Awakening: the Role Model

In Kate Chopin’s The Awakening, Edna Pontellier continuously struggles with breaking the social norms that are imposed upon her by the people around her including her own friends and husband. Throughout the novel, Edna is able to detach herself from the lifestyle that society appoints her by emulating Mademoiselle Reisz, an independent woman who has lived her life without conforming to society. Mademoiselle Reisz is not only a model for Edna’s awakening, but she also represents the freedom and individuality that Enda wishes she could attain.Through imitating Reisz, Enda realizes the woman she is capable of becoming, but later learns that she cannot truly be an independent woman because of her differences from Mademoiselle Reisz. The relationship between Edna and Reisz is constructed on the artistic connection between the two character’s. Enda, a painter, is very fond of Reisz’s musical talent. Edna specifically likes one of Reisz’s songs that she ca lls â€Å"solitude. † Chopin writes, â€Å"The name of the piece was something else, but she called it ‘Solitude. When she heard it there came before her imagination the figure of a man standing beside a desolate rock on the seashore. He was naked. His attitude was one of hopeless resignation as he looked toward a distant bird winging its flight away from him† (38). This is what the relationship between Edna and Reisz is built on. Not only is it the artistic connection, but it is also the desire to be an individual that brings the two together. The song portrays an almost a vivid painting in the mind of Enda, the form of art that she enjoys.This particularly touches her because even though it is a different form of art, Edna still is able to understand and interpret it. In her mind, Reisz’s song leaves her with the sensation of being alone and free, a feeling that Edna longs to have for herself. The sea, which resembles freedom and knowledge throughout the novel is placed as an obstacle for the man who can only look at the bird that can go the other way and fly over the water.The â€Å"resignation† that the man and Edna feel are both in response to the way that they cannot free themselves completely from the land they are on, which can be understood as society itself, unlike the bird that they have to watch simply fly the other way. From this interaction between the two, it is apparent that Edna’s relationship with Mademoiselle Reisz is based on the two understanding each other through them both being artists. Alongside of their artistic connection, Edna Pontellier looks up to Mademoiselle Reisz as the woman she aspires to be.Enda wants to be an independent artist that is a maverick among the conventional people in the society just like Reisz is. This is evident in how the two characters interact. Chopin writes, â€Å"When Mademoiselle Reisz came and touched her upon the shoulder and spoke to her, the woman seemed to e cho the thought which was ever in Edna’s mind; or, better, the feeling which constantly possessed her† (69). Edna is figuratively and literally touched by Reisz in this moment. Edna wishes to be free and give up the all of the responsibilities she has a a woman.She does not want to be in the â€Å"habit† of doing all the social responsibilities that are placed upon women. Reisz echoes the freedom that Edna wishes she had by touching her and almost giving her that independence she yearns for. We can see how Edna struggles on the inside with wanting to be free and independent from how the narrator refers to it as a â€Å"feeling which constantly possessed her. † The possession shows how Edna does not have control over this feeling and she will always want to be a free individual.Reisz communicates to Edna that it is possible break the social standards by touching her and telling her that it is possible to be different because Reisz has done it herself. The c onnection between the two in this passage is one that is very much one that is mutual and close. Mademoiselle Reisz provides Edna with enlightenment that â€Å"possesse[s] her,† while Edna gives â€Å"the most disagreeable and unpopular woman† a true friendship in a society that is bias against independent women who defy the social convention. Reisz once again touches Edna similarly to how she had earlier on in the novel.Chopin writes, â€Å"She put her arms around me and felt my shoulder blades, to see if my wings were strong, she said. ‘The bird that would soar above the level plain of tradition and prejudice must have strong wings. It is a sad spectacle to see the weaklings bruised, exhausted, fluttering back to earth† (p. 127). Similar to the man from the song that wishes that he had wings like the bird to be free. Edna’s wings that she can use overcome the tradition and prejudice