities, as sources of nutrients, as atom- and energy-storage reservoirs, and as functional species such as hormones, enzymes, receptors, and transport molecules.
-
- 7.5: Using Biochemistry to Identify Microorganisms
- Accurate identification of bacteria is essential in a clinical laboratory for diagnostic and management of epidemics, pandemics, and food poisoning caused by bacterial outbreaks. In this section, we will discuss a few methods that use biochemical characteristics to identify microorganisms.
Thumbnail: An enzyme binding site that would normally bind substrate can alternatively bind a competitive inhibitor, preventing substrate access. Dihydrofolate reductase is inhibited by methotrexate which prevents binding of its substrate, folic acid. Binding site in blue, inhibitor in green, and substrate in black (PDB: 4QI9). (CC BY 4.0; Thomas Shafee ).


<IP_ADDRESS>: Determining Evolutionary Relationships
-
- Last updated
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- Tom Buckley
- University of California, Davis
Learning Objectives
- Compare homologous and analogous traits.
- Discuss the purpose of cladistics.
- Describe the concept of maximum parsimony.
Scientists must collect accurate information that allows them to make evolutionary connections among organisms. Similar to detective work, scientists must use evidence to uncover the facts. In the case of phylogenies, evolutionary investigations focus on two types of evidence: morphologic (form and function) and genetic.
Two Options for Similarities
In general, organisms that share similar physical features and genomes tend to be more closely related than those that do not. Such features that overlap both morphologically (in form) and genetically are referred to as homologous structures and stem from developmental similarities that are based on evolution. For example, the bones in the wings of bats and birds have homologous structures (Figure \(\PageIndex{1}\)), as do the leaves of monocots and eudicots (Figure \(\PageIndex{2}\)).
Notice it is not simply a single bone, but rather a grouping of several bones arranged in a similar way. The more complex the feature, the more likely any kind of overlap is due to a common evolutionary past. Imagine two people from different countries both inventing a car with all the same parts and in exactly the same arrangement without any previous or shared knowledge. That outcome would be highly improbable. However, if two people both invented a hammer, it would be reasonable to conclude that both could have the original idea without the help of the other. The same relationship between complexity and shared evolutionary history is true for homologous structures in organisms.
In plants, we see similar trends. An example of a homologous structure in plants is the leaf. Groups of vascular plants have evolved from a shared common ancestor that formed leaves. In particular, we could look at leaves formed by flowering plants (Angiosperms), the most recent major clade within kingdom Plantae. The developmental pathway and internal anatomy of these leaves have similarities due to shared ancestry, though they may appear outwardly different.
Misleading Appearances
Some organisms may be very closely related, even though a minor genetic change caused a major morphological difference to make them look quite different. Similarly, unrelated organisms may be distantly related, but appear very much alike. This usually happens because both organisms were in common adaptations that evolved within similar environmental conditions. When similar characteristics occur because of environmental constraints and not due to a close evolutionary relationship, it is called an analogy or homoplasy. For example, insects use wings to fly like bats and birds, but the wing structure and embryonic origin is completely different. These are called analogous structures (Figure \(\PageIndex{3}\) and Figure \(\PageIndex{4}\)).
Similar traits can be either homologous or analogous. Homologous traits are shared due to common ancestry; analogous traits have a similar function but are not similar due to common ancestory. For example, the bones in the front flipper of a whale are homologous to the bones in the human arm, though one is specialized for swimming and the other climbing. These structures are not analogous. The wings of a bee and the wings of a bird are analogous but not homologous, both specialized for flying but of completely different biological arrangement. Some structures are both analogous and homologous: the wings of a bird and the wings of a bat are both homologous and analogous, both used for flight and both with a similar biological arrangement. Scientists must determine which type of similarity a feature exhibits to decipher the phylogeny of the organisms being studied.
Analogous structures are often caused by convergent evolution of structures used for similar functions. For example, there are many different groups of unrelated organisms that photosynthesize. Plants are one lineage of photosynthetic organisms, whose ancestors are shared with the green and red algae. The brown algae have a completely different evolutionary history and do not share a common ancestor with plants (they are more closely related to water molds). However, many brown algae form flat, leaf-like structures similar to plants, as both groups use these structures for photosynthesis. Many brown algae, such as the kelps, also form stem- and root-like structures (see Figure \(\PageIndex{4}\)).
