15.5: Quantitative Trait Locus (QTL) Analysis
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- Ying Liu
- City College of San Francisco
Most of the phenotypic traits commonly used in introductory genetics are qualitative, meaning that the phenotype exists in only two (or possibly a few more) discrete, alternative forms, such as either purple or white flowers, or red or white eyes. These qualitative traits are therefore said to exhibit discrete variation . On the other hand, many interesting and important traits exhibit continuous variation ; these exhibit a continuous range of phenotypes that are usually measured quantitatively, such as intelligence, body mass, blood pressure in animals (including humans), and yield, water use, or vitamin content in crops. Traits with continuous variation are often complex, and do not show the simple Mendelian segregation ratios (e.g. 3:1) observed with some qualitative traits. Many complex traits are also influenced heavily by the environment. Nevertheless, complex traits can often be shown to have a component that is heritable, and which must therefore involve one or more genes.
How can genes, which are inherited (in the case of a diploid) as at most two variants each, explain the wide range of continuous variation observed for many traits? The lack of an immediately obvious explanation to this question was one of the early objections to Mendel's explanation of the mechanisms of heredity. However, upon further consideration, it becomes clear that the more loci that contribute to trait, the more phenotypic classes may be observed for that trait (Figure \(\PageIndex{1}\)).
If the number of phenotypic classes is sufficiently large (as with three or more loci), individual classes may become indistinguishable from each other (particularly when environmental effects are included), and the phenotype appears as a continuous variation (Figure \(\PageIndex{2}\)). Thus, quantitative traits are sometimes called polygenic traits , because it is assumed that their phenotypes are controlled by the combined activity of many genes. Note that this does not imply that each of the individual genes has an equal influence on a polygenic trait – some may have major effect, while others only minor. Furthermore, any single gene may influence more than one trait, whether these traits are quantitative or qualitative traits.
We can use molecular markers to identify at least some of the genes (those with a major influence) that affect a given quantitative trait. This is essentially an extension of the mapping techniques we have already considered for discrete traits. A QTL mapping experiment will ideally start with two pure-breeding lines that differ greatly from each other in respect to one or more quantitative traits (Figure \(\PageIndex{3}\)). The parents and all of their progeny should be raised under as close to the same environmental conditions as possible, to ensure that observed variation is due to genetic rather than external environmental factors. These parental lines must also be polymorphic for a large number of molecular loci, meaning that they must have different alleles from each other at hundreds of loci. The parental lines are crossed, and then this F 1 individual, in which recombination between parental chromosomes has occurred is self-fertilized (or back-crossed). Because of recombination (both crossing over and independent assortment), each of the F 2 individuals will contain a different combination of molecular markers, and also a different combination of alleles for the genes that control the quantitative trait of interest (Table \(\PageIndex{1}\)).


5.4: Music of Wolfgang Amadeus Mozart (1756-1791)
Wolfgang Amadeus Mozart (b. 1756-91) was born in Salzburg, Austria. His father, Leopold Mozart, was an accomplished violinist of the Archbishop of Salzburg’s court. Additionally, Leopold had written a respected book on the playing of the violin. At a very young age, Wolfgang began his career as a composer and performer. A prodigy, his talent far exceeded any in music, past his contemporaries. He began writing music prior to the age of five. At the age of six, Wolfgang performed in the court of Empress Maria Theresa.
Mozart’s father was quite proud of his children, both being child prodigies. At age seven, Wolfgang, his father, and his sister Maria Anna (nicknamed “Nannerl”) embarked on a tour featuring Wolfgang in London, Munich, and Paris. As was customary at the time, Wolfgang, the son, was promoted and pushed ahead with his musical career by his father. While his sister, the female, grew up traditionally, married, and eventually took care of her father
Leopold in his later years. However, while the two siblings were still performing, these tours occurred from when Wolfgang was between the ages of six and seventeen. The tours, though, were quite demeaning for the young
musical genius in that he was often looked upon as just a superficial genre of entertainment rather than being respected as a musical prodigy. He would often be asked to identify the tonality of a piece while listening to it or asked to sight read and perform with a cloth over his hands while at the piano. Still, the tours allowed young Mozart to accumulate knowledge about musical styles across Europe. As a composer prior to his teens, the young Mozart had already composed religious works, symphonies, solo sonatas, an opera buffa, and
Bastien and Bastienne
, an operetta; in short, he had quickly mastered all the forms of music.
Back in Salzburg, Mozart was very unhappy due to being musically restrained by the restrictions of his patron the Archbishop of Salzburg, Hieronymus von Colloredo. At approximately the age of twenty-five, he moved to Vienna and became a free artist (agent) and pursued other opportunities. Another likely reason for Wolfgang’s ultimate departure to Vienna was to become independent of his father. Though Leopold was well-meaning and had sacrificed a great deal to ensure the future and happiness of his son, he was an overbearing father. Thus at the age of twenty-five, Mozart married Constance Weber. Mozart’s father did not view the marriage favorably and this marriage served as a wedge severing Wolfgang’s close ties to his father.
Wolfgang’s new life in Vienna however was not easy. For almost ten years, he struggled financially unable to find the secure financial environment in which he had grown up. The music patronage system was still the main way for musicians to prosper and thrive: several times, Mozart was considered for patron employment but was not hired. Having hired several other musicians ahead of Mozart, Emperor Joseph II hired Mozart to basically compose dances for the court’s balls. As the tasks were far beneath his musical genius, Mozart was quite bitter about this assignment.
While in Vienna, Mozart relied on his teaching to sustain him and his family. He also relied on the entertainment genre of the concert. He would write piano concertos for annual concerts. Their programs would also include some arias, solo improvisation, and possibly an overture of piece by another composer.
The peak of Mozart’s career success occurred in 1786 with the writing of The Marriage of Figaro (libretto by Lorenza da Ponte) . The opera was a hit in Prague and Vienna. The city of Prague, so impressed with the opera, commissioned another piece by Mozart. Mozart, with da Ponte again as librettist, then composed Don Giovanni. The second opera left the audience somewhat confused. Mozart’s luster and appeal seemed to have passed. As a composer, Mozart was trying to expand the spectrum, or horizons, of the musical world. Therefore, his music sometimes had to be viewed more than once by the audience in order for them to understand and appreciate it. Mozart was pushing the musical envelope beyond the standard entertainment expected by his aristocratic audience, and patrons in general did not appreciate it. In a letter to Mozart, Emperor Joseph II wrote of Don Giovanni that the opera was perhaps better than The Marriage of Figaro but that it did not set well on the pallet of the Viennese. Mozart quickly fired back, responding that the Viennese perhaps needed more time to understand it.
In the final year of his life, Mozart with librettist (actor/poet) Emanuel Schikaneder, wrote a very successful opera for the Viennese theatre, The Magic Flute . The newly acclaimed famous composer was quickly hired to write a piece (as well as attend) the coronation of the new Emperor, Leopold II, as King of Bohemia. The festive opera that Mozart composed for this event was called The Clemency of Ti- tus. Its audience, overly indulged and exhausted from the coronation, was not impressed with Mozart’s work. Mozart returned home depressed and broken, and began working on a Requiem, which, coincidentally, would be his last composition.
The Requiem was commissioned by a count who intended to pass the work off as his own. Mozart’s health failed shortly after receiving this commission and the composer died, just before his thirty sixth birthday, before completing the piece. Mozart’s favorite student, Franz Xaver Sűssmayr, completed the mass from Mozart’s sketch scores, with some insertions of his own, while rumors spread that Mozart was possibly poisoned by another contemporary composer. In debt at the time of his death, Mozart was given a common burial. As one commentator wrote:
Thus, “without a note of music, forsaken by all he held dear, the remains of this Prince of Harmony were committed to the earth, not even in a grave of their own, but in the common fosse affected to the indiscriminate sepulture of homeless mendicants and nameless waifs.”
footnote: 2 Crowest , “An Estimate of Mozart,” The Eclectic Magazine: Foreign Literature Vol . 55; Vol 118 P. 464
5.6.1 Overview of Mozart’s Music
From Mozart’s youth, his musical intellect and capability were unmatched. His contemporaries often noted that Mozart seemed to have already heard, edited, listened to, and visualized entire musical works in his mind before raising a pen to com- pose them on paper. When he took pen in hand, he would basically transcribe the work in his head onto the manuscript paper. Observers also said that Mozart could listen and carry on conversations with others while transcribing his music to paper.
Mozart was musically very prolific in his short life. He composed operas, church music, a Requiem, string quartets, string quintets, mixed quintets and quartets, concertos, piano sonatas, and many lighter chamber pieces (such as divertimentos), including his superb
A Little Night Music
(
Eine kleine Nachtmusik).
His violin and piano sonatas are among the best ever written both in form and emotional content. Six of his quartets were dedicated to Haydn, whose influence Mozart celebrated in their preface.
Mozart additionally wrote exceptional keyboard music, particularly since he was respected as one of the finest pianists of the Classical period. He loved the instrument dearly and wrote many solo works, as well as more than twenty pia- no concertos for piano and orchestra, thus contributing greatly to the concerto’s popularity as an acceptable medium. Many of these concerti were premiered at Mozart’s annual public fundraising concerts. Of his many piano solo pieces, the Fantasia in C minor K 475 and the Sonata (in C minor) K 457 are representative of his most famous.
And Mozart composed more than forty symphonies, the writing of which extend- ed across his entire career. He was known for the full and rich instrumentation and voicing of his symphonies. His conveying of emotion and mood are especially portrayed in these works. His final six symphonies, written in the last decade of his life, are the most artistically self-motivated independent of art patronage and supervision that might stifle creativity. Mozart’s late and great symphonies include the Haffner in D (1782), the Linz in C (1783), the Prague in D (1786), and his last three symphonies composed in 1788. Mozart’s final symphony probably was not performed prior to his death. In addition to the symphonies and piano concertos, Mozart composed other major instrumental works for clarinet, violin and French horn in concertos.