of society are being checked by Mademoiselle Reisz to see if she is strong enough to fly on her own. In addition, Edna s reached out to by Reisz and is comforted by her knowledge on how to be an individual. Edna wants to be free and is happy to relieved by the fact that Reisz is there to help her. Although Reisz is there to help Edna, Reisz also does think it is a shame if Edna were to fail in obtaining her independence. Mademoiselle Reisz calls it a spectacle which makes those who fail look ridiculous or like a fool. She is also telling Edna if she doesn’t succeed that she will make herself a spectacle that the entire tradition on the ground, society, is going to see her fall as she makes herself look like a fool.We can also see that Edna does enjoy the presence of Resiz although it may be hard on her at times. Chopin writes, â€Å"There was nothing which so quieted the turmoil of Edna’s senses as visit to Mademoiselle Reisz. It was then, in the presence of that personality which was offensive to her, that the woman, by her divine art, seemed to reach Edna’s spirit and set it free† (p. 120). At this point, Edna Pontellier feels as if the personality of Reisz, which she seems to envy because of its complete freedom, is the only thing that â€Å"reach[es] Edna’s spirit and set[s] it free. Edna’s world that is filled with struggle to be independent can only be calmed by the presence of her role model and deity, Mademoiselle Reisz. Since the relationship between Edna and Reisz is clearly one based on being independent women in a society that is prejudice against those whom that contravene the societal laws, the Edna’s life and suicide can be understood with more lucidity. Edna’s life through the novel is incontrovertibly a mimic of the life of Mademoiselle Reisz. Since Reisz is the independent and free woman Edna strives to be, Edna simply follows all the things that Reisz does.Edna returns back to painting{what does she want from painting}, she no longer â€Å"go[es] t hrough the daily treadmill of the life which has been portioned out to us,’ and she no longer let’s society command her what to do. Even though Edna is a free and independent woman by following the lifestyle of her counterpart, Mademoiselle Reisz, Edna struggles to be completely free. She still has to deal with the return of her husband and most importantly living with her children. This struggle makes the seemingly independent woman, Edna, ultimately commit suicide.Although Edna is fulfilled by her ability to initially take flight, gain freedom, Edna is just like â€Å"weaklings bruised, exhausted, fluttering back to earth† (p. 127). Because Edna’s wings are weak she is unable to fly and be free. This is because of the burden on her placed by her family. With Robert’s return, Edna again begins to feel the societal pressures that were absent while Robert was in Mexico. Edna is pressured into falling backing into â€Å"the daily treadmill of lifeâ €  because of her husband. This is one reason that she deicides to discontinue her life.Unlike Mademoiselle Reisz, Edna has a spouse whereas Reisz does not have a spouse that pressures her into conforming to society. Therefore Edna’s independence is challenged in her own home unlike Reisz whom is free to do as she wishes. Alongside of not having a spouse, Reisz does not have to worry about children dissimilar to Edna. This is key in understanding Edna’s suicide because of the extent to which he children were a major component in her deciding to give up her life. Reisz does not have to worry about children so she is much more capable of being a free woman. On the other hand, Edna has to take care of her children.This makes a major difference for Edna because her children will most likely be affected by society’s thoughts and opinions on their mother. Her children, the only people who should be able to love her unconditionally, will have to ultimately ostracize their mother if she was to be an independent woman. Edna also gives her life because she does not want to burden her own offspring with society’s judgement and beliefs of their own mother. In conclusion, Edna is weak considering that she is unable to remain an independent women and that she decides to end her life instead of taking power over her life.By submitting to death, Edna loses to society and ends her life for the interest of her children. Because she conforms in the end to what society wants her to do, take care of her children, Edna’s death can be considered as a defeat. Mademoiselle Ratignolle, the prime example of someone that conforms to society expectations and beliefs, says that women should give their lives for their children. Edna does exactly that and therefore is not only weak, but dies as a woman with no independence or freedom.

