9.1: Early Byzantine Art
The Byzantine Empire
The Byzantine Empire began as a continuation of the Roman Empire but gradually became distinct through cultural changes.
Explain the rise and duration of the Byzantine Empire
Key Points
- The Byzantine Empire, so-called for the former name of Constantinople, was the Eastern portion of the Roman Empire. After the Western Empire fell in 476, the Byzantine Empire would continue for another millennium.
- Those living within the borders of the empire called themselves Romans, as opposed to Byzantines. Cultural shifts between them emerged with the change of the official language in the early seventh century, and the Byzantine split with the Roman Catholic Church in the eleventh century.
- The surviving Byzantine art is predominantly religious and follow traditional models that translate their carefully controlled church theology into artistic terms.
- Byzantine churches began in the style of many Western Roman churches but gradually shifted to centrally planned and then to Greek-cross structures over the course of the empire’s history.
Key Terms
- Greek-cross : The dominant architectural form of middle- and late-period Byzantine churches, featuring a square center with an internal structure shaped like a cross, topped by a dome.
- centrally planned : Having a central nave with an aisle on either side separated by a colonnade, and an apse at one end.
The East–West Schism
After the death of Theodosius I in 395, the Roman Empire was divided into an Eastern half, based in Constantinople, and a Western, half based in Rome . Less than a century later, in 476, the last Western emperor Romulus Augustulus abdicated to a Germanic warlord who placed his own rule under that of the Eastern emperor. This act effectively ended the line of Western emperors and marked the end of the Western Empire. However, the Eastern portion (what historians call the Byzantine Empire) would continue for approximately another millennium.
The word Byzantine derives from Byzantium , the original name of Constantinople before Constantine moved the Roman imperial capital there in the fourth century. Despite this present-day appellation, those living within the borders of the Byzantine Empire did not call themselves Byzantine. They continued to call themselves Romans and, until the early seventh century, continued to speak Latin. Even Roman Catholicism remained the official religion of the Byzantine Empire until the eleventh century.
In an effort to recreate a unified Roman Empire, Justinian I (r. 527–565) was able to reconquer most of the Mediterranean coast, including North Africa, Rome, and southern Spain. This swath of territory remained in the Byzantine Empire for two centuries.
A significant cultural shift occurred in the early seventh century when Heraclius (r. 610–641) replaced Latin with Greek as the official language of the Empire. This caused religious tensions with the church in Rome that began in the fourth century, and resulted in seven Ecumenical Councils over six hundred years. Finally, in 1054, the East–West Schism officially made the Eastern Orthodox Church, centered in Constantinople, its own separate entity from the Roman Catholic Church.
From the tenth century to the fifteenth, the empire experienced periods of peace and prosperity, as well as war and economic downturns. In the late eleventh century, the empire lost much of Asia Minor to the Turks, a temporary setback that foreshadowed the eventual weakening of Constantinople and the further loss of territory to the growing Ottoman Empire . In 1453, the Ottoman Turks invaded and captured Constantinople, bringing the Byzantine Empire to an end.
Byzantine Art and Architecture
Surviving Byzantine art is mostly religious and, for the most part, highly conventionalized, following traditional models that translate their carefully controlled church theology into artistic terms. Painting in frescos , mosaics , and illuminated manuscripts , and on wood panels were the main, two-dimensional media . Manuscript painting preserved some of the classical realist tradition that was missing in larger works. Figurative sculpture was very rare except for small, carved ivories .
Byzantine art was highly prestigious and sought-after in Western Europe, where it maintained a continuous influence on medieval art until near the end of the period. This was especially true in Italy, where Byzantine styles persisted in modified form through the twelfth century.
However, few incoming influences affected Byzantine style. By means of the expansion of the Eastern Orthodox church, Byzantine forms and styles spread throughout the Orthodox world and beyond.
Early Byzantine architecture drew upon the earlier elements of Roman architecture. After the fall of the Western Empire, several churches, including the Hagia Sophia in Constantinople and San Vitale in Ravenna, were built as centrally planned structures. However, stylistic drift, technological advancement, and political and territorial changes gradually resulted in the Greek-cross plan in church architecture.
Buildings increased in geometric complexity. Brick and plaster were used in addition to stone for the decoration of important public structures. Classical orders were used more freely. Mosaics replaced carved decoration. Complex domes rested upon massive piers , and windows filtered light through thin sheets of alabaster to softly illuminate interiors.
Influences from Byzantine architecture, particularly in religious buildings, can be found in diverse regions from Egypt and Arabia to Russia and Romania. Most of the surviving structures are sacred in nature; secular buildings are mostly known through contemporaneous descriptions.
Architecture in the Early Byzantine Empire
The Byzantine Emperor Justinian I launched an ambitious building program to develop holy sites to restore the glory of the Roman Empire.
Describe the characteristics of Byzantine architecture
Key Points
- Christian architecture was a significant component of Justinian’s project of imperial renovation.
- The church-building program of Justinian was intended to assist the Emperor in his mission of religious unification.
- Justinian hoped to recreate the glory of the Roman Empire, partly through his building projects in Constantinople.
- The Hagia Sophia was the most notable of Justinian’s projects, intriguing scholars and architects for centuries and influencing the designs of religious architecture, particularly mosques .
- Justinian also ordered the construction of the Church of Saints Sergius and Bacchus, and the reconstruction of the Church of the Holy Apostles. Isidorus of Miletus and Anthemius of Tralles, who also designed the Hagia Sophia, designed both structures.
Key Terms
- pendentive : A constructive device that permits the placing of a circular dome over a square room or an elliptical dome over a rectangular space.
- buttress : An architectural structure built against or projecting from a wall that serves to support or reinforce the wall.
- narthex : An architectural element typical of early Christian and Byzantine basilicas and churches consisting of the entrance or lobby area, located at the west end of the nave.
Justinian I devoted much of his reign (527–565 CE) to reconquering Italy, North Africa, and Spain. During his reign, he sought to revive the empire’s greatness and reconquer the lost western half of the historical Roman Empire. This attempt at restoration included an ambitious building program in Constantinople and elsewhere in the empire, and is the most substantial architectural achievement by one person in history.
Hagia Sophia
One notable structure for which Justinian was responsible is the Hagia Sophia, or Church of Holy Wisdom, built by Isidorus of Miletus and Anthemius of Tralles, both of whom would oversee most building projects that Justinian ordered within Constantinople. Like most Byzantine churches of this time, the Hagia Sophia is centrally planned , with the dome serving as its focal point.
The vast interior has a complex structure. The nave is covered by a central dome that at its maximum is over 180 feet from floor level and rests on an arcade of 40 arched windows. Although the dome appears circular at first glance, repairs to its structure have left it somewhat elliptical, with its diameter varying between 101 and nearly 103 feet.
The dome of Hagia Sophia has spurred particular interest for many art historians, architects, and engineers because of the innovative way the original architects envisioned it. The cupola is carried on four, spherical, triangular pendentives , an element that was first fully realized in this building.
The pendentives implement the transition from the circular base of the dome to the rectangular base below to restrain the lateral forces of the dome and allow its weight to flow downwards. They were later reinforced with buttresses .
At the western entrance side and the eastern liturgical side are arched openings that are extended by half domes of identical diameter to the central dome, and carried on smaller semi-domed exedras . A hierarchy of dome-headed elements creates a vast, oblong interior crowned by the central dome, with a span of 250 feet.
The Imperial Gate, reserved only for the emperor, was the main entrance of the cathedral . A long ramp from the northern part of the outer narthex leads up to the upper gallery, which was traditionally reserved for the empress and her entourage. It is laid out in a horseshoe shape that encloses the nave until it reaches the apse .
After the Ottoman conquest of Constantinople, the plan of the Hagia Sophia would significantly influence the construction and design of the Süleymaniye Mosque (1550–1557).
The Church of the Holy Apostles
The Church of the Holy Apostles, originally built under the purview of Constantine in 330, was no longer considered grand enough when Justinian ascended the throne. Because of this, the architects Isidorus of Miletus and Anthemius of Tralles designed and built a new church on the same site in the late 540s (consecrated in 550).
Like the original church, Justinian’s replacement had a cruciform plan and and was surmounted by five domes: one above each arm of the cross and one above the central bay where the arms intersected. The western arm of the cross extended farther than the others to form an atrium . Because blueprints did not exist yet, and because the church was demolished shortly after the Ottoman conquest, the design details of the building are a matter of dispute.
The Church of Saints Sergius and Bacchus
The Church of Saints Sergius and Bacchus (527–536), known today as Little Hagia Sophia, was probably a model for the actual Hagia Sophia. It was recognized at the time as an adornment to all of Constantinople.
During the reign of Justinian’s uncle Justin I, the future emperor faced accusations of conspiring against the current emperor and was killed for it. However, the Saints Sergius and Bacchus were said to intervene and vouched to Justin that his nephew was innocent. After the restoration of his title, Justinian commissioned Isidorus of Miletus and Anthemius of Tralles to construct the church as a gesture of thanksgiving.
When the church was built, it shared its narthex, atrium and propylaea with another church. It became one of the most important religious structures in Constantinople.
Painting in the Early Byzantine Empire
The Early Byzantine period witnessed the establishment of strict guidelines for the production of icons.
Contrast Early Byzantine representations of religious figures to those of earlier Christian art
Key Points
- As Christians were able to practice their religion openly, paintings depicting the stories of martyrs became popular.
- Byzantine icons follow a strict code of symbolism based on color and imagery .