Focus Composition:
Mozart,
Don Giovanni
[1787]
The plot for
Don Giovanni
may be found at:
http://www.geocities.jp/wakaru_opera...ngiovanni.html
|
Listening Guide For audio, go to: http://semprelibera.altervista.org/w...rt/don-giovan- ni/deh-vieni-alla-finestra/ |
| Composer: Wolfgang Amadeus Mozart |
| Librettist: Lorenzo Da Ponte |
| Composition: Deh, vieni alla finestra, Testo (Aria) from Don Giovanni , in Italian |
| Date: 1787, First performed October 29, 1787 |
| Genre: Aria for baritone voice |
|
Form: binary |
|
Nature of Text: Originally in Italian Translation from Italian to English available at: http://semprelibera.altervista.org/w...rt/don-giovan- ni/deh-vieni-alla-finestra/ |
|
Performing Forces: Baritone and Classical Orchestra |
|
What we want you to remember about this composition: This is a really a beautiful love-song where the womanizer Don Giovanni tries to woo Elvira’s maid. The piece in D major begins in a 6/8 meter. The musical scoring includes a mandolin in the orchestra with light plucked accompaniments from the violins which supplement the feel of the mandolin. The atmosphere created by the aria tends to convince the audience of a heartfelt personal love and attraction The piece is written in a way to present a very light secular style canzonetta in binary form, which tends to help capture the playfulness of the Don Giovanni character. |
|
Other things to listen for: This piece could very easily be used in a contemporary opera or musical. |
Focus Composition:
Mozart, Piano Concerto No. 20 in D Minor, K. 466 [1785]
Classical composers like Mozart took the Baroque concerto for soloist and orchestra and expanded it into a much larger form. Like Vivaldi’s concertos, Mozart’s concertos were generally in three movements, with fast, slow, and fast tempos, respectively. The first movements of Mozart’s concertos also featured the alternation of ritornello sections and solo sections, like we heard in the concerto by Vivaldi in the previous chapter. Mozart, however, also applied the dynamics of sonata form to the first movements of his concertos, resulting in a form that we now call double exposition form . In double exposition form, the first statement of the exposition was assigned to the orchestra, and the second statement of the exposition was assigned to the soloist with orchestral accompaniment in the background. The alternation between orchestra and soloist sections continues in the development and recapitulation. Near the end of the recapitulation and during the final orchestra exposition, the orchestra holds a suspenseful chord, at which point the soloist enters and the orchestra drops out. For a minute or longer, the soloist plays a cadenza. A cadenza is a solo section that sounds improvised, though sometimes composers or performers wrote these ahead of time, as is the case with this concerto (the recording cited by the text features a cadenza that was written by Beethoven). A cadenza normally ends with the pianist sustaining a chord (often with a trill) signaling the orchestra’s final entrance in the piece, playing the last phrase of the ritornello to bring the movement to a conclusion. You can see an example how ritornello form and sonata form were merged in a double exposition form:
|
Ritornello Form |
Ritornello |
Solo Section |
Ritornello |
Solo Section |
Ritornello |
Solo Section |
Ritornello (including cadenza) |
| Sonata |
[Orchestral] EXPOSITION |
[Solo] EXPOSITION |
DEVELOPMENT |
RECAPITULATION |
The first movement of Mozart’s Concerto No. 20 in D minor, K. 466 is a good example of double exposition form. As the program annotator for the Burgess Hill Symphony Orchestra puts it:
The orchestral tutti opens with the D minor first subject. This suggests dark threatening skies, emphasised [sic] by syncopation and dynamic contrasts. For a brief while the louring mood is relieved by the second subject, which has modulated into F major. The solo piano makes its entry with a plaintive new theme back in D minor - a little theme that refuses to go away. As the development progresses Mozart reviews all his themes, and press- es onwards to a rather stormy climax leading to the cadenza. Mozart left no written cadenzas for this work. When the score came into the hands of Beethoven, he immediately decided that such a dramatic movement as this sorely needed one. He promptly sat down and wrote the shadowed bril- liance that will be played by today’s soloist. (3. footnote)
footnote: 3 “Mozart: Piano Concerto no 20 in D Minor.” Burgess Hill Symphony Orchestra. Burgess Hill Sympho- ny Orchestra, n.d. Web. 18 December 2015
You might also listen to and take notes on to the lecture recital about the first movement of the concerto at:
http://www.bbc.co.uk/programmes/p01yh30s .
|
Listening Guide For audio, go to: https://www.youtube.com/watch?v=UGld...list=RDUGldgW- 6mDnY#t=517 Martha Argerich, piano, with the Orchestra di Padova e del Veneto, conducted by Alexandre Rabinovitch |
| Composer: Wolfgang Amadeus Mozart |
|
Composition : Piano Concerto No. 20 in D minor, K466, First Movement 1. Allegro (Cadenzas by Beethoven) |
| Date: 1785 |
| Genre: Piano Concerto |
| Form: Double exposition form |
| Performing Forces: piano soloist and Classical orchestra |
|
What we want you to remember about this composition:
|
| Timing | Performing Forces, Melody, and Texture | Text and Form |
| Orchestra alone, in a minor key Orchestral Exposition throughout. | Orchestral Exposition | |
|
2:18 |
Spotlight on the solo piano, with some accompaniment from the orchestra; the key modulates to F majors. |
Solo Exposition |
|
5:05 |
Focus switches back and forth from solo piano and the orchestra while the music develops the themes, motives, and harmonies from the exposition. |
Development |
|
7:23 |
Back in D minor with the first themes from the exposition. Frequent alternation between the soloist and orchestra as they share the themes. |
Recapitulation: Ritornello & solo sections |
|
10:17 |
Orchestra begins the final ritornello and then sustains a suspenseful chord. |
Recapitulation: Final ritornello |
|
10:35 |
The pianist plays in a improvisatory manner, shifting suddenly between different motives, tempos, and styles. Listen for many ornaments such as trills and rapid and virtuosic scales. After a final, extended series of trills (starting at 12:17), the orchestra returns for... |
Recapitulation: Cadenza |
|
12:30 |
the final phrase of the ritornello and movement (which ends in D minor). |
Recapitulation: Ritornello con- cludes |
Focus Composition:
Mozart, Symphony No. 41 in C Major, K. 551 (1788)
Like Haydn, Mozart also wrote symphonies. Mozart’s final symphony, the Symphony No. 41 in major, K. 551 is one of his greatest compositions. It very quickly acquired the nickname “Jupiter,” a reference to the Greek god, perhaps because of its grand scale and use of complex musical techniques. For example, Mozart introduced more modulations and key changes in this piece than was typical. The symphony opens with a first movement in sonata form with an exposition, development, and recapitulation. Listen to the first movement with the listening guide below.
You can also find an animated listening guide providing guidance to various sections and identifying the different musical elements as they are introduced at:
https://www.youtube.com/watch?v=YgUf2eMdi28 .
|
Listening Guide For audio, go to: www.youtube.com/watch?v=zK5295yEQMQ (Video of live orchestral performance); The Chamber Orchestra of Europe, conducted by Nikolaus Harnoncourt |
| Composer: Wolfgang Amadeus Mozart |
| Composition: Symphony No. 41 in C Major, K. 551 — 1st Movement, Allegro Vivace |
| Date: 1788 |
| Genre: Symphony |
| Form: Sonata form |
| Performing Forces: Classical orchestra |
|
What we want you to remember about this composition:
|
||
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Other things to listen for:
|
||
|
I: Allegro Vivace Time index follows the performance linked below: |
||
|
Timing |
Performing Forces, Melody, and Texture |
Text and Form |
|
0:00 |
Full orchestra.
|
EXPOSITION: Opening triplet motive |
|
0:18 |
The forte dynamic continues, with emphasis on dotted rhythms. Winds perform opening melody followed by staccato string answer; Full bowed motion in strings. |
First theme in C major |
|
1:30 |
Motive of three notes continues; Soft lyrical theme with moving ornamentation in accompaniment. |
Pause followed by second theme of the exposition |
|
2:08 |
Sudden forte dynamic. Energy increases until sudden softening to third pause;
|
Second Pause followed by transition to build tension |
|
2:41 |
Theme played in the strings with grace notes used.
|
After the third pause, the third theme is introduced |
| 3:12 | The entire exposition repeats itself |
|
6:21 |
Transition played by flute, oboe and bassoon followed by third theme in strings;
|
DEVELOPMENT SECTION: Transition to third theme |
|
6:40 |
Modulations in this section add to the instability of the section; Starts like the exposition but with repetition in different keys. |
Modulation to the minor |
|
7:21 |
Slight introduction of third theme motif;
|
Implied recapitulation: “Tran- sition” |
|
8:05 |
Now started by the oboes and bas- soons;
|
Recapitulation in original key: First theme |
| 9:29 | Pause followed by second theme | |
| 10:39 |
After a sudden piano articulation of the SSSL motive, suddenly ends in a loud and bombastic manner: Fate threatens; Re-emphasizes C minor. |
Third Theme |
| 10:53 | Closing material similar to exposition | |
| 11:09 | Full orchestra at forte dynamic. | Closing cadence for the movement |
It is impossible to know how many more operas and symphonies Mozart would have written had he lived into his forties, fifties, or even sixties. Haydn’s music written after the death of Mozart shows the influence of his younger contemporary, and Beethoven’s early music was also shaped by Mozart’s. In fact, in 1792, a twenty-something Beethoven was sent to Vienna with the expressed purpose of receiving “the spirit of Mozart from the hands of Haydn.”


4.9: Putting It Together- Nonlinear Models
Let’s Summarize
This is what we have learned about exponential models:
The general form of an exponential model is y = C · b x .
- Exponential models are nonlinear. More specifically, exponential models predict that y increases or decreases by a constant percentage for each 1-unit increase in x .
- C is the initial value . It is the y -value when x = 0. It is also the y -intercept.
-
b
is the
growth factor
or
decay factor
.
b
is always positive.
- If b is greater than 1, b is a growth factor. In this case, the association is positive, and y is increasing. This makes sense because multiplying by a number greater than 1 increases the initial value. From the growth factor, we can determine the percent increase in y for each additional 1-unit increase in x .
- Similarly, if b is greater than 0 and less than 1, b is a decay factor. In this case, the association is negative, and y is decreasing. From the decay factor, we can determine the percentage decrease in y for each additional 1-unit increase in x .
Let’s compare the general form of an exponential model to the general form for a linear model: y = a + bx .