Molecular Comparisons
With the advancement of DNA technology, the area of molecular systematics , which describes the use of information on the molecular level including DNA analysis, has blossomed. New computer programs not only confirm many earlier classified organisms, but also uncover previously made errors. As with physical characteristics, even the DNA sequence can be tricky to read in some cases. For some situations, two very closely related organisms can appear unrelated if a mutation occurred that caused a shift in the genetic code. An insertion or deletion mutation would move each nucleotide base over one place, causing two similar codes to appear unrelated.
Sometimes two segments of DNA code in distantly related organisms randomly share a high percentage of bases in the same locations, causing these organisms to appear closely related when they are not. For both of these situations, computer technologies have been developed to help identify the actual relationships, and, ultimately, the coupled use of both morphologic and molecular information is more effective in determining phylogeny.
Why does phylogeny matter? Evolutionary biologists could list many reasons why understanding phylogeny is important to everyday life in human society. For botanists, phylogeny acts as a guide to discovering new plants that can be used to benefit people. Think of all the ways humans use plants—food, medicine, and clothing are a few examples. If a plant contains a compound that is effective in treating cancer, scientists might want to examine all of the relatives of that plant for other useful drugs.
A research team in China identified a segment of DNA thought to be common to some medicinal plants in the family Fabaceae (the legume family) and worked to identify which species had this segment (Figure \(\PageIndex{6}\)). After testing plant species in this family, the team found a DNA marker (a known location on a chromosome that enabled them to identify the species) present. Then, using the DNA to uncover phylogenetic relationships, the team could identify whether a newly discovered plant was in this family and assess its potential medicinal properties.
Building Phylogenetic Trees
How do scientists construct phylogenetic trees? After the homologous and analogous traits are sorted, scientists often organize the homologous traits using a system called cladistics . This system sorts organisms into clades : groups of organisms that descended from a single ancestor. For example, in Figure \(\PageIndex{7}\), all of the organisms in the orange region evolved from a single ancestor that had amniotic eggs. Consequently, all of these organisms also have amniotic eggs and make a single clade, also called a monophyletic group . Clades must include all of the descendants from a branch point.
Clades can vary in size depending on which branch point is being referenced. The important factor is that all of the organisms in the clade or monophyletic group stem from a single point on the tree. This can be remembered because monophyletic breaks down into “mono,” meaning one, and “phyletic,” meaning evolutionary relationship. Figure \(\PageIndex{8}\) shows various examples of clades. Notice how each clade comes from a single point, whereas the non-clade groups show branches that do not share a single point.
Phylogenetic trees can be constructed by scoring similarities and differences between the taxa of interest (check out this supplementary video to see how it is done). These traits can be morphological or developmental features (Figure \(\PageIndex{7}\)) or genetic traits called single nucleotide polymorphisms (SNPs, or snips, for short). Taxa with the most similarities are placed into the same clade.
Shared Characteristics
Organisms evolve from common ancestors and then diversify. Scientists use the phrase “descent with modification” because even though related organisms have many of the same characteristics and genetic codes, changes occur. This pattern repeats over and over as one goes through the phylogenetic tree of life:
- A change in the genetic makeup of an organism leads to a new trait which becomes prevalent in the group.
- Many organisms descend from this point and have this trait.
- New variations continue to arise: some are adaptive and persist, leading to new traits.
- With new traits, a new branch point is determined (go back to step 1 and repeat).
If a characteristic is found in the ancestor of a group, it is considered a shared ancestral character because all of the organisms in the taxon or clade have that trait. The vertebrate in Figure \(\PageIndex{7}\) is a shared ancestral character. Now consider the amniotic egg characteristic in the same figure. Only some of the organisms in Figure \(\PageIndex{7}\) have this trait, and to those that do, it is called a shared derived character because this trait derived at some point but does not include all of the ancestors in the tree.
The tricky aspect to shared ancestral and shared derived characters is the fact that these terms are relative. The same trait can be considered one or the other depending on the particular diagram being used. Returning to Figure \(\PageIndex{8}\), note that the amniotic egg is a shared ancestral character for the Amniota clade, while having hair is a shared derived character for some organisms in this group. These terms help scientists distinguish between clades in the building of phylogenetic trees.