- Early Byzantine icons were wooden panels covered with encaustic paint. Icons from the sixth century and earlier were incredibly lifelike and sometimes caused veneration of the objects, as opposed to who the objects represented. This led to a fifth-century ban on the representation of secular imagery.
Key Terms
- iconoclastic : Pertaining to the belief in, participation in, or sanction of destroying religious icons and other symbols or monuments, usually with religious or political motives.
- icon : An image, symbol, picture, or other representation that is usually an object of religious devotion.
- pagan : A person not adhering to any major or recognized religion; a follower of a pantheistic or nature-worshipping religion.
- hagiography : The study of saints.
Icon Painting
Icon painting, as distinct from other forms of painting, emerged in the Early Byzantine period as an aid to religious devotion. In contrast , earlier Christian art had relied more on allegory and symbolism. For example, earlier art might have featured a lamb or a fish rather than Christ in human form.
Before long, religious figures were being depicted in their human form to emphasize their humanity as well as their spirituality. While this issue would be debated and challenged during the later Iconoclastic period, for a time, images of the saints in icon paintings flourished.
After the adoption of Christianity as the only permissible Roman state religion under Theodosius I, Christian art began to change not only in quality and sophistication but also in nature. Paintings of martyrs and their feats began to appear, and early writers commented on their lifelike effect. Statues in the round were avoided as being too close to the principal artistic focus of pagan cult practices, as they have continued to be (with some small-scale exceptions) throughout the history of Eastern Christianity.
Icons were more religious than aesthetic in nature. They were understood to manifest the unique presence of the figure depicted by means of a likeness to that figure maintained through carefully maintained canons of representation. Therefore, very little room is made for artistic license.
Almost every aspect of the subject matter has a symbolic aspect. Christ, the saints, and the angels all have halos. Angels, as well as some depictions of the Holy Trinity, have wings because they are messengers. Figures have consistent facial appearances, hold attributes personal to them, and use a few conventional poses.
Use of Color
Color plays an important role, as well. Gold represents the radiance of Heaven.  White is the Uncreated Light of God, only used for scenes depicting the resurrection and transfiguration of Christ.  Thus, the doctrine of deification is conveyed by icons. Most icons incorporate some calligraphic text naming the person or event depicted. Because letters also carry symbolic significance, writing is often presented in a stylized manner.
Early Byzantine icons were painted in encaustic on wooden panel and, like Egyptian funerary portraits produced in the same media , they appeared very lifelike. Nilus of Sinai, in his fifth-century Letter to Heliodorus Silentiarius, recounts a miracle in which St. Plato of Ankyra appeared to a Christian in a dream. The Saint was recognized because the young man had often seen his portrait.
Veneration of Icons
This recognition of a religious apparition from its likeness to an image was also a characteristic of pagan, pious accounts of appearances of gods to humans and was a common theme in hagiography . During this period, the church began to discourage all non-religious human images, with the Emperor and donor figures counting as religious.
By the second half of the sixth century, there were isolated cases of direct veneration of the icons themselves, as opposed to the figures represented on them, due to continued claims of icon-associated miracles. This perceived misuse, in part, justified the banning and destruction of icons in the eighth century.
Documentation exists to prove the use of icons as early as the fourth century. However, there are no surviving examples produced before the sixth century, primarily due to the period of Iconoclasm that ended the Early Byzantine period.
The surviving evidence of the earliest depictions of Christ, Mary, and the saints therefore comes from wall paintings, mosaics , and some carvings. Because Augustine of Hippo (354–430 CE) argued that no one knew the appearance of Jesus or that of Mary, the earliest depictions of Jesus were generic, rather than portrait images, and generally represented him as a beardless young man. Such an example can be seen in a mosaic in the Mausoleum of Galla Placidia, which houses the remains of the daughter of Theodosius I.
Mosaics in the Early Byzantine Empire
In the Byzantine period, a building’s interior decoration often took the form of mosaic paintings, but with an added sense of spiritual drama that ordinary paintings could not convey.
Explain how the Byzantines used mosaics to convey a sense of spirituality in their architecture
Key Points
-
Mosaic tiles were more costly than the materials for traditional painting, and demonstrate the wealth of the Byzantine empire.
The use of mosaics in Greek and Roman design was reserved for placement in the floor. Byzantine artists continued this precedent but also went further and adorned walls and ceilings with dramatic scenes. - Mosaics in Middle Eastern locations like Mount Nebo and Mount Sinai provide examples of both dramatically spiritual and seemingly mundane imagery .
- The Italian city of Ravenna is the site of many of the great Byzantine structures that incorporated mosaic. The Mausoleum of Galla Placidia and the Arian Baptistery are prime examples of the powerful impact and spiritual effect of the Byzantine-mosaic style .
Key Terms
- tesserae : Small square pieces of stone, wood, ivory, or glass used for making a mosaic.
- mandorla : A luminous cloud that surrounds the figures of Christ and the Virgin Mary in traditional Christian art.
- mosaic : A piece of artwork created by placing colored squares (usually tiles) in a pattern to create a picture.
- mausoleum : A large, stately tomb or a building housing such a tomb or several tombs.
Mosaic Art
Mosaic art flourished in the Byzantine Empire from the sixth to the fifteenth centuries. Whereas in Antiquity , walls were usually decorated with less-expensive painted scenes, the Byzantine aesthetic favored the more sumptuous, glittering effect of mosaic decoration.
Some of the finest surviving Byzantine mosaics are preserved in the Middle East and in the Italian city of Ravenna. Mosaics were not a Byzantine invention. In fact, some of the most famous surviving mosaics are from ancient Greece and Rome .
The artists of the Early Byzantine period expanded upon precedent by celebrating the possibilities of the mosaic technique. They began to use it on wall surfaces as a type of painting technique in stone. Unlike traditional wall paintings, however, mosaics could create a glittering, shimmering effect that lent itself to a heightened sense of spirituality. The imagery befit the Byzantine culture that emphasized the authority of one, true religion.
The mosaic technique was more expensive than traditional wall painting, but its effects were so desirable as to make it worth the cost. Further, technological advances (lighter-weight tesserae and a new cement recipe) made wall mosaics easier than they had been in the preceding centuries, when floor mosaics were favored.
The mosaic technique involved fitting together small pieces of stone and glass (tesserae). When set together, the tesserae create a paint-like effect in which different colors meld into one another to create shadows and a sense of depth. Moreover, Byzantine artists often placed gold backing behind the clear glass tesserae, such that the mosaics would appear to emit a mysterious light of their own. This play of light added a sense of drama and spiritualism to the images that suited the symbolism and magic inherent in the Byzantine religious ceremony .
Mount Nebo, Jordan
Most often, however, mosaic decoration in the classical world was reserved for floor surfaces. Byzantine churches continued this tradition in locations such as Mount Nebo in Jordan, a medieval pilgrimage site where Moses is believed to have died.
The Church of Saints Lot and Procopius (founded 567 CE) has a richly tiled floor that depicts activities like grape harvesting. Seemingly mundane, the grape harvest could be symbolic of the wine component of the Eucharist. The mosaic is located in the baptistery, where infants were initiated into the Christian faith and, according to biblical teachings, be cleansed of Original Sin. Thus, a symbolic depiction of the next sacrament in the religion would help to underscore the theme of salvation.
Another Mount Nebo floor mosaic (c. 530) depicts four registers of men and animals. The first two registers are hunting scenes in which the men hunt big cats and wild boars with the help of domesticated dogs. On the bottom two registers, the animals appear more domesticated, peacefully eating fruit from trees as a shepherd observes them at the left; they wear leashes pulled by their human masters.  As in the Church of Saints Lot and Procopius, this mosaic likely has a religious message beneath its seemingly mundane subject matter.
Monastery of Saint Catherine on Mount Sinai
Important Justinian-era mosaics (c. 548–565) decorate Saint Catherine’s Monastery on Mount Sinai. In the apse is a depiction of the Transfiguration on a golden background, that denotes the otherworldliness of the event. Christ, standing in the center as the focal point, is crowned with a halo and surrounded by a mandorla as his awestruck apostles observe the event. The apse is surrounded with bands containing the medallions of Biblical apostles and prophets, and two contemporary figures who are identified as Abbot Longinos and John the Deacon.
Ravenna
Arian Baptistery
Inside the Arian Baptistery in Ravenna are four niches and a dome with mosaics that depict the baptism of Jesus by Saint John the Baptist. Although the mosaics were produced before Justinian I annexed Italy to the Byzantine Empire, their overall design is very similar to those produced under Byzantine rule.
Jesus is shown as a beardless, half-submerged youth in the Jordan River. John the Baptist, wearing a leopard skin, stands on the right, while the personification of the Jordan River stands to the left. Above, the Holy Spirit in the form of a dove sprays holy water from its beak. Below, a procession of the Apostles, led in separate directions by Saint Peter and Saint Paul circle the dome, meeting at a throne with a bejeweled crucifix resting on a purple cushion.
It took the artists several years to complete these mosaics, as can be clearly seen from the different colors of the stones used to depict the grass at the feet of the apostles. The designs are quite simple, but the use of a gold background should be noted, as it was typically used in this era to infuse these simple scenes with an ethereal glow.
Mausoleum of Galla Placidia
The Mausoleum of Galla Placidia is one of the earliest Byzantine buildings in Ravenna. While the exterior is plain, the interior is extensively decorated in elaborate mosaics. These mosaics create a truly spiritual space–a world removed from the ordinary. The vaulting is covered with floral motifs (possibly symbolic of the Garden of Eden) and the stars that stand out against a blue background seem to sparkle with their own mystical light.