- In the linear model, a is the initial value . It is the y -value when x = 0. It is also the y -intercept.
- b is the slope . From the slope, we can determine the amount and direction the y -value changes for each additional 1-unit increase in x . When b is positive, there is a positive association, and y increases. When b is negative, there is a negative association, and y decreases.
Contributors and Attributions
CC licensed content, Shared previously
- Concepts in Statistics. Provided by : Open Learning Initiative. Located at : http://oli.cmu.edu . License : CC BY: Attribution


6.13: Learning Activities
Learning Activities
(Answers to “Learning Activities” can be found in the ‘”Answer Key'” at the end of the book. Answers to interactive activity elements will be provided within the element as immediate feedback.)
1. A male client has an impairment of cranial nerve II. Specific to this impairment, the nurse would plan to do which of the following to ensure client safety?
- Use loud a tone when speaking to the client
- Test the temperature of the shower water
- Check the temperature of the food prior to eating
- Remove obstacles when ambulating
2. The nurse is performing a mental status examination on a client with confusion.
This test assesses which of the following?
- Cerebral function
- Cerebellar function
- Sensory function
- Intellectual function
Query \(\PageIndex{1}\)
Query \(\PageIndex{2}\)


2.4D: Determining the Research Design
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The research design is the methodology and procedure a researcher follows to answer their sociological question.
Learning Objectives
- Compare and contrast quantitive methods and qualitative methods
Key Points
- Research design defines the study type, research question, hypotheses, variables, and data collection methods. Some examples of research designs include descriptive, correlational, and experimental. Another distinction can be made between quantitative and qualitative methods.
- Sociological research can be conducted via quantitative or qualitative methods. Quantitative methods are useful when a researcher seeks to study large-scale patterns of behavior, while qualitative methods are more effective when dealing with interactions and relationships in detail.
- Quantitative methods include experiments, surveys, and statistical analysis, among others. Qualitative methods include participant observation, interviews, and content analysis.
- An interpretive framework is one that seeks to understand the social world from the perspective of participants.
- Although sociologists often specialize in one approach, many sociologists use a complementary combination of design types and research methods in their research. Even in the same study a researcher may employ multiple methods.
Key Terms
- quantitative methods : Quantitative research refers to the systematic empirical investigation of social phenomena via statistical, mathematical, or computational techniques.
- qualitative methods : Qualitative research is a method of inquiry employed in many different academic disciplines, traditionally in the social sciences, but also in market research and further contexts. Qualitative researchers aim to gather an in-depth understanding of human behavior and the reasons that govern such behavior. The qualitative method investigates the why and how of decision making, not just what, where, and when. Hence, smaller but focused samples are more often needed than large samples.
- scientific method : A method of discovering knowledge about the natural world based in making falsifiable predictions (hypotheses), testing them empirically, and developing peer-reviewed theories that best explain the known data.
A research design encompasses the methodology and procedure employed to conduct scientific research. Although procedures vary from one field of inquiry to another, identifiable features distinguish scientific inquiry from other methods of obtaining knowledge. In general, scientific researchers propose hypotheses as explanations of phenomena, and design research to test these hypotheses via predictions which can be derived from them.
The design of a study defines the study type, research question and hypotheses, independent and dependent variables, and data collection methods. There are many ways to classify research designs, but some examples include descriptive (case studies, surveys), correlational (observational study), semi-experimental (field experiment), experimental (with random assignment), review, and meta-analytic, among others. Another distinction can be made between quantitative methods and qualitative methods.
Quantitative Methods
Quantitative methods are generally useful when a researcher seeks to study large-scale patterns of behavior, while qualitative methods are often more effective when dealing with interactions and relationships in detail. Quantitative methods of sociological research approach social phenomena from the perspective that they can be measured and quantified. For instance, socio-economic status (often referred to by sociologists as SES) can be divided into different groups such as working-class, middle-class, and wealthy, and can be measured using any of a number of variables, such as income and educational attainment.
Qualitative versus Quantitative Methods : These two researchers are debating the relative merits of using qualitative or quantitative methods to study social phenomena such as the learning processes of children.
Qualitative Methods
Qualitative methods are often used to develop a deeper understanding of a particular phenomenon. They also often deliberately give up on quantity, which is necessary for statistical analysis, in order to reach a greater depth in analysis of the phenomenon being studied. While quantitative methods involve experiments, surveys, secondary data analysis, and statistical analysis, qualitatively oriented sociologists tend to employ different methods of data collection and hypothesis testing, including participant observation, interviews, focus groups, content analysis, and historical comparison.
Qualitative sociological research is often associated with an interpretive framework, which is more descriptive or narrative in its findings. In contrast to the scientific method, which follows the hypothesis-testing model in order to find generalizable results, the interpretive framework seeks to understand social worlds from the point of view of participants.
Although sociologists often specialize in one approach, many sociologists use a complementary combination of design types and research methods in their research. Even in the same study a researcher may employ multiple methods.


2.4: Removable Media
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- Ly-Huong T. Pham, Tejal Desai-Naik, Laurie Hammond, & Wael Abdeljabbar
- ASCCC Open Educational Resources Initiative (OERI)
Removable Media
Removable storage has changed greatly over the four decades of PCs. CD-ROM drives have replaced floppy disks , and then they were replaced by USB (Universal Serial Bus) drives. USB (Universal Serial Bus) drives are now standard on all PCs with capacities approaching 512 gigabytes. Speeds have also increased from 480 Megabits in USB 2.0 to 10 Gigabits in USB 3.1. USB devices also use EEPROM technology. Since the USB is a cross-platform technology, it is supported by most operating systems. This helps connect to other devices such as printers, tv’s external hard drives, and the list goes on. “There are now by one count six billion USB devices in the world.” (Johnson, 2019)
Network Connection
When personal computers were first developed, they were stand-alone units, which meant that data was brought into the computer or removed from the computer via removable media, such as the floppy disk. Engineers as early as 1965 saw merit in being able to connect and share information with other computers. The term used was networking as the connections increased to multiple users, it grew to inter-networking. The abbreviated version is now called the internet. In the mid-1980s, organizations began to see the value in connecting computers together via a digital network. Because of this, personal computers needed the ability to connect to these networks. Initially, this was done by adding an expansion card to the computer that enabled the network connection. By the mid-1990s, network ports were standard on most personal computers. The configuration of these ports has evolved over the years, becoming more standardized over time. Today, almost all devices plug into a computer through the use of a USB port. This port type, first introduced in 1996, has increased in its capabilities, both in its data transfer rate and power suppl y .
For a personal computer to be useful, it must have channels for receiving input from the user and channels for delivering output to the user. These input and output devices connect to the computer via various connection ports, which generally are part of the motherboard and are accessible outside the computer case. In early personal computers, specific ports were designed for each type of output device. The configuration of these ports has evolved over the years, becoming more and more standardized over time. Today, almost all devices plug into a computer through the use of a USB port. This port type, first introduced in 1996, has increased in its capabilities, both in its data transfer rate and power supplied.
Bluetooth
Besides USB, some input and output devices connect to the computer via a wireless-technology standard called Bluetooth. Bluetooth was first invented in the 1990s and exchanges data over short distances using radio waves.
Bluetooth generally has a range of 100 to 150 feet. It was not until 1999 that it reached its first general public users. Two devices communicating with Bluetooth must both have a Bluetooth communication chip installed. Bluetooth devices include pairing your phone to your car, computer keyboards, speakers, headsets, and home security, to name just a few.
Input Devices
All personal computers need components that allow the user to input data. Early computers used simply a keyboard to allow the user to enter data or select an item from a menu to run a program. With the advent of the graphical user interface, the mouse became a standard component of a computer. These two components are still the primary input devices to a personal computer, though variations of each have been introduced with varying levels of success over the years. For example, many new devices now use a touch screen as the primary way of entering data. Besides the keyboard and mouse, additional input devices are becoming more common. Scanners allow users to input documents into a computer, either as images or as text. Microphones can be used to record audio or give voice commands. Webcams and other video cameras can be used to record video or participate in a video chat session. The list continues to grow, such as joysticks used for gaming, digital cameras, and touch screens. Smartwatches are wearable compact computers on the wrist. The watch's functionality is similar to the smartphone offering mobile apps and WiFi/Bluetooth connectivity. Specialized watches for health and sports enthusiasts have also emerged, offering counts of steps taken, heart rate, and blood pressure monitoring; a popular brand is Fitbit.
Output Devices
Output devices are essential as well. The most obvious output device is a display, visually representing the state of the computer. In some cases, a personal computer can support multiple displays or be connected to larger-format displays such as a projector or large-screen television. Besides displays, other output devices include speakers for audio output and printers for printed output. 3D printers have changed the way we build toys, tools, homes, and even body parts. The process of 3D printing that differentiates itself from a regular printer is called additive manufacturing.
Additive manufacturing breaks down an object and builds it layer by layer, making three-dimensional objects.
The most popular material used is plastic, but other materials can be used, such as gold and bio-material, to make human parts such as a nose or ear. The 3D printers have proven themselves in many different industries and have offered an inexpensive route for prototyping.
Sidebar: What Hardware Components Contribute to the Speed of My Computer?
A computer's speed is determined by many elements, some related to hardware and some related to software. In hardware, speed is improved by giving the electrons shorter distances to traverse to complete a circuit. Since the first CPU was created in the early 1970s, engineers have constantly worked to figure out how to shrink these circuits and put more and more circuits onto the same chip. And this work has paid off – the speed of computing devices has been continuously improving ever since.
The hardware components that contribute to a personal computer's speed are the CPU, the motherboard, RAM, and the hard disk. In most cases, these items can be replaced with newer, faster components. In the case of RAM, simply adding more RAM can also speed up the computer.