Choosing the Right Relationships
Imagine being the person responsible for organizing all of the items in a department store properly—an overwhelming task. Organizing the evolutionary relationships of all life on Earth proves much more difficult: scientists must span enormous blocks of time and work with information from long-extinct organisms. Trying to decipher the proper connections, especially given the presence of homologies and analogies, makes the task of building an accurate tree of life extraordinarily difficult. Add to that the advancement of DNA technology, which now provides large quantities of genetic sequences to be used and analyzed. Taxonomy is a subjective discipline: many organisms have more than one connection to each other, so each taxonomist will decide the order of connections.
To aid in the tremendous task of describing phylogenies accurately, scientists often use a concept called maximum parsimony. Maximum parsimony is a principles that assumes the fewest evolutionary events occurred in a given phylogeny. This is also called Ockham's razer - that we should also select the simplest hypothesis that explains the data. Maximum likelihood , another principle used when constructing phylogenies, suggests that the most likely sequence of evolutionary events most likely occured.
For example, if you saw a friend who was wearing a blue shirt, then saw them again in the evening and they were still wearing that blue shirt, you'd probably assume that they had been wearing that same blue shirt all day. However, it is possible that they went home, changed, and changed back or changed into a shirt that looks very similar. It is just less likely, and so we often assume the former.
For scientists deciphering evolutionary pathways, the same idea is used: the pathway of evolution probably includes the fewest major events that coincide with the evidence at hand. Starting with all of the homologous traits in a group of organisms, scientists look for the most obvious and simple order of evolutionary events that led to the occurrence of those traits.
These tools and concepts are only a few of the strategies scientists use to tackle the task of revealing the evolutionary history of life on Earth. Recently, newer technologies have uncovered surprising discoveries with unexpected relationships, such as the fact that people seem to be more closely related to fungi than fungi are to plants. Sound unbelievable? As the information about DNA sequences grows, scientists will become closer to mapping the evolutionary history of all life on Earth.
Summary
To build phylogenetic trees, scientists must collect accurate information that allows them to make evolutionary connections between organisms. Using morphologic and molecular data, scientists work to identify homologous characteristics and genes. Similarities between organisms can stem either from shared evolutionary history (homologies) or from separate evolutionary paths (analogies). Newer technologies can be used to help distinguish homologies from analogies. After homologous information is identified, scientists use cladistics to organize these events as a means to determine an evolutionary timeline. Scientists apply the principles of maximum parsimony and maximum likelihood, which state that the order of events probably occurred in the most obvious and simple way with the least amount of steps and that the the most likely sequence of evolutionary events probably occured. For evolutionary events, this would be the path with the least number of major divergences that correlate with the evidence.
Contributors and Attributions
Curated and authored by Maria Morrow using the following sources:
- 20.2 Determining Evolutionary Relationships from Biology by OpenStax (licensed CC-BY ). Access for free at openstax.org .


7.8: Chapter 7 Homework Problems
A car with an initial velocity of 30 m/s accelerates at a constant rate of 12 m/s² . Find the time required for the car to reach a speed of 60 m/s, and the distance traveled during this time.
- Solution
-
Time = \(2.5 \, s\)
Distance = \(112.5 \, m\)
A car traveling at 60 miles per hour approaches a fallen log in the road 400 feet away. Assuming the driver immediately slams on the brakes, what is the required rate of deceleration needed to assure the driver does not hit the log?
- Solution
-
Minimum acceleration: \(-9.68 \, ft/s^2\)
A train experiences the acceleration over time detailed below. Draw the velocity-time and position-time diagrams with all key points and equations labeled, and determine the total distance traveled by the train.
- Solution
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Total distance = \(4950 \, m\), plus v-t and s-t diagrams
As a roller coaster cart comes into the gate at the end of the ride, it goes through two sets of brakes. The cart's velocity over time is shown in the graph below. Draw the acceleration-time and position-time diagrams with all key points and equations labeled. Determine the total distance the cart travels during this seven-second period.
- Solution
-
Total distance = \(25.5 \, ft\), plus a-t and s-t diagrams.
A tank fires a round at a 30-degree angle with a muzzle velocity of 600 m/s. The round is expected to hit a mountainside one kilometer away. The mountainside also has an average angle of 30 degrees. How far up the mountainside will the round be expected to travel before hitting the ground \((d)\) if we ignore air resistance?