Mosaics cover the walls of the vault , the lunettes , and the bell tower. The iconographic themes developed in the decorations represent the victory of eternal life over death. The inside contains two famous mosaic lunettes, and the rest of the interior is filled with mosaics of Christian symbols.
The central bay ‘s upper walls are decorated with four pairs of apostles, including Saints Peter and Paul, who acclaim a giant gold cross in the center of the dome against a blue sky of stars. Symbols of the four evangelists float among the clouds. The other four apostles appear in the barrel vaults of the transepts .
Ivory Carving in the Early Byzantine Empire
Carved, ivory relief sculptures were central features of Early Byzantine art.
Describe the ivory miniature sculptures of the early Byzantine period
Key Points
- Ivory carving has a special importance to the Byzantine Empire because it has no bullion value and cannot be melted down or otherwise recycled. Elaborate ivory diptychs were central to the art of this period. Early Christians valued the small scale of these relief sculptures that contrasted with the monumental sculpture favored by pagans .
- The Barberini Diptych and the Archangel Ivory are two significant examples of ivory carving from the first half of the sixth century.
- Ivory panels were used as book covers, usually as a centerpiece that was surrounded by metalwork and gems. They were assembled from up to five smaller panels because of the limited width of the tusk. Carved ivory covers were used for treasure bindings on the most precious illuminated manuscripts .
- Western art gradually began to focus on monumental sculpture and ivory carving declined in importance. However, in the Eastern Orthodox tradition, it remained significant.
Key Terms
- diptych : A picture or series of pictures painted on two tablets, usually connected by hinges.
- relief : A type of artwork in which shapes or figures protrude from a flat background.
The Appeal of the Miniature
Ivory carving is the manual or mechanical carving of either animal tooth or tusk, wherein very fine detail can be achieved, and the surviving works often demonstrate intricate and complicated designs. This art form has a special importance to the history of Byzantine art because it has no bullion value and is not easily recycled like precious metals or jewels. Because of this, many ivory carvings from the Early Byzantine period still survive. Ivory diptychs, often elaborately decorated, were issued as gifts by newly appointed consuls.
In the Early Christian period, Christians avoided monumental sculpture, which was associated with the old pagan Roman religion and sculpted almost exclusively in relief. During the persecution of Christians, such reliefs were typically kept small in scale, no larger than the reliefs on sarcophagi.
Objects that were small-scale and lightweight are more easily carried and hidden, attributes that a persecuted class worshiping in secret would have found necessary. When Christianity was legalized and later became the official religion of the Empire these attitudes remained. As a result, small-scale sculpture—for which ivory was in many ways the best material—was central to art in a way that it rarely was at other times.
Consuls—civil officers who played an important administrative role until 541—gave Roman consular diptychs as presents. The form was later adopted for Christian use, with images of Christ, the Theotokos (the Virgin Mary), and saints. Such ivory panels were used as treasure bindings (elaborate book covers) from the sixth century, usually as centerpieces, and surrounded by metalwork and gems. These book covers were sometimes assembled from up to five smaller panels due to the limited width of the tusk. Carved ivory covers were used as treasure bindings on the most precious illuminated manuscripts.
The Barberini Diptych
The Barberini Diptych (c. 500–550 CE) is a Byzantine ivory leaf from an imperial diptych dating from Late Antiquity . It is carved in the style known as Late Theodosian, representing the emperor as triumphant victor .
The Barberini Diptych is attributed to an imperial workshop in Constantinople. The emperor depicted in it is usually identified as Justinian, or possibly Anastasius I or Zeno. Although it is not a consular diptych, it shares many features of their decorative schemes.
The emperor is accompanied in the main panel by a conquered barbarian in trousers to the left, and a crouching allegorical figure on the right that probably represents territory conquered or reconquered, and who holds his foot in gratitude or submission. An angel or Victory crowning the emperor with the traditional palm of victory, which is now lost.
The spear that partially conceals the barbarian does not wound him. He seems more astonished and overawed than combative. Above, Christ, with a fashionable, curled hairstyle, is flanked by two more angels in the style of pagan victory figures. He reigns above, while the emperor represents him below on Earth.
In the bottom panel barbarians from the West (left, in trousers) and East (right, with ivory tusks, a tiger and a small elephant) bring tribute, which includes wild animals. The figure in the left panel, apparently representing not a saint but a soldier, carries a statuette of Victory; his counterpart on the right is lost.
The Archangel Ivory
Dating to approximately the same period as the Barberini Diptych is the Archangel Ivory (c. 525–550 CE), the largest surviving half of an ivory diptych from the Early Byzantine period. The subject matter is an archangel, possibly Michael, who holds a scepter in his left hand and an orb capped with a cross in his right hand, which he extends in a gesture of offering .
This is the insignia of imperial power. Above the angel hovers a Greek cross surrounded by a laurel wreath, possibly signifying victory. Its missing half might have depicted Justinian I, to whom the archangel would be offering the insignia. It and the Barberini Diptych are the two most important surviving sixth-century Byzantine ivories attributed to the imperial workshops of Constantinople under Justinian.
The figure is depicted in a highly classical style, wearing Greek or Roman garb, and with a youthful face and proportions that conform to the ideals of classical sculpture. Although the architectural elements consist of a classical round arch supported by Composite columns , the space is more typically Byzantine in its bending of spatial logic.
The archangel’s feet are at the top of a staircase that recedes from the base of the columns, but his arms and wings are in front of the columns. His feet are also not firmly planted on the steps. The top of the ivory bears a Greek inscription that translates as, “Receive this suppliant, despite his sinfulness;” it is possibly an expression of humility on the part of Justinian.
In the Byzantine and Eastern Orthodox world, the disapproval of large religious sculpture was to remain unchanged to the present day. However, in the West it was overcome, probably beginning with the court of Charlemagne in the ninth century. As large monumental sculpture in other materials became more important, the centrality of ivory carving slowly lessened.
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4.2: Looking at a rainbow, what do you see?
The rainbow – with all of its myths and legends – is an indicator of the data astronomers examine.
Light
Light is Radiative energy , which can be split into a spectrum . A spectrum is the light’s component colors or wavelengths. Light can be split into its component colors or wavelengths by using a prism or diffraction grating.
Light comes in particle bundles, called photons. These photons travel at 186,000 mi/s or 300,000 km/s (3 X 108 m/s) . The Speed of Light, c, is an absolute; you cannot go faster than c. (the speed of light).
Light also moves in waves . Particles moving in waves are referred to as an Electromagnetic wave ; a wave in which both electric and magnetic waves “interact” or vibrate. The Wavelength is the distance between adjacent peaks on the wave, and the wave’s Frequency is the number of peaks that pass a specific point in a second.


15.1: Tracing a Broad Issue in the Individual
By the end of this section, you will be able to:
- Define the term case studies.
- Explain the purpose of case studies in academic research.
- Identify ethical considerations of research on human subjects.
To gain more knowledge of or insights into human behavior, thoughts, or emotions, researchers conduct observations of participants. Case studies are the written results of these observations. Because authors of case studies interpret results within the context of a limited setting and sample size, these authors often theorize about their findings and aim to discover opportunities for further research rather than draw hard, universal conclusions.
Case studies depend on qualitative research and analysis. Qualitative research involves subjective evidence that is difficult to control and difficult to replicate. For example, if a researcher observes a classroom, business, or hospital setting, their observations are limited to what they observe at that particular location on that particular day at that particular time.
Case studies also depend on quantitative research . Quantitative research involves hard, specific data that can be replicated in a controlled environment. You may have read about health studies that suggest a moderate amount of red wine or chocolate is good for your health or that eating red meat is bad for your health. Authors of case studies use quantitative research by looking at data drawn from a group and using it as a basis for their findings. In other words, the data, not the researchers’ observations, form the primary evidence.
Another thing to know about case studies is that their authors attempt to observe participants in their natural environments. For example, to learn something about customer-service skills for a case study, an author would observe employees at a call center or in a retail store as they do their jobs. Similarly, to learn about how people use language, an author might observe people communicating naturally with their friends, family, or colleagues. Because case studies take place in the participants’ natural environments, analyzing case studies can help readers imagine themselves in that environment. For example, as part of their training, a nurse or doctor might read a case study about a patient to think about what they would do in the same situation. Examining case studies helps readers imagine a wide range of outcomes, while conducting case studies helps researchers discover opportunities for further research.
Case Study Ethics
Professional researchers must abide by a complex ethical and legal framework when conducting case studies. More importantly, participants must give their permission to be part of the study and to have their information shared. Researchers are obligated to act ethically when conducting case studies, but what does “act ethically” mean, exactly? Most people would agree that it is unethical to inflict harm on a case study participant, yet there are instances of researchers injuring their participants either physically or psychologically. One of the best-known examples of a case study conducted unethically ( https://openstax.org/r/conductedunethically ) is the Milgram Experiment ( https://openstax.org/r/milgramexperiment ), in which Yale University psychologist Stanley Milgram ( https://openstax.org/r/stanleymilgram ) (1933–1984) attempted to study the extent of people’s willingness to submit to authority when ordered to do something they know is wrong. Participants were instructed to deliver a range of electric shocks to other participants, who in fact were not actual participants but other researchers. Unbeknownst to the participants, the shocks were not real, and no electric current was delivered when participants pressed the button to deliver the shocks. Responses to shocks—screams and other indications of pain—were prerecorded. Yet some participants reported suffering psychological trauma from what they believed were their actions.