The table below shows how each of these components contributes to the speed of a computer. Besides upgrading hardware, many changes can be made to the software to enhance the computer's speed.
|
Component |
Speed measured by |
Units |
Description |
|---|---|---|---|
|
CPU |
Clock speed |
GHz |
The time it takes to complete a circuit. Memory does affect computer speed. The CPU moves information from the memory while retrieving information from running applications. |
|
Motherboard |
Bus speed |
MHz |
How much data can move across the bus simultaneously. |
|
RAM |
Data transfer rate |
MB/s |
The time it takes for data to be transferred from the memory to the system. |
|
Hard Disk |
Access time |
ms |
The time it takes before the disk can transfer data. |
|
Router |
Data transfer rate |
MBit/s |
The time it takes for data to be transferred from disk to system. |
Reference
Johnson, J. (2019). The unlikely origins of USB, the port that changed everything . FastCompany. Retrieved August 6, 2020, from https://www.fastcompany.com/3060705/an-oral-history-of-the-usb


10.6: Discussion- Compensation and Benefits
Pay equity issues run rampant in the United States. Women, on average, only earn a portion of what a man does, and a minority woman could earn even less yet. Organizations need only look in their own backyards to see the pay gap rearing its ugly head—almost every organization has one.
Discussion Prompt
You’re an HR professional at an organization that thinks it’s paying its women fairly. Still, you want to make sure. Bias and pay discrepancies come in all shapes and sizes, and symptoms of the pay gap could be lurking in the shadows. So, you start doing some research.
Where do you look? What are your plans? Online searches can provide you with a variety of places to look and steps to take to uncover pay gaps at your organization. List two or three different steps that you, as an HR professional, would take to ensure that the company is doing everything it can to ensure pay equity. Provide a quick explanation of each of those plans, if necessary, and share your sources. Once you’ve put together your list and explanation, review the lists of at least two other classmates, and provide them with suggestions.
Grading
Share your opinions below and respond to two of your classmates’ thoughts.
| Criteria | Not Evident | Developing | Exemplary | Points |
|---|---|---|---|---|
| Submit your initial response |
0 pts
No post made |
5 pts
Post is either late or off-topic |
10 pts
Post is made on time and is focused on the prompt |
10 pts |
| Respond to at least two peers’ presentations |
0 pts
No response to peers |
2
pts
Responded to only one peer |
5 pts
Responded to two peers |
5 pts |
| Total: | 15 pts |
Contributors and Attributions
- Discussion: Compensation and Benefits. Authored by : Freedom Learning Group. Provided by : Lumen Learning. License : CC BY: Attribution


6.8: Administering Topical Medications
In this section, we address how to administer topical medication using three distinct delivery methods: transdermal patch; creams, lotions, or ointments; and powder. Always wear gloves and maintain standard precautions when administering topical medications to the skin, mucous membranes, and tissues. Do not touch any preparations to your own skin, and turn your face away from powdered applications. Always clean the skin or wound before applying a new dose of topical medication.
Checklist 53 lists the steps for applying a transdermal patch.
Checklist 53: Applying a Transdermal PatchDisclaimer: Always review and follow your hospital policy regarding this specific skill. |
|||
Safety considerations:
|
|||
Steps |
Additional Information |
||
| 1. Check MAR against doctor’s orders. |
Check that MAR and doctor’s orders are consistent.
Night staff usually complete and verify this check as well. |
||
2. Perform the SEVEN RIGHTS x 3 (must be done with each individual medication):
Med calculation: D/H x S = A (desired dosage/have available x stock = amount prepared) |
The right patient: check that you have the correct patient using two patient identifiers (e.g., name and date of birth).
The right medication (drug): check that you have the correct medication and that it is appropriate for the patient in the current context. The right dose: check that the dose makes sense for the age, size, and condition of the patient. Different dosages may be indicated for different conditions. The right route: check that the route is appropriate for the patient’s current condition. The right time: adhere to the prescribed dose and schedule. The right reason: check that the patient is receiving the medication for the appropriate reason. The right documentation: always verify any unclear or inaccurate documentation prior to administering medications. NEVER document that you have given a medication until you have actually administered it. |
||
3. The label on the medication must be checked for name, dose, and route, and compared with the MAR at three different times:
|
These checks are done before administering the medication to your patient. If taking drug to bedside (e.g., eye drops), do third check at bedside. |
||
|
4. Before applying a transdermal patch, remove the old patch if it is still in place. Clean area thoroughly.
Observe for signs of skin irritation at old patch and document as per agency policy. |
Not removing previous patch may result in overdose of the medication. Check between skin folds for old patch. | ||
| 5. Dispose of old patch as per agency policy (usually in a biohazard trash bag) by folding in half with sticky sides together and wrapping it in a glove, or cutting it before disposal. | This prevents accidental exposure to the medication. | ||
| 6. Use a felt tip or soft tip pen to write the date, time, and your initials on the outside of the new patch. DO NOT use a ballpoint pen. |
Initialling patch communicates application date and time to other health care providers.
Ballpoint pen can damage patch and thus affect medication delivery. |
||
| 7. Apply the new patch to a new site that is clear, dry, hairless, and free of skin irritations. |
If it is necessary to remove hair, clip the hair instead of shaving to avoid skin irritation.
A consistent surface ensures even medication distribution. |
||
| NOTE : It is usual to have a “patch-free period” of 10 to 12 hours when the patch is removed, because tolerance to the medication may develop if the patch is worn 24 hours/day. Check doctor’s orders to determine if the patch should be removed overnight. | |||
| 8. Carefully remove the backing from the patch, taking care to hold it at the edges and not touch the medication with your fingers. | This prevents interference with medication and maintains stickiness of patch. | ||
| 9. Apply patch by holding one hand firmly over the patch for 10 seconds, then press around the edges to make sure that the patch is securely attached to the skin. | This prevents loss of patch and ensures effectiveness of medication delivery. | ||
| 10. Perform hand hygiene. | This prevents the transfer of microorganisms. | ||
NOTE:
|
|||
| 11. Document as per agency policy, making sure to include site of administration on the MAR. | Accurate and timely documentation improves patient safety. | ||
| Data source: BCIT, 2015; Lilley et al., 2011; Perry et al., 2014 |
Checklist 54 lists the steps for applying topical medications as creams, lotions, and ointments.
Checklist 54: Applying Topical Creams, Lotions, and OintmentsDisclaimer: Always review and follow your hospital policy regarding this specific skill. |
|||
Safety considerations:
|
|||
Steps |
Additional Information |
||
| 1. Check MAR against doctor’s orders. |
Check that MAR and doctor’s orders are consistent. Night staff usually complete and verify this check as well. |
||
2. Perform the SEVEN RIGHTS x 3 (must be done with each individual medication):
Medication calculation: D/H x S = A ( D or d esired dosage/ H or h ave available x S or s tock = A or a mount prepared) |
The right patient: check that you have the correct patient using two patient identifiers (e.g., name and date of birth).
The right medication (drug): check that you have the correct medication and that it is appropriate for the patient in the current context. The right dose: check that the dose makes sense for the age, size, and condition of the patient. Different dosages may be indicated for different conditions. The right route: check that the route is appropriate for the patient’s current condition. The right time: adhere to the prescribed dose and schedule. The right reason: check that the patient is receiving the medication for the appropriate reason. The right documentation: always verify any unclear or inaccurate documentation prior to administering medications. NEVER document that you have given a medication until you have actually administered it. |
||
3. The label on the medication must be checked for name, dose, and route, and compared with the MAR at three different times:
|
These checks are done before administering the medication to your patient. If taking drug to bedside (e.g., eye drops), do third check at bedside. |
||
| 4. Apply non-sterile gloves unless skin is broken; then apply sterile gloves. |
Using gloves protects health care provider from contact with medication.
If skin is broken, sterile gloves will prevent the spread of microorganisms. |
||
| 5. Wash, rinse, and dry the affected area with water and a clean cloth. | This removes previous topical medications. | ||
| 6. If skin is very dry and flaking, apply topical medication while skin is still damp. | Applying while skin is damp helps to retain moisture within skin layers. | ||
| 7. Change gloves, performing hand hygiene in between. | Use sterile gloves for open skin lesions to prevent spread of microorganisms. | ||
| 8. Place required amount of medication in palm of hands and soften by rubbing palms together. | Softening makes topical medication easier to spread. | ||
| 9. Let patient know that initial application may feel cold. Apply medication using long even strokes that follow the direction of the hair. Do not rub vigorously. | This prevents irritation of hair follicles. | ||
| 10. Let patient know that skin may feel greasy after application. | Some topical medications contain oils. | ||
| 11. Document as per agency policy, making sure to include site of administration on the MAR. | Accurate and timely documentation improves patient safety. | ||
| 12. Perform hand hygiene. | This step prevents the transfer of microorganisms. | ||
| Data source: BCIT, 2015; Lilley et al., 2011; Perry et al., 2014 |
Checklist 55 lists the steps for applying medicinal powder topically.
Checklist 55: Applying Topical PowderDisclaimer: Always review and follow your hospital policy regarding this specific skill. |
|||
Safety considerations:
|
|||
Steps |
Additional Information |
||
| 1. Check MAR against doctor’s orders. |
Check that MAR and doctor’s orders are consistent. Night staff usually complete and verify this check as well. |
||
2. Perform the SEVEN RIGHTS x 3 (must be done with each individual medication):
Medication calculation: D/H x S = A ( D or d esired dosage/ H or h ave available x S or s tock = A or a mount prepared) |
The right patient: check that you have the correct patient using two patient identifiers (e.g., name and date of birth).
The right medication (drug): check that you have the correct medication and that it is appropriate for the patient in the current context. The right dose: check that the dose makes sense for the age, size, and condition of the patient. Different dosages may be indicated for different conditions. The right route: check that the route is appropriate for the patient’s current condition. The right time: adhere to the prescribed dose and schedule. The right reason: check that the patient is receiving the medication for the appropriate reason. The right documentation: always verify any unclear or inaccurate documentation prior to administering medications. NEVER document that you have given a medication until you have actually administered it. |
||
3. The label on the medication must be checked for name, dose, and route, and compared with the MAR at three different times:
|
These checks are done before administering the medication to your patient. If taking drug to bedside (e.g., eye drops), do third check at bedside. |
||
| 4. Ensure that skin is completely dry and clean before application. | This minimizes potential for powder to cake and crust. | ||
| 5. If application is near patient’s face, ask patient to turn away from powder or briefly cover face with a clean towel. | This prevents patient from inhaling powder. | ||
| 6. Dust skin with a light layer of powder. | Too thick a layer of powder will congeal and crust. | ||
| 7. If ordered, cover the affected site with the prescribed dressing. | Covering site prevents soiling of patient’s clothes and linens. | ||
| 8. Document as per agency policy, making sure to include site of administration on the MAR. | Accurate and timely documentation improves patient safety. | ||
| 9. Perform hand hygiene. | Prevents transfer of microorganisms. | ||
| Data source: BCIT, 2015; Lilley et al., 2011; Perry et al., 2014 |
Critical Thinking Exercises
- Your patient’s MAR states that their Nitro-Patch should be removed at night. Please explain why this is considered safe practice.