The Significance of Spring and Summer in Thomas Hardy’s Poems

Weathers By Thomas Hardy This is the weather the cuckoo likes, And so do I; When showers betumble the chestnut spikes, And nestlings fly; And the little brown nightingale bills his best, And they sit outside at ‘The Traveller's Rest,' And maids come forth sprig-muslin drest, And citizens dream of the south and west, And so do I. This is the weather the shepherd shuns, And so do I; When beeches drip in browns and duns, And thresh and ply; And hill-hid tides throb, throe on throe, And meadow rivulets overflow, And drops on gate bars hang in a row, And rooks in families homeward go, And so do I. The Significance Of Spring And Summer In Thomas Hardy’s Poems – Document Transcript 1. The Significance of Spring and Summer in Thomas Hardy's Poems, If It's Ever Spring Again, and It Never Looks Like Summer Mehdi Hassanian esfahani (GS22456) The Victorian Age (BBL5101) Lecturer: Dr. Wan Roselezam February 2009 2. Introduction: Reading about Thomas Hardy, and as the master students of English Literature, we all know that Hardy had a pessimist view on life and love, was watchful about relationships and interested in psychology of behaviors. His meticulous description of events and characters is not limited to humans, and even nature and animals play a role in the setting of what he narrates and are related to the theme. The following study examines the description of ‘summer’ and ‘spring’ in two selected poems by Thomas Hardy, to observe the significance of climate and seasons in the theme of the poems. The reason of this particular selection is the similarity between the two, in their mood, atmosphere, theme and even the ending. As a result, the analysis will claim the same thing, although it may seem inappropriate to generalize it to Hardy’s poetry. Interpreting imagery, particularly visual imagery in these two poems helps to understand their usage and the role they play to create the theme and setting of time and place. In this way, figurative language and the relationship between words would be examined to lead us to the theme and bring about the importance of summer and spring regarding the poems. It is expected that Hardy uses seasons to refer to nature and its beauty, in order to create a romantic setting, like other Victorian poets, and also uses ‘summer’ and ‘spring’ in the sense attributed to optimistic qualities, hope, [2] 3. warmth and love. But the careful observation of this may reveal a contrast which is made to intensify the underlying theme, and lead us to a pessimist view of Hardy in these poems. Accordingly, it will show that the mood of these poems â€Å"differs from Victorian sorrow; it is sterner, [and] more skeptical as though braced by a long look at the worst† (Stallworthy & Ramazani, 1852). If It's Ever Spring Again (Song) If it's ever spring again, Spring again, I shall go where went I when Down the moor-cock splashed, and hen, Seeing me not, amid their flounder, Standing with my arm around her; If it's ever spring again, Spring again, I shall go where went I then. If it's ever summer-time, summer-time, With the hay crop at the prime, [3] 4. And the cuckoos – two – in rhyme, As they used to be, or seemed to, We shall do as long we've dreamed to, If it's ever summer-time, Summer-time, With the hay, and bees achime (594). The poem, or as Hardy called it the ‘song' If It's Ever Spring Again deals with spring and summer; two bright and shiny seasons which normally warm the nature and people by the energy and hope they spread around. Kinesthetic imagery of ‘going out’ in line three, stanza one and the plashing moor-cock supports the excitement which is in the air. Hardy depicts spring with many positive qualities, when happiness is all around. He doesn’t talk of common characters, but moor-cock and moor-hen, which according to Morgon, the editor and publisher of the annual Hardy Review, are â€Å"shy, undemonstrative creatures rarely drawn from their coverture under the river-bank to gladden the heart of spring† to emphasize this supreme enthusiasm. As a result of this depiction, the prominent imagery in this poem is the visual imagery; which suddenly puts us in the middle of the nature; but there are also auditory and, as we saw, some hints of kinesthetic imagery. 