Most people also would consider it unethical to be dishonest about a case study. Researchers are expected to conduct their studies and analyze their data objectively, without bias. Over the years, laws and ethical codes have been implemented to protect case study participants. If you pursue an academic or career field that uses case studies, you will learn more about ethical and legal considerations specific to that field. For example, most academic case studies must be approved by an institutional review board (IRB) before the research can be conducted. Most universities have specific guidance on how faculty and students should go about research involving human subjects and most likely will have strict guidelines for conducting case studies. The assignment in this chapter, however, asks only that you conduct an informal case study. Your instructor will be your best resource to get answers to questions you have about your college’s policies on conducting research and whether and how they apply to the research you intend to do.


6.6: Set Theory - Normal Order
Normal order (sometimes called normal form) has a lot in common with the concept of triad “root position.” Among other things, root position is a standard way to order the pitch-classes of triads and seventh chords so that we can classify and compare them easily. Normal order does the same, but in a more generalized way so as to apply to chords containing a variety of notes and intervals.
Normal order is the most compressed way to write a given collection of pitch classes. Often, you’ll be able to determine normal order intuitively using a keyboard or a clockface, but it’s good to learn a process that will always give you the correct answer.
- Write as a collection of pitch classes (eliminating duplicates) in ascending order and within a single octave. There are many possible answers.
- Duplicate the first pitch class at the end.
- Find the largest ordered pitch-class interval between adjacent pitch classes.
- Rewrite the collection beginning with the pitch class to the right of the largest interval and write your answer in square brackets.
For example, given {G-sharp4, A2, D-sharp3, A4}:
- Write as a collection of pitch classes (eliminating duplicates) in ascending order and within a single octave. {8,9,3}
- Duplicate the first pitch class at the end. {8,9,3,8}
- Find the largest ordered pitch-class interval between adjacent pitch classes. In this case, the largest interval is between “9” and “3.”
- Rewrite the collection beginning with the pitch class to the right of the largest interval and write your answer in square brackets. [3,8,9]
Occasionally you’ll have a tie in step 3. In these cases, write the ordering implied by each tie and calculate the interval from the first to the penultimate pitch class. The ordering with the smallest interval is the normal order.


6.E: Uniform Circular Motion and Gravitation (Excercise)
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Conceptual Questions
6.1: Rotation Angle and Angular Velocity
1. There is an analogy between rotational and linear physical quantities. What rotational quantities are analogous to distance and velocity?
6.2: Centripetal Acceleration
2. Can centripetal acceleration change the speed of circular motion? Explain.
6.3: Centripetal Force
3. If you wish to reduce the stress (which is related to centripetal force) on high-speed tires, would you use large- or small-diameter tires? Explain.
4. Define centripetal force. Can any type of force (for example, tension, gravitational force, friction, and so on) be a centripetal force? Can any combination of forces be a centripetal force?
5. If centripetal force is directed toward the center, why do you feel that you are ‘thrown’ away from the center as a car goes around a curve? Explain.
6. Race car drivers routinely cut corners as shown in Figure. Explain how this allows the curve to be taken at the greatest speed.
Two paths around a race track curve are shown. Race car drivers will take the inside path (called cutting the corner) whenever possible because it allows them to take the curve at the highest speed.
7. A number of amusement parks have rides that make vertical loops like the one shown in Figure. For safety, the cars are attached to the rails in such a way that they cannot fall off. If the car goes over the top at just the right speed, gravity alone will supply the centripetal force. What other force acts and what is its direction if:
(a) The car goes over the top at faster than this speed?
(b)The car goes over the top at slower than this speed?
Amusement rides with a vertical loop are an example of a form of curved motion.
8. What is the direction of the force exerted by the car on the passenger as the car goes over the top of the amusement ride pictured in Figure under the following circumstances:
(a) The car goes over the top at such a speed that the gravitational force is the only force acting?
(b) The car goes over the top faster than this speed?
(c) The car goes over the top slower than this speed?
9. As a skater forms a circle, what force is responsible for making her turn? Use a free body diagram in your answer.
10. Suppose a child is riding on a merry-go-round at a distance about halfway between its center and edge. She has a lunch box resting on wax paper, so that there is very little friction between it and the merry-go-round. Which path shown in Figure will the lunch box take when she lets go? The lunch box leaves a trail in the dust on the merry-go-round. Is that trail straight, curved to the left, or curved to the right? Explain your answer.
A child riding on a merry-go-round releases her lunch box at point P. This is a view from above the clockwise rotation. Assuming it slides with negligible friction, will it follow path A, B, or C, as viewed from Earth’s frame of reference? What will be the shape of the path it leaves in the dust on the merry-go-round?
11. Do you feel yourself thrown to either side when you negotiate a curve that is ideally banked for your car’s speed? What is the direction of the force exerted on you by the car seat?
12. Suppose a mass is moving in a circular path on a frictionless table as shown in figure. In the Earth’s frame of reference, there is no centrifugal force pulling the mass away from the centre of rotation, yet there is a very real force stretching the string attaching the mass to the nail. Using concepts related to centripetal force and Newton’s third law, explain what force stretches the string, identifying its physical origin.
A mass attached to a nail on a frictionless table moves in a circular path. The force stretching the string is real and not fictional. What is the physical origin of the force on the string?
6.4: Fictitious Forces and Non-inertial Frames: The Coriolis Force
13. When a toilet is flushed or a sink is drained, the water (and other material) begins to rotate about the drain on the way down. Assuming no initial rotation and a flow initially directly straight toward the drain, explain what causes the rotation and which direction it has in the northern hemisphere. (Note that this is a small effect and in most toilets the rotation is caused by directional water jets.) Would the direction of rotation reverse if water were forced up the drain?
14. Is there a real force that throws water from clothes during the spin cycle of a washing machine? Explain how the water is removed.
15. In one amusement park ride, riders enter a large vertical barrel and stand against the wall on its horizontal floor. The barrel is spun up and the floor drops away. Riders feel as if they are pinned to the wall by a force something like the gravitational force. This is a fictitious force sensed and used by the riders to explain events in the rotating frame of reference of the barrel. Explain in an inertial frame of reference (Earth is nearly one) what pins the riders to the wall, and identify all of the real forces acting on them.
16. Action at a distance, such as is the case for gravity, was once thought to be illogical and therefore untrue. What is the ultimate determinant of the truth in physics, and why was this action ultimately accepted?
17. Two friends are having a conversation. Anna says a satellite in orbit is in freefall because the satellite keeps falling toward Earth. Tom says a satellite in orbit is not in freefall because the acceleration due to gravity is not 9.80 \(\displaystyle m/s^2\). Who do you agree with and why?
18. A non-rotating frame of reference placed at the center of the Sun is very nearly an inertial one. Why is it not exactly an inertial frame?
6.5: Newton’s Universal Law of Gravitation
19. Action at a distance, such as is the case for gravity, was once thought to be illogical and therefore untrue. What is the ultimate determinant of the truth in physics, and why was this action ultimately accepted?
20. Two friends are having a conversation. Anna says a satellite in orbit is in freefall because the satellite keeps falling toward Earth. Tom says a satellite in orbit is not in freefall because the acceleration due to gravity is not \(\displaystyle 9.80 m/s^2\). Who do you agree with and why?
21. Draw a free body diagram for a satellite in an elliptical orbit showing why its speed increases as it approaches its parent body and decreases as it moves away.
22. Newton’s laws of motion and gravity were among the first to convincingly demonstrate the underlying simplicity and unity in nature. Many other examples have since been discovered, and we now expect to find such underlying order in complex situations. Is there proof that such order will always be found in new explorations?
6.6: Satellites and Kepler’s Laws: An Argument for Simplicity
23. In what frame(s) of reference are Kepler’s laws valid? Are Kepler’s laws purely descriptive, or do they contain causal information?
Problem Exercises
6.1: Rotation Angle and Angular Velocity
24. Semi-trailer trucks have an odometer on one hub of a trailer wheel. The hub is weighted so that it does not rotate, but it contains gears to count the number of wheel revolutions—it then calculates the distance traveled. If the wheel has a 1.15 m diameter and goes through 200,000 rotations, how many kilometers should the odometer read?
Solution
723 km
25. Microwave ovens rotate at a rate of about 6 rev/min. What is this in revolutions per second? What is the angular velocity in radians per second?
26. An automobile with 0.260 m radius tires travels 80,000 km before wearing them out. How many revolutions do the tires make, neglecting any backing up and any change in radius due to wear?
Solution
\(\displaystyle 5×10^7\) rotations
27. (a) What is the period of rotation of Earth in seconds?
(b) What is the angular velocity of Earth?
(c) Given that Earth has a radius of \(\displaystyle 6.4×10^6m\) at its equator, what is the linear velocity at Earth’s surface?
28. A baseball pitcher brings his arm forward during a pitch, rotating the forearm about the elbow. If the velocity of the ball in the pitcher’s hand is 35.0 m/s and the ball is 0.300 m from the elbow joint, what is the angular velocity of the forearm?
Solution
117 rad/s
29. In lacrosse, a ball is thrown from a net on the end of a stick by rotating the stick and forearm about the elbow. If the angular velocity of the ball about the elbow joint is 30.0 rad/s and the ball is 1.30 m from the elbow joint, what is the velocity of the ball?
30. A truck with 0.420-m-radius tires travels at 32.0 m/s. What is the angular velocity of the rotating tires in radians per second? What is this in rev/min?
Solution
76.2 rad/s
728 rpm
31. Integrated Concepts
When kicking a football, the kicker rotates his leg about the hip joint.
(a) If the velocity of the tip of the kicker’s shoe is 35.0 m/s and the hip joint is 1.05 m from the tip of the shoe, what is the shoe tip’s angular velocity?
(b) The shoe is in contact with the initially stationary 0.500 kg football for 20.0 ms. What average force is exerted on the football to give it a velocity of 20.0 m/s?