- Discuss the steps you would take to administer a lotion for a patient with a rash that has several open lesions.
- Discuss why it is necessary to ensure that your patient’s skin is clean and dry prior to applying a prescribed topical powder.


1.5.3: Acid-Base Neutralization
Learning Objectives
- Write balanced chemical equations for neutralization reactions and determine if the resulting solution will be acidic, basic, or neutral.
As we have seen in the section on chemical reactions, when an acid and base are mixed, they undergo a neutralization reaction. The word “neutralization” seems to imply that a stoichiometrically equivalent solution of an acid and a base would be neutral. This is sometimes true, but the salts that are formed in these reactions may have acidic or basic properties of their own, as we shall now see.
Acid-Base Neutralization
A solution is neutral when it contains equal concentrations of hydronium and hydroxide ions. When we mix solutions of an acid and a base, an acid-base neutralization reaction occurs. However, even if we mix stoichiometrically equivalent quantities, we may find that the resulting solution is not neutral. It could contain either an excess of hydronium ions or an excess of hydroxide ions because the nature of the salt formed determines whether the solution is acidic, neutral, or basic. The following four situations illustrate how solutions with various pH values can arise following a neutralization reaction using stoichiometrically equivalent quantities:
- A strong acid and a strong base, such as HCl( aq ) and NaOH( aq ) will react to form a neutral solution since the conjugate partners produced are of negligible strength: \[\ce{HCl}(aq)+\ce{NaOH}(aq)⇌\ce{NaCl}(aq)+\ce{H2O}(l)\]
- A strong acid and a weak base yield a weakly acidic solution, not because of the strong acid involved, but because of the conjugate acid of the weak base.
- A weak acid and a strong base yield a weakly basic solution. A solution of a weak acid reacts with a solution of a strong base to form the conjugate base of the weak acid and the conjugate acid of the strong base. The conjugate acid of the strong base is a weaker acid than water and has no effect on the acidity of the resulting solution. However, the conjugate base of the weak acid is a weak base and ionizes slightly in water. This increases the amount of hydroxide ion in the solution produced in the reaction and renders it slightly basic.
- A weak acid plus a weak base can yield either an acidic, basic, or neutral solution. This is the most complex of the four types of reactions. When the conjugate acid and the conjugate base are of unequal strengths, the solution can be either acidic or basic, depending on the relative strengths of the two conjugates. Occasionally the weak acid and the weak base will have the same strength, so their respective conjugate base and acid will have the same strength, and the solution will be neutral. To predict whether a particular combination will be acidic, basic or neutral, tabulated K values of the conjugates must be compared.
Neutralization Reactions
This is the general format for a neutralization reaction:
Acid + Base → Salt + Water
It is important to note that neutralization reactions are just a specific type of double displacement redox reaction . Remember the rules for writing displacement reactions.
-
Figure out what the reactants and products will be.
- The cations will switch places in the products for double replacement reactions.
- The element will replace the cation in the reacting compound and result in a new product for single replacement reactions.
- Make sure that all of the compound formulas are correctly written based on the oxidation state of the elements involved.
- Balance the equation.
Example \(\PageIndex{6}\): Predicting the outcome of a neutralization reaction
Write the balanced chemical equation for the neutralization of HCl with Mg(OH) 2. Hint: neutralization reactions are a specialized type of double replacement reaction.
2HCl + Mg(OH) 2 → Mg(Cl) 2 + 2H 2 O
Since HCl is a strong acid and Mg(OH) 2 is a strong base, the resulting solution would be neutral.
Stomach Antacids
Our stomachs contain a solution of roughly 0.03 M HCl, which helps us digest the food we eat. The burning sensation associated with heartburn is a result of the acid of the stomach leaking through the muscular valve at the top of the stomach into the lower reaches of the esophagus. The lining of the esophagus is not protected from the corrosive effects of stomach acid the way the lining of the stomach is, and the results can be very painful. When we have heartburn, it feels better if we reduce the excess acid in the esophagus by taking an antacid. As you may have guessed, antacids are bases. One of the most common antacids is calcium carbonate, CaCO 3 . The reaction,
\[CaCO_3(s)+2HCl(aq)⇌CaCl_2(aq)+H_2O(l)+CO_2(g)\]
not only neutralizes stomach acid, it also produces CO 2 ( g ), which may result in a satisfying belch.
Milk of Magnesia is a suspension of the sparingly soluble base magnesium hydroxide, Mg(OH) 2 . It works according to the reaction:
\[Mg(OH)_2(s)⇌Mg^{2+}(aq)+2OH^-(aq)\]
The hydroxide ions generated in this equilibrium then go on to react with the hydronium ions from the stomach acid, so that :
\[H_3O^+ + OH^- ⇌ 2H_2O(l)\]
This reaction does not produce carbon dioxide, but magnesium-containing antacids can have a laxative effect. Several antacids have aluminum hydroxide, Al(OH) 3 , as an active ingredient. The aluminum hydroxide tends to cause constipation, and some antacids use aluminum hydroxide in concert with magnesium hydroxide to balance the side effects of the two substances.
Culinary Aspects of Chemistry
Cooking is essentially synthetic chemistry that happens to be safe to eat. There are a number of examples of acid-base chemistry in the culinary world. One example is the use of baking soda, or sodium bicarbonate in baking. NaHCO 3 is a base. When it reacts with an acid such as lemon juice, buttermilk, or sour cream in a batter, bubbles of carbon dioxide gas are formed from decomposition of the resulting carbonic acid, and the batter “rises.” Baking powder is a combination of sodium bicarbonate, and one or more acid salts that react when the two chemicals come in contact with water in the batter.
Many people like to put lemon juice or vinegar, both of which are acids, on cooked fish (Figure \(\PageIndex{1}\)). It turns out that fish have volatile amines (bases) in their systems, which are neutralized by the acids to yield involatile ammonium salts. This reduces the odor of the fish, and also adds a “sour” taste that we seem to enjoy.
Pickling is a method used to preserve vegetables using a naturally produced acidic environment. The vegetable, such as a cucumber, is placed in a sealed jar submerged in a brine solution. The brine solution favors the growth of beneficial bacteria and suppresses the growth of harmful bacteria. The beneficial bacteria feed on starches in the cucumber and produce lactic acid as a waste product in a process called fermentation. The lactic acid eventually increases the acidity of the brine to a level that kills any harmful bacteria, which require a basic environment. Without the harmful bacteria consuming the cucumbers they are able to last much longer than if they were unprotected. A byproduct of the pickling process changes the flavor of the vegetables with the acid making them taste sour.
Summary
The characteristic properties of aqueous solutions of Brønsted-Lowry acids are due to the presence of hydronium ions; those of aqueous solutions of Brønsted-Lowry bases are due to the presence of hydroxide ions. The neutralization that occurs when aqueous solutions of acids and bases are combined results from the reaction of the hydronium and hydroxide ions to form water. Some salts formed in neutralization reactions may make the product solutions slightly acidic or slightly basic.
Contributors and Attributions
-
Paul Flowers (University of North Carolina - Pembroke), Klaus Theopold (University of Delaware) and Richard Langley (Stephen F. Austin State University) with contributing authors. Textbook content produced by OpenStax College is licensed under a Creative Commons Attribution License 4.0 license. Download for free at<EMAIL_ADDRESS>).


19: Aldehydes and Ketones- Nucleophilic Addition Reactions Last updated Save as PDF Page ID 429669 19.1: Chapter Objectives and Preview of Carbonyl Chemistry 19.2: Naming Aldehydes and Ketones 19.3: Preparing Aldehydes and Ketones 19.4: Oxidation of Aldehydes and Ketones 19.5: Nucleophilic Addition Reactions of Aldehydes and Ketones 19.6: Nucleophilic Addition of Water- Hydration 19.7: Nucleophilic Addition of HCN- Cyanohydrin Formation 19.8: Nucleophilic Addition of Hydride and Grignard Reagents- Alcohol Formation 19.9: Nucleophilic Addition of Amines- Imine and Enamine Formation 19.10: Nucleophilic Addition of Hydrazine - The Wolff-Kishner Reaction 19.11: Nucleophilic Addition of Alcohols- Acetal Formation 19.12: Nucleophilic Addition of Phosphorus Ylides- The Wittig Reaction 19.13: Biological Reductions 19.14: Conjugate Nucleophilic Addition to alpha, beta-unsaturated Aldehydes and Ketones 19.15: Spectroscopy of Aldehydes and Ketones 19.S: Aldehydes and Ketones (Summary)


6.2: Synthesis and Stability
-
- Last updated
- Save as PDF
Learning Objectives
In this lecture you will learn the following
- Understand the role lead by ligands in stabilizing organometallic transition metal complexes.
- Know about various synthetic methods available for preparing the organometallic transition metal complexes.
- Understand the various factors like β-elimination and other bimolecular decomposition pathways that contribute to the observed instability of the organometallic transition metal complexes.
- Obtain insight about making stable organometallic transition metal complexes by suppression of the destabilizing factors mentioned.
Ligands play a vital role in stabilizing transition metal complexes. The stability as well as the reactivity of a metal in its complex form thus depend upon the number and the type of ligands it is bound to. In this regard, the organometallic carbon based ligands come in diverse varieties displaying a wide range of binding modes to a metal. In general, the binding modes of the carbon-derived ligands depend upon the hybridization state of the metal bound carbon atom. These ligands can thus bind to a metal in many different ways as depicted below. Lastly, these ligands can either be of (a) purely σ−donor type, or depending upon the capability of the ligand to form the multiple bonds may also be of (b) a σ−donor/π−acceptor type, in which the σ−interaction is supplemented by a varying degree of π−interaction.