- Solution
-
\(d = 5.37 \, km\)
A plane with a current speed of 600 ft/s is increasing in speed while also making a turn. The acceleration is measured at 40 ft/s² at an angle 35° from its current heading. Based on this information, determine the rate at which the plane is increasing its speed (tangential acceleration) and the radius of the turn for the plane.
- Solution
-
\(a_t = 32.77 \, ft/s^2\)
\(r = 15,690 \, ft\)
A radar station is tracking a rocket with a speed of 400 m/s and an acceleration of 3 m/s² in the direction shown below. The rocket is 3.6 km away (\(r\) = 3600 m) at an angle of 25°. What would you expect \(\dot{r}\), \(\ddot{r}\), \(\dot{\theta}\), and \(\ddot{\theta}\) to be?
- Solution
-
\(\dot{r} = 282.8 \,\, m/s, \, \ddot{r} = 24.34 \,\, m/s^2\)
\(\dot{\theta} = 0.0786 \,\, rad/s, \, \ddot{\theta} \,\, -0.01176 \, rad/s^2\)
The pulley system below is being used to lift a heavy load. Assuming the end of the cable is being pulled at a velocity of 2 ft/s, what is the expected upwards velocity of the load?
- Solution
-
\(v_L = 0.5 \, ft/s\)
A cable is anchored at A, goes around a pulley on a movable collar at B, and finally goes around a pulley at C as shown below. If the end of the rope is pulled with a velocity of 0.5 m/s, what is the expected velocity of the collar at this instant?
- Solution
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\(v_B = 0.3 \, m/s\)
You are driving at a velocity of 90 ft/s in the rain while you notice that the rain is hitting your car at an angle 35° from the vertical, from your perspective. Assuming the rain is actually coming straight down (when observed by a stationary person), what is the velocity of the rain with respect to the ground?
- Solution
-
\(v_r = 128.5 \, ft/s\)


2.7: Claudius Ptolemy
Another ancient Greek astronomer and philosopher, Claudius Ptolemy (100-170 AD), developed a Geocentric Solar System which placed the “stellar” universe on a crystal sphere. Earth stood still (didn’t rotate) and the Sun orbited Earth, producing our day and night cycles. To account for the retrograde of the planets, Ptolemy used looping small circles called epicycles on the orbits. It was an ingenious system accepted, as Law… except a Geocentric Universe was wrong!Even though Ptolemy was Greek, he was born in Egypt. All of his observations and work was done from Alexandria, Egypt. He was also a geographer and mathematician, and Ptolemy’s “Almagest” (1515) is one of the most influential scientific texts of all times.
If Ptolemy’s Geocentric Universe is incorrect, why do we see Retrograde Motion? Each planet orbits the Sun at a different velocity; the closer the planet to the Sun, the faster it orbits. Earth catches up then passes planets further away from the Sun, giving the illusion that the planet is moving backwards for a while. The planet does retrograde, but due to the two bodies’ orbital motions.
The correct solution would ultimately come nearly 1,500 years later. However, the Geocentric Solar System was deemed Scientific Law – and in some cases Church Law; no one could challenge the Geocentric Solar System until overwhelming evidence made accepting it impossible.


4.6: Non-Membrane Lipid Assemblies (Micelles)
Amphipathic compounds (detergents) are a unique set of molecules with the ability of manipulation (distortion or formation) of the hydrophobic-hydrophilic interactions in biological samples. Detergents in an aqueous solution self-associate to colloid particles. The formation of the colloidal aggregates by detergents are termed micelles 1 . In research micelle-forming detergents provide an amphipathic environment that can mimic lipid bilayers, be used to lyse cells (release soluble proteins), solubilize membrane proteins and lipids, and control protein crystallization.
Detergents and Critical Micelles Concentration
As mentioned above detergents are amphipathic molecules (Figure \(\PageIndex{1}\)), which are composed of a hydrophilic head group (polar) and a hydrophobic tail (non-polar). The hydrophilic head group detergents can be either ionic (charged anion or cation), nonionic (uncharged), or zwitterionic (containing both positive and negative charged components to have a net zero charge).