(c) Find the maximum range of the football, neglecting air resistance.
Solution
(a) 33.3 rad/s
(b) 500 N
(c) 40.8 m
32. Construct Your Own Problem
Consider an amusement park ride in which participants are rotated about a vertical axis in a cylinder with vertical walls. Once the angular velocity reaches its full value, the floor drops away and friction between the walls and the riders prevents them from sliding down. Construct a problem in which you calculate the necessary angular velocity that assures the riders will not slide down the wall. Include a free body diagram of a single rider. Among the variables to consider are the radius of the cylinder and the coefficients of friction between the riders’ clothing and the wall.
6.2: Centripetal Acceleration
33. A fairground ride spins its occupants inside a flying saucer-shaped container. If the horizontal circular path the riders follow has an 8.00 m radius, at how many revolutions per minute will the riders be subjected to a centripetal acceleration whose magnitude is 1.50 times that due to gravity?
Solution
12.9 rev/min
34. A runner taking part in the 200 m dash must run around the end of a track that has a circular arc with a radius of curvature of 30 m. If he completes the 200 m dash in 23.2 s and runs at constant speed throughout the race, what is the magnitude of his centripetal acceleration as he runs the curved portion of the track?
35. Taking the age of Earth to be about \(\displaystyle 4×10^9\) years and assuming its orbital radius of \(\displaystyle 1.5 ×10^{11}\) m has not changed and is circular, calculate the approximate total distance Earth has traveled since its birth (in a frame of reference stationary with respect to the Sun).
Solution
\(\displaystyle 4×10^{21}m\)
36. The propeller of a World War II fighter plane is 2.30 m in diameter.
(a) What is its angular velocity in radians per second if it spins at 1200 rev/min?
(b) What is the linear speed of its tip at this angular velocity if the plane is stationary on the tarmac?
(c) What is the centripetal acceleration of the propeller tip under these conditions? Calculate it in meters per second squared and convert to multiples of \(\displaystyle g\).
37. An ordinary workshop grindstone has a radius of 7.50 cm and rotates at 6500 rev/min.
(a) Calculate the magnitude of the centripetal acceleration at its edge in meters per second squared and convert it to multiples of \(\displaystyle g\).
(b) What is the linear speed of a point on its edge?
Solution
a) \(\displaystyle 3.47×10^4m/s^2, 3.55×10^3g\)
b) \(\displaystyle 51.1m/s\)
38. Helicopter blades withstand tremendous stresses. In addition to supporting the weight of a helicopter, they are spun at rapid rates and experience large centripetal accelerations, especially at the tip.
(a) Calculate the magnitude of the centripetal acceleration at the tip of a 4.00 m long helicopter blade that rotates at 300 rev/min.
(b) Compare the linear speed of the tip with the speed of sound (taken to be 340 m/s).
39. Olympic ice skaters are able to spin at about 5 rev/s.
(a) What is their angular velocity in radians per second?
(b) What is the centripetal acceleration of the skater’s nose if it is 0.120 m from the axis of rotation?
(c) An exceptional skater named Dick Button was able to spin much faster in the 1950s than anyone since—at about 9 rev/s. What was the centripetal acceleration of the tip of his nose, assuming it is at 0.120 m radius?
(d) Comment on the magnitudes of the accelerations found. It is reputed that Button ruptured small blood vessels during his spins.
Solution
a) 31.4 rad/s
b) 118 m/s
c) 384 m/s
d)The centripetal acceleration felt by Olympic skaters is 12 times larger than the acceleration due to gravity. That’s quite a lot of acceleration in itself. The centripetal acceleration felt by Button’s nose was 39.2 times larger than the acceleration due to gravity. It is no wonder that he ruptured small blood vessels in his spins.
40. What percentage of the acceleration at Earth’s surface is the acceleration due to gravity at the position of a satellite located 300 km above Earth?
41. Verify that the linear speed of an ultracentrifuge is about 0.50 km/s, and Earth in its orbit is about 30 km/s by calculating:
(a) The linear speed of a point on an ultracentrifuge 0.100 m from its center, rotating at 50,000 rev/min.
(b) The linear speed of Earth in its orbit about the Sun (use data from the text on the radius of Earth’s orbit and approximate it as being circular).
Solution
a) 0.524 km/s
b) 29.7 km/s
42. A rotating space station is said to create “artificial gravity”—a loosely-defined term used for an acceleration that would be crudely similar to gravity. The outer wall of the rotating space station would become a floor for the astronauts, and centripetal acceleration supplied by the floor would allow astronauts to exercise and maintain muscle and bone strength more naturally than in non-rotating space environments. If the space station is 200 m in diameter, what angular velocity would produce an “artificial gravity” of \(\displaystyle 9.80m/s^2\) at the rim?
43. At takeoff, a commercial jet has a 60.0 m/s speed. Its tires have a diameter of 0.850 m.
(a) At how many rev/min are the tires rotating?
(b) What is the centripetal acceleration at the edge of the tire?
(c) With what force must a determined \(\displaystyle 1.00×10^{−15}kg\) bacterium cling to the rim?
(d) Take the ratio of this force to the bacterium’s weight.
Solution
(a) \(\displaystyle 1.35×10^3rpm\)
(b) \(\displaystyle 8.47×10^3m/s^2\)
(c) \(\displaystyle 8.47×10^{–12}N\)
(d) 865
44.  Sometime near the middle of the ride, the ship is momentarily motionless at the top of its circular arc. The ship then swings down under the influence of gravity.
(a) Assuming negligible friction, find the speed of the riders at the bottom of its arc, given the system's center of mass travels in an arc having a radius of 14.0 m and the riders are near the center of mass.
(b) What is the centripetal acceleration at the bottom of the arc?
(c) Draw a free body diagram of the forces acting on a rider at the bottom of the arc.
(d) Find the force exerted by the ride on a 60.0 kg rider and compare it to her weight.
(e) Discuss whether the answer seems reasonable.
Solution
(a) \(\displaystyle 16.6m/s\)
(b) \(\displaystyle 19.6m/s^2\)
(c)
(d) \(\displaystyle 1.76×10^3N\) or \(\displaystyle 3.00w\), that is, the normal force (upward) is three times her weight.
(e) This answer seems reasonable, since she feels like she’s being forced into the chair MUCH stronger than just by gravity.
45.  The swing is suspended 2.00 m above the child’s center of mass.
(a) What is the magnitude of the centripetal acceleration of the child at the low point?
(b) What is the magnitude of the force the child exerts on the seat if his mass is 18.0 kg?
(c) What is unreasonable about these results?
(d) Which premises are unreasonable or inconsistent?
Solution
a) \(\displaystyle 40.5m/s^2\)
b) 905 N
c) The force in part (b) is very large. The acceleration in part (a) is too much, about 4 g.
d) The speed of the swing is too large. At the given velocity at the bottom of the swing, there is enough kinetic energy to send the child all the way over the top, ignoring friction.
6.3: Centripetal Force
46. (a) A 22.0 kg child is riding a playground merry-go-round that is rotating at 40.0 rev/min. What centripetal force must she exert to stay on if she is 1.25 m from its center?
(b) What centripetal force does she need to stay on an amusement park merry-go-round that rotates at 3.00 rev/min if she is 8.00 m from its center?
(c) Compare each force with her weight.
 Calculate the centripetal force on the end of a 100 m (radius) wind turbine blade that is rotating at 0.5 rev/s. Assume the mass is 4 kg.
48. What is the ideal banking angle for a gentle turn of 1.20 km radius on a highway with a 105 km/h speed limit (about 65 mi/h), assuming everyone travels at the limit?
Solution
\(\displaystyle 4.14º\)
48. What is the ideal speed to take a 100 m radius curve banked at a 20.0° angle?
49. (a) What is the radius of a bobsled turn banked at 75.0° and taken at 30.0 m/s, assuming it is ideally banked?
(b) Calculate the centripetal acceleration.
(c) Does this acceleration seem large to you?
Solution
a) 24.6 m
b) \(\displaystyle 36.6 m/s^2\)
c) \(\displaystyle a_c=3.73g.\) This does not seem too large, but it is clear that bobsledders feel a lot of force on them going through sharply banked turns.
50. Part of riding a bicycle involves leaning at the correct angle when making a turn, as seen in Figure. To be stable, the force exerted by the ground must be on a line going through the center of gravity. The force on the bicycle wheel can be resolved into two perpendicular components—friction parallel to the road (this must supply the centripetal force), and the vertical normal force (which must equal the system’s weight).
(a) Show that \(\displaystyle θ\) (as defined in the figure) is related to the speed v size 12{v} {} and radius of curvature r size 12{r} {} of the turn in the same way as for an ideally banked roadway—that is, \(\displaystyle θ=tan^{–1}v^2/rg\)
(b) Calculate \(\displaystyle θ\) for a 12.0 m/s turn of radius 30.0 m (as in a race).
A bicyclist negotiating a turn on level ground must lean at the correct angle—the ability to do this becomes instinctive. The force of the ground on the wheel needs to be on a line through the center of gravity. The net external force on the system is the centripetal force. The vertical component of the force on the wheel cancels the weight of the system while its horizontal component must supply the centripetal force. This process produces a relationship among the angle θ, the speed v, and the radius of curvature r of the turn similar to that for the ideal banking of roadways.
51. A large centrifuge, like the one shown in Figure(a), is used to expose aspiring astronauts to accelerations similar to those experienced in rocket launches and atmospheric reentries.
(a) At what angular velocity is the centripetal acceleration \(\displaystyle 10g\) if the rider is 15.0 m from the center of rotation?