Preparation of transition metal-alkyl and transition metal-aryl complexes
The transition metal−alkyl and transition−metal aryl complexes are usually prepared by the following routes discussed below,
a. Metathesis
This involves the reactions of metal halides with organolithium, organomagnesium, organoaluminium, organotin and organozinc reagents.
Of the different organoalkyl compounds listed above, the organolithium and organomagnesium compounds are strongly carbanionic while the remaining main group organometallics like the organoalkyl, organozinc and organotin reagents are relatively less carbanionic in nature. Thus, the main group organometallic reagents have attenuated alkylating power, that can be productively used in partial exchange of halide ligands.
\[\ce{TiCl4 ->[Al2Me6] MeTiCl3} \nonumber \]
\[\ce{NbCl5 ->[ZnMe2] Me2NbCl3} \nonumber \]
b. Alkene insertion or Hydrometallation
As the name implies, this category of reaction involves an insertion reaction between metal hydride and alkene as shown below. These type reactions are relevant to certain homogeneous catalytic processes in which insertion of an olefin to M−H bond is often observed.
c.
Carbene insertion
This category represents the reaction of metal hydrides with carbenes.
d. Metallate alkylation reaction
This category represents the reaction of carbonylate anions with alkyl halides as shown below.
e. Metallate acylation reaction
This category involves the reaction of carbonylate anions with acyl halides
f. Oxidative addition reaction
Many unsaturated 16 VE transition metal complexes having
d
8
or
d
10
configuration undergo oxidative addition reactions with alkyl halides. The oxidative addition reactions proceed with the oxidation state as well as coordination number of the metal increasing by +2.
g. Addition reaction
This category involves the reaction of an activated metal bound olefin complex with a nucleophile as shown below.
Thermodynamic Stability and Kinetic Lability
The transition metal organometallic compounds are often difficult to synthesize under ordinary laboratory conditions and require stringent experimental protocols involving the exclusion of air and moisture for doing so. As a consequence, many homoleptic binary transition metal−alkyl and transition metal−aryl compounds like, Et
2
Fe or Me
2
Ni cannot be made under normal laboratory conditions. More interestingly, most of the examples of transition metal−aryl and transition metal−alkyl compounds, known in the literature, invariably contain additional ligands like η
5
-C
5
H
5
, CO, PR
3
or halides.
For example,
Transition metal−carbon (TM−C) bond energy values are important for understanding the instability of transition metal organometallic compounds. In general, the TM−C bonds are weaker than the transition metal−main group element (TM−MGE) bonds (MGE = F, O, Cl, and N) and more interestingly so, unlike the TM−MGE bond energies, the TM−C bond energy values increase with increasing atomic number. The steric effects of the ligands also play a crucial role in influencing the TM−C bond energies and thus have to be given due consideration.
Contrary to the popular belief, the difficulty in obtaining transition metal−aryl and transition metal−alkyl complexes does primarily arise from the thermodynamic reasons but rather the kinetic ones. β−elimination is by far the most general decomposition mechanism that contribute to the instability of transition metal organometallic compounds. β−elimination results in the formation of metal hydrides and olefin as shown below.
β−elimination can also be reversible as shown below.
The instability of transition metal organometallic compounds can arise out of kinetic lability like in the case of the β−elimination reactions that trigger decomposition of these complexes. Thus, the suppression of the decomposition reactions provides a viable option for the stabilization of the transition metal organometallic complexes. The β−elimination reactions in transition metal organometallic complexes may be suppressed under any of the following three conditions.
a. Formation of the leaving olefin becomes sterically or energetically unfavorable
In the course of β−elimination, this situation arises when the olefinic bond is formed at a bridgehead carbon atom or when a double bond is formed with the elements of higher periods. For instance, the norbornyl group is less prone to decomposition by β−elimination because that would require the formation of olefinic double bond at a bridgehead carbon atom in the subsequent olefin,
i.e
. norbornene, and which is energetically unfavorable.
b. Absence of β−hydrogen atom in organic ligands
Transition metal bound ligands that do not possess β−hydrogen cannot decompose by β−elimination pathway and hence such complexes are generally more stable than the ones containing β−hydrogen atoms. For example, the neopentyl complex, Ti[CH
2
C(CH
3
)
3
]
4
(m.p 90 °C), and the benzyl complex, Zr(CH
2
Ph)
4
(m.p. 132 °C), exhibit higher thermal stability as both of the neopentyl and benzyl ligands lack β−hydrogens.
c. Central metal atom is coordinatively saturated
Transition metal organometallic complexes in which the central metal atom is coordinatively saturated tend to be more stable due to the lack of coordination space available around the metal center to facilitate β−elimination reaction or other decomposition reactions. Thus, the absence of free coordination sites at the metal is crucial towards enhancing the stability of the transition metal organometallic complexes. For example, Ti(Me)
4
, which is coordinatively unsaturated can undergo a bimolecular decomposition reaction
via
a binuclear intermediate (
A
), is unstable and exhibits a decomposition temperature of –40 °C. On the contrary, Pb(Me)
4
, that cannot undergo decomposition by such bimolecular pathway, is more stable and distills at 110 °C at 1 bar atmospheric pressure.
The Ti(Me)
4
decomposes by dimerization involving the formation of Ti−C (
3c−2e
) bonds. For Pb(Me)
4
, such bimolecular decomposition pathway is not feasible, as being a main group element it has higher outer
d
orbital for extending the coordination number. If the free coordination site of Ti(Me)
4
is blocked by another ligand, as in [(bipy)Ti(Me)
4
], then the thermal stability of the complex, [(bipy)Ti(Me)
4
], increased significantly. Other bidentate chelating ligands like
bis
(dimethylphosphano)ethane (dmpe) also serve the same purpose.
Coordinative saturation thus brings in kinetic stabilization in complexes. For example, Ti(Me)
4
is extremely reactive as it is coordinatively unsaturated, while W(Me)
4
is relatively inert for reasons of being sterically shielded and hence, coordinatively saturated. Thus, if all of the above discussed criteria for the suppression of β-elimination are taken care of, then extremely stable organometallic complexes can be obtained like the one shown below.
Problems
1. Arrange the following compounds in the order of their stability.
- Ti(Et) 4
- Ti(Me) 4 and
- Ti(6-norbornyl) 4
Ans: Ti(Et) 4 < Ti(Me) 4 < Ti(6-norbornyl) 4
2. Predict the product of the reaction given below.
\[\ce{(BuP)CuCH2CD2C2H5 -> } \nonumber \]
Ans: Equi molar amounts of (Bu 3 P)CuD and CH 2 =CDC 2 H 5
3. Will the compound β-eliminate,
\[\ce{PtH(C≡CH)L2 ->[\Beta -elimination] } \nonumber \]
(a). readily, (b). slowly and (c). not at all.
Explain your answer with proper reasoning.
Ans: Not at all as the ß-hydrogens are pointing away from the metal and cannot participate in ß-elimination recation.
Self Assessment test
1. Write the product(s) of the reactions.
Ans:
Summary
Ligands assume a pivotal role in the stabilization of the organometallic transition metal complexes. There are several methods available for the preparation of the organometallic transition metal complexes. The observed instability of the organometallic transition metal complexes can be attributed to two main phenomena namely β-elimination and bimolecular decomposition reaction that severely undermine the instability of these complexes. The suppression of these decomposition pathway thus pave way for obtaining highly stable organometallic transition metal complexes.


7.1: Cultural Notes and Extra/Optional Online Materials
Cultural Notes
| Topics | Explanation | |
| 1. | Food habits | In Hindi, there is no separate words for lunch and dinner. खाना “food” is used for both lunch and dinner. Typically, for both lunch and dinner, people eat full meal. |
| 2. | चाय | चाय is one of the drink that Indian love to drink in the morning and in the evening with snacks. Additionally, चाय is served in office often and it is a drink for a break between work/study. |
| 3. | क्या चल रहा है ? | क्या चल रहा है ? Literally, it means “what is moving?” But this is used to express “What’s up?” or “What is going on?” |
| 4. | Folk tales | Each Indian festival has some sort of folk tale behind it. Mostly, it is based on religion. For example, diwali is celebrated because, it is assumed that Lord Ram returned to Ayodhya with his wife Sita and brother Lakshaman after killing the devil king Rawan. To be culturally appropriate, you should learn the folk tales behind each festivals Indian celebrates. |
| 5. | School and Office hours. | In America, people generally go to work at 8 AM. In India and South Asia, the office starts at 10 AM. This gives enough time in the morning for morning rituals such as yoga, making break-fast, eating breakfast, and packing lunch. |
| 6. | Daily Routine | When you ask about daily routine to Indian and South Asian, they may just talk about their work/study. They may say how long they work and study. |
Extra/Optional Online Materials
History of Chai:
Indian Mom Daily Routine:
Holi’s Folk Tale:
दशहरा की कहानी:
धन्यवाद !


18.4: Symbolism and Meaning of Animals
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- Jennifer Hasty, David G. Lewis, & Marjorie M. Snipes
- OpenStax
Learning Objectives
By the end of this section, you will be able to:
- Identify totemism.
- Identify the roles of animals in the oral traditions of many human cultures.
- Describe the various ways animals are used in religious practices.
When we think of animals, we usually picture them as pets, food, or wildlife, but animals play a central role in the symbolism of human lives as well. Humans relate to animals not only as tangible beings but also as images and symbols that carry personal meaning and communicate cultural norms. While we can find animal symbols almost everywhere in human cultures, they play a particularly significant role in group identity.
Totemism
Totemism is a belief system in which a subcultural group acknowledges kinship with a spirit being, typically a plant or animal, that serves as the group’s emblem or herald. Relationships with their totems mirror the social relationships they have with each other as subgroups within their society. Totemic groups, often referred to as clans, view themselves as descendants of nonhuman ancestors and maintain special relationships of respect with other species in the natural world. Totemism is an example of a metaphorical relationship between humans and the natural world, one that links humans, animals, plants, landforms, and even weather events into a unified web of life. Many Indigenous groups practice totemism and have ancestral alliances with certain animals and plants, demonstrated by the ways in which they talk about them in their myths and depict them in their artwork. Totemic cultures frequently practice shamanism as a way to communicate with animal and plant species.