The hydrophobic tail is an acyl chain (a long chain of aliphatic hydrocarbons, aka a carbon chain with hydrogen side groups). Its amphipathic properties allow detergents to dissolve both water and oil soluble compounds, such as soap 2 . In soap, particles insoluble in water (oil/fat) become associated with the hydrophobic tail of a micelle (Figure \(\PageIndex{2}\)), shielding the insoluble particles from water, making it soluble. Detergents at low concentration in aqueous solution form a monolayer at the air-liquid interface. The detergents monomers can then begin to self-assemble into aggregates at and above the critical micelle concentration 3 (CMC) into structures called micelles (Figure \(\PageIndex{2}\)). The viscosity of micelle core was found to be 17-50cP (cP: centipoise) by depolarization study of a fluorescence probe 4 . Thus, the interior is liquid like. But in some case, the interior is found to be more solid-like, with viscous rising to 151 cP. Basic micelles are generally described as roughly spherical (Figure \(\PageIndex{2}\)A) with a separation of hydrophilic and hydrophobic parts.
Depending on the structure and physicochemical conditions, viz,. temperature, the presence of electrolytes, the self-aggregates structures can also be cylindrical (Figure \(\PageIndex{2}\)B) or worm-like (Figure \(\PageIndex{2}\)C). The detergent monomers bury the nonpolar tails by orienting them inward to avoid water contact and orienting the polar head groups outward to interact with the water. In detergents with more than one hydrophobic chain, similar to natural occurring lipids, the formation of cylindrical micelle may occur. The cylindrical micelle can then span into a two dimensions forming a bilayer.
Below the CMC, an increase of detergent will lower the surface tension while raising the osmotic pressure of the solution (Figure \(\PageIndex{4}\)) 5 . This correlates to the lipids in the solution gathering almost exclusively at the air-water interface as shown below. At the CMC surface tension has been minimized to the greatest possible extent corresponding to the lipids fully saturating the air-water interface so that the entire surface is now a continuous lipid layer.  Thus the excess lipids will be forced into the water and will form micelles to protect their hydrophobic tails, which will then be able to dissolve previously insoluble compounds (like grease). The surface saturation process follows Langmuir (saturation) kinetics and can be described using a Langmuir isotherm.
Micelle formation can be described by the Gibbs adsorption isotherm 6 . The number of monomer detergents “n” to form micelles is called aggregation number and is characteristic of the surfactant molecule. Therefore, micellization can be described by an equilibrium (Figure \(\PageIndex{5}\)) expression. With an equilibrium constant, K m =[Z m ]/[Z] m . A unitary free energy ∆G m ° for transfer of a single amphiphile from aqueous solution to a micelle of size m . The free energy expression can be calculated by replacing RT ln K m by - m ∆G m °, with concentrations expressed in mole fraction units.  Equation 1 can be considered to be micelle size distribution function, giving X m as a function of m at any given value of X 1 . The cooperatively of micelle formation is reflected in the term m ln X 1 , and limits the value of X 1 to a narrow range close to the CMC if reasonable values of X m are to be obtained.
Over 70 types of methods have been deployed to determining the CMC from 1962-2010. Such as spectroscopic measurements (fluorescence probe, absorbance dye), electrochemical measurement (electrophoresis, capillary electrophoresis, conductimetric), surface tension measurements (contact angle measurements), optical measures (light scattering, optical fibers, refractro-metric), and many others 7 . Yet, the most common method is surface tension. This method determines the surface tension of solution towards several different concentrations. The turning points of a plot of the surface tension against log[C] (C: concentrations) graph is the CMC. Surface tension method commonly used because it’s simple and convenient.
Research Applications
Detergents are crucial for the solubilization, purification, and crystallization processes needed for membrane protein structure determination 6 . Detergents are often used to solubilize important membrane proteins by generating a water-soluble protein-detergent-lipid complex (Figure \(\PageIndex{6}\) a). The detergents mimic the lipid membrane by surrounding the hydrophobic region of the integral membrane protein and leaving the hydrophilic region oriented toward the water. Maltosides and glucosides two of the most common used detergents for membrane protein crystallography, although there are is still a large variety of classes of detergents. Therefore, it's common to do a screening to determine the most suitable detergent for the desired target protein. For each detergent, varieties of hydrocarbon tail length are commonly available, allowing for fine tuning the size and stability of the protein-detergent-lipid complex.