(b) The rider’s cage hangs on a pivot at the end of the arm, allowing it to swing outward during rotation as shown in Figure(b). At what angle \(\displaystyle θ\) below the horizontal will the cage hang when the centripetal acceleration is \(\displaystyle 10g\)?
(Hint: The arm supplies centripetal force and supports the weight of the cage. Draw a free body diagram of the forces to see what the angle θ size 12{θ} {} should be.)
(a) NASA centrifuge used to subject trainees to accelerations similar to those experienced in rocket launches and reentries. (credit: NASA) (b) Rider in cage showing how the cage pivots outward during rotation. This allows the total force exerted on the rider by the cage to be along its axis at all times.
Solution
a) 2.56 rad/s
b) 5.71º
bIntegrated Concepts
If a car takes a banked curve at less than the ideal speed, friction is needed to keep it from sliding toward the inside of the curve (a real problem on icy mountain roads).
(a) Calculate the ideal speed to take a 100 m radius curve banked at 15.0º.
(b) What is the minimum coefficient of friction needed for a frightened driver to take the same curve at 20.0 km/h?
Solution
a) 16.2 m/s
b) 0.234
53. Modern roller coasters have vertical loops like the one shown in Figure. The radius of curvature is smaller at the top than on the sides so that the downward centripetal acceleration at the top will be greater than the acceleration due to gravity, keeping the passengers pressed firmly into their seats. What is the speed of the roller coaster at the top of the loop if the radius of curvature there is 15.0 m and the downward acceleration of the car is 1.50 g?
Teardrop-shaped loops are used in the latest roller coasters so that the radius of curvature gradually decreases to a minimum at the top. This means that the centripetal acceleration builds from zero to a maximum at the top and gradually decreases again. A circular loop would cause a jolting change in acceleration at entry, a disadvantage discovered long ago in railroad curve design. With a small radius of curvature at the top, the centripetal acceleration can more easily be kept greater than g so that the passengers do not lose contact with their seats nor do they need seat belts to keep them in place.
54. Unreasonable Results
(a) Calculate the minimum coefficient of friction needed for a car to negotiate an unbanked 50.0 m radius curve at 30.0 m/s.
(b) What is unreasonable about the result?
(c) Which premises are unreasonable or inconsistent?
Solution
a) 1.84
b) A coefficient of friction this much greater than 1 is unreasonable .
c) The assumed speed is too great for the tight curve.
6.5: Newton’s Universal Law of Gravitation
55. (a) Calculate Earth’s mass given the acceleration due to gravity at the North Pole is \(\displaystyle 9.830 m/s^2\)and the radius of the Earth is 6371 km from center to pole.
(b) Compare this with the accepted value of \(\displaystyle 5.979×10^{24}kg\).
Solution
a) \(\displaystyle 5.979×10^{24}kg\)
b) This is identical to the best value to three significant figures.
56. (a) Calculate the magnitude of the acceleration due to gravity on the surface of Earth due to the Moon.
(b) Calculate the magnitude of the acceleration due to gravity at Earth due to the Sun.
(c) Take the ratio of the Moon’s acceleration to the Sun’s and comment on why the tides are predominantly due to the Moon in spite of this number.
57. (a) What is the acceleration due to gravity on the surface of the Moon?
(b) On the surface of Mars? The mass of Mars is \(\displaystyle 6.418×10^{23}kg\) and its radius is \(\displaystyle 3.38×10^6m\)
Solution
a) \(\displaystyle 1.62m/s^2\)
b) \(\displaystyle 3.75m/s^2\)
58. (a) Calculate the acceleration due to gravity on the surface of the Sun.
(b) By what factor would your weight increase if you could stand on the Sun? (Never mind that you cannot.)
59. The Moon and Earth rotate about their common center of mass, which is located about 4700 km from the center of Earth. (This is 1690 km below the surface.)
(a) Calculate the magnitude of the acceleration due to the Moon’s gravity at that point.
(b) Calculate the magnitude of the centripetal acceleration of the center of Earth as it rotates about that point once each lunar month (about 27.3 d) and compare it with the acceleration found in part (a). Comment on whether or not they are equal and why they should or should not be.
Solution
a) \(\displaystyle 3.42×10^{–5}m/s^2\)
b) \(\displaystyle 3.34×10^{–5}m/s^2\)
The values are nearly identical. One would expect the gravitational force to be the same as the centripetal force at the core of the system.
60. Solve part (b) of Example using \(\displaystyle a_c=v^2/r\).
61. Astrology, that unlikely and vague pseudo science, makes much of the position of the planets at the moment of one’s birth. The only known force a planet exerts on Earth is gravitational.
(a) Calculate the magnitude of the gravitational force exerted on a 4.20 kg baby by a 100 kg father 0.200 m away at birth (he is assisting, so he is close to the child).
(b) Calculate the magnitude of the force on the baby due to Jupiter if it is at its closest distance to Earth, some \(\displaystyle 6.29×10^{11}m\) away. How does the force of Jupiter on the baby compare to the force of the father on the baby? Other objects in the room and the hospital building also exert similar gravitational forces. (Of course, there could be an unknown force acting, but scientists first need to be convinced that there is even an effect, much less that an unknown force causes it.)
Solution
a) \(\displaystyle 7.01×10^{–7}N\)
b) \(\displaystyle 1.35×10^{–6}N\)
62. The existence of the dwarf planet Pluto was proposed based on irregularities in Neptune’s orbit. Pluto was subsequently discovered near its predicted position. But it now appears that the discovery was fortuitous, because Pluto is small and the irregularities in Neptune’s orbit were not well known. To illustrate that Pluto has a minor effect on the orbit of Neptune compared with the closest planet to Neptune:
(a) Calculate the acceleration due to gravity at Neptune due to Pluto when they are \(\displaystyle 4.50×10^{12}m\) apart, as they are at present. The mass of Pluto is \(\displaystyle 1.4×10^{22}kg\).
(b) Calculate the acceleration due to gravity at Neptune due to Uranus, presently about \(\displaystyle 2.50×10^{12}m\) apart, and compare it with that due to Pluto. The mass of Uranus is \(\displaystyle 8.62×10^{25}kg\).
63. (a) The Sun orbits the Milky Way galaxy once each \(\displaystyle 2.60 x 10^8y\), with a roughly circular orbit averaging \(\displaystyle 3.00 x 10^4\) light years in radius. (A light year is the distance traveled by light in 1 y.) Calculate the centripetal acceleration of the Sun in its galactic orbit. Does your result support the contention that a nearly inertial frame of reference can be located at the Sun?
(b) Calculate the average speed of the Sun in its galactic orbit. Does the answer surprise you?
Solution
a) \(\displaystyle 1.66×10^{–10}m/s^2\)
b) \(\displaystyle 2.17×10^5m/s\)
64. Unreasonable Result
A mountain 10.0 km from a person exerts a gravitational force on him equal to 2.00% of his weight.
(a) Calculate the mass of the mountain.
(b) Compare the mountain’s mass with that of Earth.
(c) What is unreasonable about these results?
(d) Which premises are unreasonable or inconsistent? (Note that accurate gravitational measurements can easily detect the effect of nearby mountains and variations in local geology.)
Solution
a) \(\displaystyle 2.937×10^{17}kg\)
b) \(\displaystyle 4.91×10^{–8}\) of the Earth’s mass.
c) The mass of the mountain and its fraction of the Earth’s mass are too great.
d) The gravitational force assumed to be exerted by the mountain is too great.
6.6: Satellites and Kepler’s Laws: An Argument for Simplicity
65. A geosynchronous Earth satellite is one that has an orbital period of precisely 1 day. Such orbits are useful for communication and weather observation because the satellite remains above the same point on Earth (provided it orbits in the equatorial plane in the same direction as Earth’s rotation). Calculate the radius of such an orbit based on the data for the moon in Table.
66. Calculate the mass of the Sun based on data for Earth’s orbit and compare the value obtained with the Sun’s actual mass.
Solution
\(\displaystyle 1.98×10^{30}kg\)
67. Find the mass of Jupiter based on data for the orbit of one of its moons, and compare your result with its actual mass.
68. Find the ratio of the mass of Jupiter to that of Earth based on data in Table.
Solution
\(\displaystyle \frac{M_J}{M_E}=316\)
69. Astronomical observations of our Milky Way galaxy indicate that it has a mass of about \(\displaystyle 8.0×10^{11}\) solar masses. A star orbiting on the galaxy’s periphery is about \(\displaystyle 6.0×10^4\) light years from its center. (a) What should the orbital period of that star be? (b) If its period is \(\displaystyle 6.0×10^7\) instead, what is the mass of the galaxy? Such calculations are used to imply the existence of “dark matter” in the universe and have indicated, for example, the existence of very massive black holes at the centers of some galaxies.
70. Integrated Concepts
Space debris left from old satellites and their launchers is becoming a hazard to other satellites.
(a) Calculate the speed of a satellite in an orbit 900 km above Earth’s surface.
(b) Suppose a loose rivet is in an orbit of the same radius that intersects the satellite’s orbit at an angle of \(\displaystyle 90º\) relative to Earth. What is the velocity of the rivet relative to the satellite just before striking it?
(c) Given the rivet is 3.00 mm in size, how long will its collision with the satellite last?
(d) If its mass is 0.500 g, what is the average force it exerts on the satellite?
(e) How much energy in joules is generated by the collision? (The satellite’s velocity does not change appreciably, because its mass is much greater than the rivet’s.)