The totem , an animal or plant believed to be spiritually connected to a group of people, is a symbol of identity for the subgroup. The Anishinaabe, a North American Indigenous tribe located along the midwestern border between Canada and the United States, was historically divided into various doodeman (clans), most of which had local animals as their totems. Examples of their totem animals include a loon, a crane, a fish, a bird, a bear, a marten, and a deer. All members of the same totemic clan identified with one another as descendants and relatives. The totemic identification that children received at birth (from their fathers’ affiliations) connected individuals not otherwise linked by close social or biological relationships, creating a spiritual kinship within the clan through the common totem. Clans were often associated with specific occupations and work assignments within the larger tribe. Clans also determined marriage rules; members of the same clan could not marry one another, as it was considered to be incest. While the Anishinaabe today have fewer clans, and thus fewer animal totems, than when their population was higher, and the importance of clans and totems has lessened, they continue to value the identities that their ancestors constructed through the natural world.
The totem pole is a form of monumental architecture displaying the significant totems and historical events in a clan or family’s ancestral history. It functions as a signpost that identifies the occupants of an area to those passing through and proclaims the pride that a people have in their ancestry. Extended families are grouped together in a clan. The totem pole serves to proclaim the clan membership that an extended family has had throughout its history. The story of the first creation of the Indigenous group and the major events that occurred in the life of that family, its clan, and its tribe are all depicted on the totem pole. Many, though not all, Indigenous groups in North America make totem poles. These poles are historical landmarks of cultural identity.
Although Western societies do not construct physical totem poles, they do utilize some of the same symbolism in sports mascots and family heraldry. Sports teams use different types of symbolism, but animal symbols are common. Often, teams choose animals that are local to their immediate environment or that connect with certain characteristics and behaviors with which the group wishes to identify. Some well-known teams with animal mascots are the Detroit Lions, the Tampa Bay Rays, and the Boston Bruins. What animal mascots do you know?
Animals in Oral Tradition
Animals play an important role in nearly all oral traditions and religions. Across cultures, including Western cultures in Europe and the United States, animals appear as protagonists in myths and stories. The animal characters in nursery rhymes, fairy tales, fables, and folktales teach adults and children lessons and morals and model personal characteristics, some peculiar to a specific culture and others more universal. For example, the story of Chicken Little, also known in the UK as Henny Penny, is one that many US children learn at an early age. It was collected in print in the early 19th century, but it has older roots as a European folktale.  She panics—the sky must be falling! She runs around the farm warning all the animals about the calamity that she believes is happening: “The sky is falling! The sky is falling!” The moral of the story is to have courage and not believe everything you hear.
“The Queen Bee” is an interesting European reflection on animals, recorded from oral tradition by the Grimm brothers in 1812 . In this story, three princes, all brothers, leave their castle home to seek their fortunes and travel around the world. Two of the brothers move about haphazardly, paying no attention to the animals around them, but the youngest son, with the insulting name of Simpleton, is more considerate to the animals they encounter. When the older brothers try to destroy an anthill, kill ducks, and chase bees out of their hive, Simpleton intervenes to protect the animals and stop his brothers from causing harm. Eventually, the three princes arrive at another castle, in which everything living has been turned to stone except for one very old man. The old man tells the princes that if they can perform three tasks, all of which depend on the help of animals, they will be able to wake up the castle and earn the hand of a princess. The animals, remembering how they were treated, agree to help only young Simpleton, who thereby gains the keys of the kingdom. The moral is that even the smallest animals serve a mighty purpose.
Many of the animal stories that are still told in Western societies were either collected by the Grimm brothers in the early 1800s (1812–1857) or taken from Aesop’s Fables, a collection of stories supposedly told by Aesop, an enslaved Greek storyteller, around 500 BCE. These stories have made their way into children’s storybooks and animated movies—including an animated version of Chicken Little.
Indigenous societies across cultures have their own sets of animal stories that provide instruction and wisdom. Some of the most common animal symbols among Native American cultures are the coyote, the raven, the bear, and the spider. Coyote and Raven often appear in stories as tricksters , animal spirits or deities who are lively and clever and get into trouble through thoughtless or unconventional actions. In the story of Coyote and Bluebird from the Pima people of the southeastern United States, Coyote envies Bluebird’s plumage and asks for the secret to the beautiful blue color of the bird’s feathers. Bluebird tells Coyote that these pretty blue feathers came from bathing in blue water. Coyote does the same and comes out with a fine blue coat. In his vanity, he tries to outrun his shadow so that he can see his beautiful blue body in the light, and he crashes into a stump head-on, landing in the dirt, which coats his blue fur and paints him a “dirty” color that he still has today. The moral of this tale is that vanity does not serve an individual well.
In West Africa, many myths focus on a supernatural figure named Anansi, the spider. Anansi is a culture hero who teaches lessons of bravery and morality. Culture heroes are typically associated with supernatural feats and are particular to each cultural group, exhibiting specific traits, actions, and discoveries that are significant in that culture. In one Anansi story cycle brought by enslaved Africans to the Caribbean area during the time of the Atlantic slave trade, Anansi goes fishing and fills his basket with many different sizes of fish. On his way home, he crosses paths with Tiger, who demands to know what Anansi is carrying in the basket. Scared, Anansi lies and says he has nothing. Tiger takes the basket and sees the fish. In a series of back-and-forth interactions, Anansi succeeds in outsmarting Tiger by agreeing to clean his fur. Tiger shakes down his long hair, and then Anansi uses it to tie Tiger to the trunk of a tree, picks up his basket of fish, and continues home. The moral of the story?  Or, perhaps, Don’t let a bully get the best of you .
Animals in Religion
Animals play a role in most religions. Common functions include as objects of ritual sacrifice and as tokens symbolizing gifts, payments, or even messages between the human world and the divine. As just one example, think of the use of a dove in the Noah and the ark myth (Genesis 8:6–12). The dove is the first animal to bring back a piece of greenery, evidence that the flood had receded. With this promise, Noah begins preparations to leave the ark and start over. This use of animals as messengers and forms of sacred communication is seen across cultures.
In prehistoric Peru, wild guinea pigs were sacrificed and buried either alone or with humans. They appear in archaeological deposits in Peru as early as 9000 BP (Sandweiss and Wing 1997), and they continue to appear as sacrifices after their domestication around 4500 BP and through the Inca period that ended in the 16th century. Some of the sacrificed animals are whole and intact, mummified and desiccated, while others have been burned and their charred bones stored as ritual offerings inside elaborate ceramic jars. Guinea pigs were and still are a dependable source of meat in the Andes, where they traditionally live inside kitchens, nesting around the warmth of the cooking area. They are also used medicinally, their fat rubbed on areas of sickness to draw out pain and infection, and employed as divination tools. During divination rituals today, some Andean healers will rub a living guinea pig on a patient’s body to draw out some of the illness and then cut the animal open to “read” it, looking for a sign of some type of abnormality in the guinea pig’s organs that would mirror the location of the illness in the human patient. At Lo Demás, an ancient Inca fishing site south of Lima, Peru (ca. 1480–1540 CE), archaeologists have excavated multiple guinea pig sacrifices, some of which show characteristic signs of having been used for divination and healing prior to burial.
In India, where Hinduism is the predominant religion, it is common to see cows walking along city streets, undisturbed and roaming freely. Many Hindus practice vegetarianism, but even those who eat meat do not usually eat beef. Cattle are sacred in Hinduism. In the Vedas, the Hindu sacred texts, the cow is associated with Aditi, the mother of all gods. In a very famous study, “The Cultural Ecology of India’s Sacred Cattle” (1966), cultural anthropologist Marvin Harris explores the economic rationale associated with revering cattle, arguing that cattle are considered sacred because they are more useful when allowed to live out their natural lifespans than when slaughtered at a young age for meat alone. In India, cattle provide dung that can be dried and used as fuel, traction for plowing fields, some limited milk production, and reproductive capacity. When cattle die of old age, beef and leather are then harvested by those in the lowest socioeconomic class. Keeping cattle alive as long as possible thus provides for a greater range of material assets than raising them for food. This economic rationale, however true it may be, does not negate the cultural and religious importance of cattle to Indian people. Understanding animals’ symbolic roles is critical to understanding human belief systems.
Buddhism is a religion that reveres all life and sees humans and animals as intertwined, each capable of being reincarnated into the other, reborn into a new cycle of life inhabiting a new body of the same or another species. Because Buddhists believe in karma , a spiritual principle of cause and effect in which an individual’s words, actions, and deeds in one life affect their conditions in the next life cycle, the relationship between humans and other animals should ideally be based on respect and sympathy. All forms of life are working toward enlightenment, a state of awakening and having a complete knowledge of the life process.
Animals are important in human belief systems. English art critic and poet John Berger ([1980] 1991) writes about the gaze between humans and other animals, saying that animals remind humans that we are not here on Earth alone, that we are all companion species. Many religious systems reflect the awareness that life is not the exclusive domain of the human species and that our world is a shared community. For more on animals and belief systems, see the Ethnographic Sketch at the end of the chapter.


4.9: Sample problems and solutions
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Exercise \(\PageIndex{1}\)
Ethan is jumping hurdles. He gets a running start, moving with a speed of \(3\text{m/s}\) . The hurdle is \(0.5\text{m}\) high and the maximum speed that he can have when he leaves the ground is \(5\text{m/s}\) . (You can assume Ethan is a point particle, and ignore air resistance).
- What is the closest distance from the hurdle at which Ethan can jump and still clear the hurdle?
- What maximum height does he reach?