Once the integral membrane protein is solubilized and purified, it’s necessary to concentrate (via. centrifugation and dialysis) to a supersaturated solution for crystallization to be successful. While concentrating it's important to maintain the CMC to ensure free detergent micelles and retain the protein-detergent-lipid complex. If CMC is not retained, the integral membrane protein will aggregate out of solution. The detergent used during solubilization may be the same used while crystallization but is most commonly changed or an additive detergent is added. There are several physicochemical parameters to consider besides detergents for the crystallizing integral membrane proteins, such as buffers, pH, precipitants, salts, additives, and many others 8 . Over the past few years there has been an exponential increase of integral membrane protein structures published in the Protein Data Bank and many unique insights have been provided into successful conditions for membrane protein crystallization (Figure \(\PageIndex{7}\)).
Reference
- McBain, J. B. Trans Faraday Soc, 1913, 9, 93-107
- Wennerstrom, H.; Lindman, B. Physics Reports, 1997, 52, 1-86
- Ruckenstein, E.; Nagarajan, R journal of Colloid and Interface Science, 1976, 57, 388-390
- Zoller, U.; Broze, G. Handbook of detergents; Marcel Dekker: New York, 1999
- Chakrabory, T. el alt. Arabian Hournal of Chemistry, 2011, 4, 265-270
- Tanford, C. Proc. Nat. Acad. Sci. USA, 1974, 71, 1811-15
- Newby, Z. E. R. el. Alt. Nature Protocols, 2009, 4, 619-638
- Newstead, S.; Ferrandon, S.; Iwata, S. Protein Sci., 2008, 17, 466-476
- Moraes, I. el alt. Biochemistry & Biophysical, 2014, 1838, 78-87Moraes, I. el alt. Biochemistry & Biophysical, 2014, 1838, 78-87


4.1: Mitosis and the Cell Cycle
Mitosis is a process of equal cell division, where each of the new cells receives the same number of chromosomes as the original cell. Mitosis does not change the cells’ genotype. The goal of mitosis is to distribute pre-combined genetic material equally. Actually, mitosis is a kind of karyokinesis , or splitting of the nucleus, as opposed to cytokinesis , which is the splitting of the whole cell. Karyokinesis and cytokinesis are parts of the cell cycle .
All prokaryotes (Monera) have a simple cell division called “binary fission”. DNA duplicates (replication), segregates and then cell splits in two (Figure \(\PageIndex{1}\)).
Eukaryotes have much more DNA than prokaryotes. This is why their cell division is more complicated. There are four stages: prophase, metaphase, anaphase, and telophase. Prophase is the longest, nucleus disintegrates (except some protists like fungi) and the DNA is super-spiralized into chromosomes (“archived”). In metaphase , the chromosomes go to the cell equator, and every “double”, “X-like” chromosome is then split in two halves which schematically can be shown as
\[X \rightarrow I + I\]
In anaphase , microtubules move these \(I\)-like chromosomes to different poles of the cell. In telophase , the endoplasmic reticulum will form nuclear envelopes and DNA despiralizes (Figure \(\PageIndex{2}\)).
Figure \(\PageIndex{1}\) Binary fission of prokaryotes.
When mitosis is over, cell starts to divide (cytokinesis). Plant\(_2\) cells use vesicles to form the border whereas many protists and animals form a constriction which finally separates two cells. Normally, chloroplasts and mitochodria are equally distributed between daughter cells along with the other cell content. Chloroplasts and mitochondria may also independently divide in “bacterial” (binary fission) way.
Mitosis is the part of the bigger cell cycle (Figure 4.2.1). Cell cycle includes pre-synthetic stage , synthetic stage , post-synthetic stage (they are parts of interphase ), karyokinesis (= mitosis) and finally cytokinesis. Apart from mitosis and cytokinesis, the most important stage of cell cycle is the synthetic stage ( S-stage ) when every DNA molecule (despiralized chromosome) duplicates: \[I \rightarrow X\]
To simplify understanding of these numerous stages, one could use the following scheme. Cell cycle here has three main phases, and mitosis has four subphases:
Figure \(\PageIndex{2}\) Principal scheme of mitosis.