Solution
a) \(\displaystyle 7.4×10^3m/s\)
b) \(\displaystyle 1.05×10^3m/s\)
c) \(\displaystyle 2.86×10^{−7}s\)
d) \(\displaystyle 1.84×10^7N\)
e) \(\displaystyle 2.76×10^4J\)
71. Unreasonable Results
(a) Based on Kepler’s laws and information on the orbital characteristics of the Moon, calculate the orbital radius for an Earth satellite having a period of 1.00 h.
(b) What is unreasonable about this result?
(c) What is unreasonable or inconsistent about the premise of a 1.00 h orbit?
Solution
a) \(\displaystyle 5.08×10^3km\)
b) This radius is unreasonable because it is less than the radius of earth.
c) The premise of a one-hour orbit is inconsistent with the known radius of the earth.
72. Construct Your Own Problem
On February 14, 2000, the NEAR spacecraft was successfully inserted into orbit around Eros, becoming the first artificial satellite of an asteroid. Construct a problem in which you determine the orbital speed for a satellite near Eros. You will need to find the mass of the asteroid and consider such things as a safe distance for the orbit. Although Eros is not spherical, calculate the acceleration due to gravity on its surface at a point an average distance from its center of mass. Your instructor may also wish to have you calculate the escape velocity from this point on Eros.
Contributors and Attributions
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Paul Peter Urone (Professor Emeritus at California State University, Sacramento) and Roger Hinrichs (State University of New York, College at Oswego) with Contributing Authors: Kim Dirks (University of Auckland) and Manjula Sharma (University of Sydney). This work is licensed by OpenStax University Physics under a Creative Commons Attribution License (by 4.0) .


8.7: The Light-Independent Reactions of Photosynthesis - AM and C4 Photosynthesis
- Compare C4 and CAM photosynthesis
Photosynthesis in desert plants has evolved adaptations that conserve water. In harsh, dry heat, every drop of water must be used to survive. Because stomata must open to allow for the uptake of CO 2 , water escapes from the leaf during active photosynthesis. Desert plants have evolved processes to conserve water and deal with harsh conditions. A more efficient use of CO 2 allows plants to adapt to living with less water.
Some plants such as cacti can prepare materials for photosynthesis during the night by a temporary carbon fixation and storage process, because opening the stomata at this time conserves water due to cooler temperatures. In addition, cacti have evolved the ability to carry out low levels of photosynthesis without opening stomata at all, a mechanism for surviving extremely dry periods.
CAM Photosynthesis
Xerophytes, such as cacti and most succulents, also use
phosphoenolpyruvate (PEP) carboxylase to capture carbon dioxide in a process called crassulacean acid metabolism (CAM). In contrast to C
4
metabolism, which
physically
separates the CO
2
fixation to PEP from the Calvin cycle, CAM
temporally
separates these two processes.
CAM plants have a different leaf anatomy from C 3 plants, and fix the CO 2 at night, when their stomata are open. CAM plants store the CO 2 mostly in the form of malic acid via carboxylation of phosphoenolpyruvate to oxaloacetate, which is then reduced to malate. Decarboxylation of malate during the day releases CO 2 inside the leaves, thus allowing carbon fixation to 3-phosphoglycerate by RuBisCO. Sixteen thousand species of plants use CAM.
C
4
Carbon Fixation
The C4 pathway bears resemblance to CAM; both act to concentrate CO 2 around RuBisCO, thereby increasing its efficiency. CAM concentrates it temporally, providing CO 2 during the day and not at night, when respiration is the dominant reaction.
C 4 plants, in contrast, concentrate CO 2 spatially, with a RuBisCO reaction centre in a “bundle sheath cell” that is inundated with CO 2 . Due to the inactivity required by the CAM mechanism, C 4 carbon fixation has a greater efficiency in terms of PGA synthesis.
Cross section of maize, a C 4 plant
Cross section of a C4 plant, specifically of a maize leaf. Drawing based on microscopic images courtesy of Cambridge University Plant Sciences Department.
C 4 plants can produce more sugar than C 3 plants in conditions of high light and temperature. Many important crop plants are C 4 plants, including maize, sorghum, sugarcane, and millet. Plants that do not use PEP-carboxylase in carbon fixation are called C3 plants because the primary carboxylation reaction, catalyzed by RuBisCO, produces the three-carbon 3-phosphoglyceric acids directly in the Calvin-Benson cycle. Over 90% of plants use C 3 carbon fixation, compared to 3% that use C 4 carbon fixation; however, the evolution of C 4 in over 60 plant lineages makes it a striking example of convergent evolution.
Key Points
- The process of photosynthesis in desert plants has evolved mechanisms to conserve water.
- Plants that use crassulacean acid metabolism (CAM) photosynthesis fix CO 2 at night, when their stomata are open.
- Plants that use C4 carbon fixation concentrate carbon dioxide spatially, using “bundle sheath cells” which are inundated with CO 2.
Key Terms
- crassulacean acid metabolism : A carbon fixation pathway that evolved in some plants as an adaptation to arid conditions, in which the stomata in the leaves remain shut during the day to reduce evapotranspiration, but open at night to collect carbon dioxide (CO2).
- C4 carbon fixation : A form of photosynthesis in which plants concentrate CO2 spatially, with a RuBisCO reaction centre in a “bundle sheath cell” that is inundated with CO2


13.9: Summary
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“Step back … Before you get started putting your course online, you will want to take a step back to examine the big picture of what it is you want to do”. (Elbaum et al., 2002)
Planning an online course involves identifying and communicating the preliminary considerations that will guide course design and implementation. At the core, planning requires an examination of individual circumstances, philosophies, and skills. There is no single course planning worksheet that will suit all design projects.
This chapter began with an overview of how the planning process is influenced by context and trends. There is a continuum of design approaches ranging from flexible to linear, and emerging opinions about how our learning spaces should be shaped. Although learning-centred design is commonly acknowledged as central to the success of online courses, and a team of individuals with specific areas of expertise is ideal for effective design, in reality there are often gaps in the necessary resources, skills and knowledge to accomplish everything we need or want to do.
Certain learner characteristics can often be identified early on in the design process, but this is not always the case. Age, socio-cultural backgrounds, and lifestyles of the audience are all important considerations for course design. E-learning offers more opportunities to cater to individual learning styles by combining text and multimedia, planning for exploration, and designing activities to engage learners in a variety of ways.
Likewise, e-teaching style influences design, yet this is another element that can be unknown during the planning stage. An awareness of the general teaching style characteristics and how they influence practice will help to guide the design process.
Communicating our course design plans using mapping tools can serve to identify the important components and relationships among them. Visually organizing design ideas in this manner is particularly suitable for online courses because it can translate well into a website design. Different types of mapping tools can support the various design approaches, some being more linear than others.
The final step of the planning process, the packaging, is a culmination of all steps. Presentation, pacing, flow, and general look and feel of the course is informed by educational philosophies and beliefs of the design team, the audience, teaching and learning styles, and a preliminary sketch or map of course components and the relationships among those components in terms of time and space. There are also some important web design principles to follow.
Practice tells us that there are many different ways to approach online course design. It is easy to be swept away by the plethora of technologies available to designers but an important reminder to conclude this chapter is to keep the focus on learning. Take the time to understand the why of your course plan, and how much of the design should precede implementation.


10.1: Introduction
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Relations between the United States and the Soviet Union—erstwhile allies—soured soon after World War II. On February 22, 1946, less than a year after the end of the war, the chargé d’affaires of the U.S. embassy in Moscow, George Kennan sent a famously lengthy telegram—literally referred to as the Long Telegram—to the State Department denouncing the Soviet Union. “World communism is like a malignant parasite which feeds only on diseased tissue,” he wrote, and “the steady advance of uneasy Russian nationalism . . . in [the] new guise of international Marxism . . . is more dangerous and insidious than ever before.” 1 There could be no cooperation between the United States and the Soviet Union, Kennan wrote. Instead, the Soviets had to be “contained.” Less than two weeks later, on March 5, former British prime minister Winston Churchill visited President Harry Truman in his home state of Missouri and declared that Europe had been cut in half, divided by an “iron curtain” that had “descended across the Continent.” 2 Aggressive anti-Soviet sentiment seized the American government and soon the American people. 3
The Cold War was a global political and ideological struggle between capitalist and communist countries, particularly between the two surviving superpowers of the postwar world: the United States and the Union of Soviet Socialist Republics (USSR). “Cold” because it was never a “hot,” direct shooting war between the United States and the Soviet Union, the generations-long, multifaceted rivalry nevertheless bent the world to its whims. Tensions ran highest, perhaps, during the first Cold War, which lasted from the mid-1940s through the mid-1960s, after which followed a period of relaxed tensions and increased communication and cooperation, known by the French term détente , until the second Cold War interceded from roughly 1979 until the collapse of the Berlin Wall in 1989 and the dissolution of the Soviet Union in 1991. The Cold War reshaped the world and the generations of Americans that lived under its shadow.