- Answer
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Our approach will be to consider the \(x\) and \(y\) components of the motion separately. We start by drawing a diagram and choosing our coordinate system. We will choose \(y\) to be vertical and positive upwards and \(x\) to be in the direction that Ethan is running. We choose the origin to be the location where Ethan leaves the ground for the jump, as illustrated in Figure \(\PageIndex{1}\).
a. Ethan’s speed at the beginning of the jump is \(v_0=5\text{m/s}\) and the horizontal ( \(x\) ) component of his velocity is \(v_x=3\text{m/s}\) . The \(y\) component of his initial velocity, \(v_{0y}\) , is given by:
\[\begin{aligned} v_x^2+v_{0y}^2&=v_0^2\\[4pt] v_{0y}&=\sqrt{v_0^2-v_x^2}\\[4pt] v_{0y}&=\sqrt{(5\text{m/s})^2-(3\text{m/s})^2}=4\text{m/s}\end{aligned}\]
We chose the origin at the beginning of the jump, so that Ethan’s \(x\) and \(y\) coordinates at time \(t=0\) are \(x_0=0\) and \(y_0=0\) , respectively. Once Ethan is in the air, there will be no acceleration in the \(x\) direction, and the only acceleration is in the \(y\) direction and will be that due to gravity. Ethan’s position at any time \(t\) can be described by the following equations:
\[\begin{aligned} x(t)&=v_{x}t\\[4pt] y(t)&=v_{0y}t-\frac{1}{2}gt^2\end{aligned}\]
where \(g\) is the acceleration due to gravity, \(g=9.8\text{m/s^2}\) .
We want to determine the value of \(x(t)\) when the vertical displacement, \(y(t)\) , is equal to the height of the hurdle, \(h\) . We thus find the value of \(t\) when \(y=0.5\text{m}\) and then find the value of \(x\) at that time.
We can re-arrange the equation for \(y(t)\) and solve the resulting quadratic for \(t\) (we get two solutions):
\[\begin{aligned} 0&=-\frac{1}{2}gt^2+v_{0y}t-h\\[4pt] 0&=\frac{1}{2}(-9.8\text{m/s}^{2})t^2+(4\text{m/s})t-0.5\text{m}\\[4pt] t&=0.15\text{s},\quad 0.66\text{s}\end{aligned}\]
The jump will be a parabola, and Ethan will cross a height of \(0.5\text{m}\) twice, once on the way up, and once on the way down. We want to know when Ethan reaches \(0.5\text{m}\) for the first time (on the way up), so we choose \(t=0.15\text{s}\) . The horizontal displacement at this time is:
\[\begin{aligned} x&=v_xt\\[4pt] &=(3\text{m/s})(0.15\text{s})\\[4pt] &=0.45\text{m}\end{aligned}\]
Therefore, he can get as close as \(0.45\text{m}\) from the hurdle before he has to jump, if his initial horizontal velocity is \(3\text{m/s}\) .
b. Ethan’s motion follows a parabolic shape. At the maximum height, Ethan’s vertical velocity is equal to zero. We can model only the vertical part of the motion to solve for the value of \(y\) when \(v_y=0\) . We know the following quantities:
\[\begin{aligned} v_{0y}&=4\text{m/s}\\[4pt] v_y&=0\test{m/s}\\[4pt] g&=9.8\text{m/s}^{2}\end{aligned}\]
The easiest way to determine \(y\) is to use the formula,
\[\begin{aligned} v_y^2&=v_{0y}^2-2g(y-y_0)\\[4pt] \therefore y&=\frac{v_y^2-v_{0y}^2}{(-2g)}\end{aligned}\]
Substituting our values for \(v_y\) , \(v_{0y}\) , and \(g\) , we get:
\[\begin{aligned} y_{max}&=\frac{(-4\text{m/s})^2}{(2)(-9.8\text{m/s}^{2})}\\[4pt] y_{max}&=0.82\text{m}\end{aligned}\]
Ethan reaches a maximum height of \(0.82\text{m}\) .
Exercise \(\PageIndex{2}\)
A cowboy swings a lasso above his head. The lasso moves at a constant speed in a circle of radius \(1.5\text{m}\) in the horizontal plane. A hawk flies toward the lasso at \(50\text{km/h}\) . The hawk sees the end of the lasso moving at \(60\text{km/h}\) when the lasso is directly in front of it (see Figure \(\PageIndex{2}\)). In the reference frame of the cowboy ...
- How long does it take for the lasso to complete one revolution? (Hint: From the point of view of the hawk, the lasso is moving towards him in addition to moving in a circle. You will have to use your knowledge of relative motion to solve this problem!)
- What is the centripetal acceleration of the end of the lasso?
- What is the angular acceleration of the lasso?
- Answer
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a. We need to determine the speed of the end of the lasso in the cowboy’s frame of reference, knowing its speed in the hawk’s frame of reference and knowing the velocity of the hawk. Once we know the speed of the lasso in the cowboy’s frame of reference we can easily determine how long it takes to complete one revolution (its period).
We start by introducing coordinate systems for the hawk ( \(xy\) ) and the cowboy ( \(x'y'\) ), and choose for the \(x\) ( \(y\) ) and \(x'\) ( \(y'\) ) axes to be parallel. We choose the axes such that \(x\) is to the right (when seen from above, as in Figure \(\PageIndex{3}\)) and \(y\) is in the direction of motion of the hawk as seen in the cowboy’s reference frame. The velocity vector of the hawk in the cowboy’s frame of reference is:
\[\begin{aligned} \vec v'_H = v'_H \hat y = (50{km/h})\hat y\end{aligned}\]
In the hawk’s frame of reference, the lasso will have a \(y\) component of velocity in the negative \(y\) direction with the same magnitude as the speed of the hawk, and an unknown component, \(v_{Lx}\) , in the \(x\) direction. The velocity of the lasso in the hawk’s frame of reference is:
\[\begin{aligned} \vec v_L=v_{Lx}\hat x - v'_H \hat y\end{aligned}\]
However, we know the speed of the lasso in the hawk’s frame of reference ( \(v_L=60\text{km/h}\) ), so we can easily find \(v_{Lx}\) :
\[\begin{aligned} v_{Lx}=\sqrt{v_L^2-v'^2_H}=\sqrt{(60\text{km/h})^2-(50\text{km/h})^2}=33.17\text{km/h}\end{aligned}\]
In the cowboy’s frame of reference, the lasso will have a velocity vector (Figure 4.7.4), \(\vec v'_L\) , given by:
\[\begin{aligned} \vec v'_L &= \vec v'_H + \vec v_L\\[4pt] &= v'_H \hat y + v_{Lx}\hat x - v'_H \hat y\\[4pt] &=v_{Lx}\hat x = (33.17\text{km/h})\hat x\end{aligned}\]
That is, in the cowboy’s frame of reference, the lasso has a velocity that is in the \(x\) direction. This corresponds to the speed, \(v_s\) , of the end of the lasso in uniform circular motion about a circle of radius \(R=1.5\text{m}\) . We can thus find the time required for one revolution to be:
\[\begin{aligned} v_s &= \frac{2\pi R}{T}\\[4pt] \therefore T &= \frac{2\pi R}{v_s} =\frac{2\pi (1.5\text{m})}{(33.17\text{km/h})} = \frac{2\pi (1.5\text{m})}{(9.2\text{m/s})}=1.02\text{s}\end{aligned}\]
where we converted the speed into \(\text{m/s}\) before determining the time.
b. The motion is uniform circular motion, so it has a centripetal acceleration given by
\[\begin{aligned} a_c(t)&=\frac{v_s^2(t)}{R}\end{aligned}\]
To find the centripetal acceleration of the end of the lasso, we just user our values for \(v_s\) and \(R\) .
\[\begin{aligned} a_c(t)&=\frac{(9.2\text{m/s})^2}{1.5\text{m}}=56\text{m/s}^{2}\end{aligned}\]
c. The angular acceleration of the lasso is zero. The angular acceleration refers to the rate of change of the angular velocity (the rate at which the lasso rotates), which is constant for uniform circular motion.


12.11.5: Changing the Divide
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A New Understanding of the Digital Divide
In 2006, web-usability consultant Jakob Nielsen wrote an article that got to the heart of our understanding of this problem. In his article, he breaks the digital divide up into three stages: the economic divide, the usability divide, and the empowerment divide [7] .
What is usually called the digital divide is, in Nielsen’s terms, t he economic divide : the idea that some people can afford to have a computer and Internet access while others cannot. Because of Moore’s Law (see chapter 2), the price of hardware has continued to drop and, at this point, we can now access digital technologies, such as smartphones, for very little. This fact, Nielsen asserts, means that for all intents and purposes, the economic divide is a moot point and we should not focus our resources on solving it.
The usability divide is concerned with the fact that “technology remains so complicated that many people couldn’t use a computer even if they got one for free.” And even for those who can use a computer, accessing all the benefits of having one is beyond their understanding. Included in this group are those with low literacy and seniors. According to Nielsen, we know how to help these users, but we are not doing it because there is little profit in doing so.
The empowerment divide is the most difficult to solve. It is concerned with how we use technology to empower ourselves. Very few users truly understand the power that digital technologies can give them. In his article, Nielsen explains that his (and others’) research has shown that very few users contribute content to the Internet, use advanced search, or can even distinguish paid search ads from organic search results. Many people will limit what they can do online by accepting the basic, default settings of their computer and not work to understand how they can truly be empowered.
Understanding the digital divide using these three stages provides a more nuanced view of how we can work to alleviate it. While efforts such as One Laptop per Child are an excellent start, more work needs to be done to address the second and third stages of the digital divide for a more holistic solution.
Sidebar: Using Gaming to Bridge the Digital Divide
Paul Kim, the Assistant Dean and Chief Technology Officer of the Stanford Graduate School of Education, designed a project to address the digital divide for children in developing countries. [8] In their project, the researchers wanted to understand if children can adopt and teach themselves mobile learning technology, without help from teachers or other adults, and the processes and factors involved in this phenomenon. The researchers developed a mobile device called TeacherMate, which contained a game designed to help children learn math. The unique part of this research was that the researchers interacted directly with the children; they did not channel the mobile devices through the teachers or the schools. Another important factor to consider: in order to understand the context of the children’s educational environment, the researchers began the project by working with parents and local nonprofits six months before their visit. While the results of this research are too detailed to go into here, it can be said that the researchers found that children can, indeed, adopt and teach themselves mobile learning technologies.
What makes this research so interesting when thinking about the digital divide is that the researchers found that, in order to be effective, they had to customize their technology and tailor their implementation to the specific group they were trying to reach. One of their conclusions stated the following:
Considering the rapid advancement of technology today, mobile learning options for future projects will only increase. Consequently, researchers must continue to investigate their impact; we believe there is a specific need for more in-depth studies on ICT [information and communication technology] design variations to meet different challenges of different localities.
To read more about Dr. Kim’s project, locate the paper referenced in this sidebar.