6.6: Antipsychotics
Antipsychotic medicines are primarily used to manage psychosis (i.e., a loss of contact with reality that may include delusions or hallucinations). Psychosis can be a symptom of a physical condition (such as a high fever, head injury, or substance intoxication) or a mental disorder (such as schizophrenia, bipolar disorder, or severe depression). Antipsychotic medications may also be used in combination with other medications to treat the symptoms of other mental health conditions, including attention deficit hyperactivity disorder (ADHD), eating disorders, post-traumatic stress disorder (PTSD), obsessive-compulsive disorder (OCD), and generalized anxiety disorder. [1]
First-generation antipsychotics (also called typical antipsychotics) have several potential adverse effects, and medication is prescribed based on the client’s ability to tolerate the adverse effects. Second-generation antipsychotics (also referred to as atypical antipsychotics) have fewer adverse effects and are generally better tolerated. Clients respond differently to antipsychotic medications, so it may take several trials of different medications to find the one that works best for their symptoms. [2]
First-Generation (Typical) Antipsychotics
Common first-generation antipsychotic medications (also called “typical” antipsychotics) include chlorpromazine, haloperidol, perphenazine, and fluphenazine. [3]
First-generation antipsychotics work by blocking dopamine receptors in certain areas of the CNS, such as the limbic system and the basal ganglia. These areas are associated with emotions, cognitive function, and motor function. As a result, blockage produces a tranquilizing effect in psychotic clients. However, several adverse effects are caused by this dopamine blockade, such extrapyramidal side effects (e.g., involuntary or uncontrollable movements, tremors, and muscle contractions) and tardive dyskinesia (a syndrome of movement disorders that persists for at least one month and can last up to several years despite discontinuation of the medications).
Second-Generation (Atypical) Antipsychotics
Second-generation antipsychotics (also called atypical antipsychotics) work by blocking specific D2 dopamine receptors and serotonin receptors. Second-generation medications include risperidone, olanzapine, quetiapine, ziprasidone, aripiprazole, paliperidone, and lurasidone. Several atypical antipsychotics have a “broader spectrum” of action than the older medications and are used for treating bipolar depression or depression that has not responded to an antidepressant medication alone. They have a significantly decreased risk of extrapyramidal side effects but are associated with weight gain and the development of metabolic syndrome. [4] Metabolic syndrome increases the risk of heart disease, stroke, and type 2 diabetes. Clinical symptoms of metabolic syndrome include high blood glucose, symptoms of diabetes (i.e., increased thirst and urination, fatigue, and blurred vision), obesity with a large abdominal girth, hypertension, elevated triglyceride, and lower levels of HDL.
Clozapine
Clients with treatment-resistant schizophrenia may be prescribed clozapine, a specific atypical antipsychotic medication that binds to serotonin, as well as dopamine receptors. Clozapine also has strong anticholinergic, sedative, cardiac, and hypotensive properties and frequent drug-drug interactions. [5]
View a supplementary YouTube video [6] explaining how clozapine binds to additional neuroreceptors compared to other antipsychotic medications: The Pines, the Dones, Two Pips and a Rip
Read additional information about the mechanism of action, adverse side effects, and patient education regarding antipsychotic medications in the “ Schizophrenia ” section of the “Psychosis and Schizophrenia” chapter.
- National Institute of Mental Health. (2016, October). Mental health medications. U.S. Department of Health & Human Services. https://www.nimh.nih.gov/health/topics/mental-health-medications ↵
- National Institute of Mental Health. (2016, October). Mental health medications. U.S. Department of Health and Human Services. https://www.nimh.nih.gov/health/topics/mental-health-medications#part_2362 ↵
- National Institute of Mental Health. (2016, October). Mental health medications. U.S. Department of Health and Human Services. https://www.nimh.nih.gov/health/topics/mental-health-medications#part_2362 ↵
- This work is a derivative of StatPearls by Chokhawala and Stevens and is licensed under CC BY 4.0 ↵
- Jibson, M. D. (2021). Second-generation antipsychotic medications: Pharmacology, administration, and side effects. UpToDate. Retrieved January 14, 2022, from https://www.uptodate.com/ ↵
- NEI Psychopharm. (2014, March 18). The pines, the dones, two pips, and a rip [Video]. YouTube. All rights reserved. https://youtu.be/kuYGJOcloH8 ↵


9.6: Checklist for Abdominal Assessment
Use this checklist below to review the steps for completion of an “Abdominal Assessment.” [1]
Steps
Disclaimer: Always review and follow agency policy regarding this specific skill.
- Gather stethoscope.
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Perform safety steps:
- Perform hand hygiene.
- Check the room for transmission-based precautions.
- Introduce yourself, your role, the purpose of your visit, and an estimate of the time it will take.
- Confirm patient ID using two patient identifiers (e.g., name and date of birth).
- Explain the process to the patient and ask if they have any questions.
- Be organized and systematic.
- Use appropriate listening and questioning skills.
- Listen and attend to patient cues.
- Ensure the patient’s privacy and dignity.
- Assess ABCs.
- Conduct a focused interview related to gastrointestinal and genitourinary concerns. Ask relevant, focused questions based on patient status. See Tables for sample focused questions.
- Position the patient in the supine position and drape the patient, exposing only the areas needed for assessment.
- Inspect the abdomen for shape/contour, symmetry, pigmentation/color, lesions/scars, pulsation, and visible peristalsis.
- Auscultate using the diaphragm of the stethoscope to assess for bowel sounds.
- Lightly palpate the four quadrants of the abdomen to assess for pain or masses. Palpate the suprapubic area for bladder distention. If the patient reports abdominal pain, palpate that area last.
- Assist the patient to a comfortable position, ask if they have any questions, and thank them for their time.
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Ensure safety measures when leaving the room:
- CALL LIGHT: Within reach
- BED: Low and locked (in lowest position and brakes on)
- SIDERAILS: Secured
- TABLE: Within reach
- ROOM: Risk-free for falls (scan room and clear any obstacles)
- Perform hand hygiene.
- Document the assessment findings and report any concerns according to agency policy.
- This work is a derivative of Clinical Procedures for Safer Patient Care by British Columbia Institute of Technology and is licensed under CC BY 4.0 ↵


26.7.1: Review Questions
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Review Questions
1 .
The nurse is caring for a patient with a spontaneous abortion at 8 weeks’ gestation. What is the most common cause of first trimester loss?
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ectopic pregnancy
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spontaneous abortion
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cervical insufficiency
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stillbirth
2 .
A 29-year-old Chinese American patient is admitted for IUFD. Her blood pressure (BP) is 90/60, body mass index (BMI) is 41, and the medical and surgical history is noncontributory. She does not smoke or have substance use disorder. What part of her history places her at risk for IUFD?
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age
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obesity
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hypotension
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ethnicity
3 .
What type of testing should be offered to a patient who has had a stillbirth?
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NIPTs
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ultrasound
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placental pathology
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blood crossmatch
4 .
The nurse is providing bereavement care to a family after a stillbirth. What is an example of communication with a patient that demonstrates effective bereavement care?
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“It is so sad that you never became a parent.”
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“Don’t worry. We will take good care of the fetus.”
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“Are there any religious ceremonies you would like for us to coordinate for you?”
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“I know you are grieving. I will take care of all of the decisions for you.”
5 .
The nurse provides education on care after a first trimester loss. What is an example of communication with a patient that demonstrates effective aftercare education?
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“You will need to follow up with us in several weeks. We want to make sure you are doing well.”
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“You should call us if you are bleeding and soaking 4 maxi pads in a day.”
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“Your period will return in 2 weeks.”
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“You should wait 2 months before having intercourse.”
6 .
The nurse provides education on care after a second trimester loss. What is an example of a topic of effective discharge education?
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list of local perinatal support groups
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consent for manual removal of placenta
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signs and symptoms of chorioamnionitis
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how to donate breast milk
7 .
The nurse is caring for a patient who has been diagnosed as having a fetal death. The nurse is aware of the possible causes of intrapartum fetal death. How can the nurse explain the potential causes of IPFD to the patient?
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“We will always find the cause of fetal death with an autopsy.”
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“Infection is never a cause of fetal death.”
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“Umbilical cord entanglement can cause fetal death.”
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“Congenital anomalies cause growth restriction, not fetal death.”
8 .
After reviewing a patient’s history, what does nurse recognize as a risk factor for IPFD?
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chronic hypertension
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hypothyroidism
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depression
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asthma
9 .
The nurse manager is planning a debriefing for several of the nurses after an IPFD. What should the manager expect?
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The nurses will need to discuss fault in order to alleviate feelings of guilt.
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During the debriefing, some nurses will complain of physical tension, headache, and insomnia.
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The nurse caring for the patient will need to defend herself to the health-care provider.
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The charge nurse will discuss the nurse’s documentation to prevent a lawsuit.
10 .
Postpartum depression and anxiety are prevalent among parents experiencing an IPFD. What is an example of a statement by the parent that would alert the nurse to signs of depression?
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“I really miss feeling the baby move in my belly.”
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“My family is supportive, but my partner and I just need a few hours to ourselves.”
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“Before the baby died, I really enjoyed spending time with friends.  I really need my support group right now.”
11 .
How can the nurse explain the complications of preterm birth?
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Intraventricular hemorrhage is not a serious complication of prematurity.
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Necrotizing enterocolitis is a condition of prematurity that causes constipation.
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Respiratory distress is a cause of death related to prematurity.
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Surfactant causes premature lungs to be overly pliable and opens the lungs too quickly.
12 .
How can the nurse caring for a patient with a neonatal loss practice self-care?
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Refrain from discussing her feelings at work.
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Understand that depression is normal after neonatal loss.
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Take off work for a week.
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Debrief with manager and colleagues.
13 .
How can the nurse be culturally sensitive after a neonatal death?
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Call a priest for all families during this time of grief.
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Recognize that most religions have traditions surrounding death.
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Encourage families to have an open casket to help them deal with the death.
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Discuss cremation, as it is the best process for a neonatal death.
14 .
Supporting siblings through grief after a neonatal loss is difficult. What suggestions should the nurse give parents?
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Try not to discuss your grief with siblings.
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Wait until children are older to be honest about their sibling’s death.
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Give them permission to cry and grieve.
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Avoid displaying pictures of the newborn until the sibling is older.