4] 5. At first, Hardy reminds himself a day in spring, when he (the persona) was able to stand next to the beloved ‘with arms around her’ and enjoy the beauty of spring. He feels prospered and thinks of spring as a complete season, as well as himself. Then in stanza two, he leaps to another memory in a summer day, with again the perfection of setting and t he inner sense of fulfillment, when the ‘day crop’ is ‘at the prime’, ‘bees achime’ and cuckoos are singing in rhyme. The visual imagery which is connected to the golden color of the sun and the repetition of ‘summer’ in addition to the auditory imagery of birds singing free and cheerful, are effective devices to insure us of the blissful man, he feels inside. But it is not all. Richards explains that Hardy was interested in nature, and for him, like other Victorian writers, nature was equal to beauty, but also clarifies that â€Å"he was more interested in strangeness than conventional beauty† (190). It is as if the beauty of nature is not the ultimate goal of his poetry. Narrator’s effort to give an adequate visual imagery and create the setting of place and time is just a tool to carry out the profound meaning which is implied in the poem. The ‘if’s and ‘ever’s convey a sense of regret. Thinking of past days, the narrator cannot understand the lack which is now in his life. And the poem ends on a note, as if he lives in the past and doesn’t dare to face the future. In this sense, the whole poem seems not a delightful praise of spring, but an envy of the past. That’s Mellers’ view who considers this poem ‘a song of [5] 6. ostalgia’. Taking birds and bees, according to Cortus, the Vice President of The Thomas Hardy Association, as â€Å"collectively a trite euphemism for sex†, two cuckoos can be a metaphor of lovers (which includes the narrator), and his doubt in line 14, about their singing ‘As they used to †¦ or seemed to’ be together, demonstrates the pessim ist atmosphere which is settled in the mind, as well as the heart of this narrator that even cannot trust his beloved, and the past. This may explain the reason for the cock and hen ‘seeing not’ the narrator ‘amid their flounder’. In this case, the whole poem presents a continual abstract dreaming, disclosing the dimness melancholy that the narrator feels inside. It can suggest that the narration of past and this memory is not reliable, due to the obsession of narrator to his relationship, and the traumatic lost he has in his life. In the second poem, It never looks like summer, Hardy strongly uses ‘summer’ to display the peak of a relationship, the satisfaction and joyfulness which this season, apparently is connected to or is responsible to bring us. The poem lacks descriptive statements or cliche details of nature, and is much modern in the sense which looks like an internal monologue. It is written in a way, that one can conclude it wasn’t supposed to be published (although there is no evidence of such a thing), and is more like the private thoughts of its poet than a poem about ‘summer’. [6] 7. It Never Looks Like Summer â€Å"It never looks like summer here On Beeny by the sea. † But though she saw its look as drear, Summer it seemed to me. It never looks like summer now Whatever weather's there; But ah, it cannot anyhow, On Beeny or elsewhere (507)! Here, the image of summer is overwhelming, though it is very general and there are no details. Hardy uses contrasts to express his feeling. Again, the prominent imagery in the poem is visual imagery, like the drear summer that surrounds us; however an abstract imagery can be derived from connotations of ‘summer’. Narrator implicitly attributes some positive qualities to summer, though he never names them. In the first stanza, he remembers a day when weather was not ‘summery’ a lot, but he felt so; perhaps due to a companionship. And now, in the second stanza, he feels cold although it is summer outside. The nature in general and ‘summer’ in particular is interweaved to persona’s life (both emotionally and [7] 8. physically), though they do not always match together. In other words â€Å"the thinnest partition divides man’s existence (including his mental existence) from the rest of nature† (Richards, 196). This is remarkable which in both If It's Ever Spring Again and It never looks like summer, climate and seasons metaphorically are used to explore the feeling of the persona and â€Å"to register inner states of [his] feeling† (Blackburn, 15). The pessimist view of life and [the lost] love is repeated again; when narrator can say which season it ‘is’, but doubts if the beloved’s presence was real or the feeling was true, and claims that it ‘seemed’ summer to him. He prefers to sing bereavement poems, than face the reality and live in present, and the last two lines support this idea that he cannot think of future. He generalizes the unsatisfactory consequence of his attempts and his lost to all other happenings anytime in future and anywhere else around the world, and decides not to move and not to change; he dares not to look at the future because of his tragic experience. Talking about Hardy’s poetry, Blackburn asserts that the magnetism of his poems â€Å"is built around a complex of love and loss, memory and guilt, pain and self-pity, beauty and regret intermingled with something of delight† (12). In these two poems, he uses images of spring and summer and refers to nature to express the emotions and create the setting, so that he compares two conditions of past and present. To conclude, and as Berger states in the abstract of her PhD [8] 9. roposal, â€Å"Hardy's epistemology can be found at a meeting point of the senses– primarily visual, emotions, imagination, will, and the external world†. Here, the primary setting and the visual imagery play a strong role, metaphorically, to the oppositions, and intensifies the sense of regret. This technique is effective in a way to create the atmosphere and express the sadness this persona feels in his present life. [9]

Physics Notes

Gravitation Gravitational field strength at a point is defined as the gravitational force per unit mass at that point. Newton's law of gravitation: The (mutual) gravitational force F between two point masses M and m separated by a distance r is given by F =| GMm| (where G: Universal gravitational constant)| | r2| | or, the gravitational force of between two point masses is proportional to the product of their masses ; inversely proportional to the square of their separation. Gravitational field strength at a point is the gravitational force per unit mass at that point. It is a vector and its S. I. unit is N kg-1.By definition, g = F / m By Newton Law of Gravitation, F = GMm / r2 Combining, magnitude of g = GM / r2 Therefore g = GM / r2, M = Mass of object â€Å"creating† the field Example 1: Assuming that the Earth is a uniform sphere of radius 6. 4 x 106 m and mass 6. 0 x 1024 kg, find the gravitational field strength g at a point: (a) on the surface, g = GM / r2 = (6. 67 ? 1 0-11)(6. 0 x 1024) / (6. 4 x 106)2 = 9. 77ms-2 (b) at height 0. 50 times the radius of above the Earth's surface. g = GM / r2 = (6. 67 ? 10-11)(6. 0 x 1024) / ( (1. 5 ? 6. 4 x 106)2 = 4. 34ms-2 Example 2: The acceleration due to gravity at the Earth's surface is 9. 0ms-2. Calculate the acceleration due to gravity on a planet which has the same density but twice the radius of Earth. g = GM / r2 gP / gE = MPrE2 / MErP2 = (4/3) ? rP3rE2? P / (4/3) ? rE3rP2? E = rP / rE = 2 Hence gP = 2 x 9. 81 = 19. 6ms-2 Assuming that Earth is a uniform sphere of mass M. The magnitude of the gravitational force from Earth on a particle of mass m, located outside Earth a distance r from the centre of the Earth is F = GMm / r2. When a particle is released, it will fall towards the centre of the Earth, as a result of the gravitational force with an acceleration ag. FG = mag ag = GM / r2Hence ag = g Thus gravitational field strength g is also numerically equal to the acceleration of free fall. Example 1: A ship is at rest on the Earth's equator. Assuming the earth to be a perfect sphere of radius R and the acceleration due to gravity at the poles is go, express its apparent weight, N, of a body of mass m in terms of m, go, R and T (the period of the earth's rotation about its axis, which is one day). At the North Pole, the gravitational attraction is F = GMEm / R2 = mgo At the equator, Normal Reaction Force on ship by Earth = Gravitational attraction – centripetal force N = mgo – mR? = mgo – mR (2? / T)2 Gravitational potential at a point is defined as the work done (by an external agent) in bringing a unit mass from infinity to that point (without changing its kinetic energy). ? = W / m = -GM / r Why gravitational potential values are always negative? As the gravitational force on the mass is attractive, the work done by an ext agent in bringing unit mass from infinity to any point in the field will be negative work {as the force exerted by the ext agent is opp osite in direction to the displacement to ensure that ? KE = 0} Hence by the definition of negative work, all values of ? re negative. g = -| d? | = – gradient of ? -r graph {Analogy: E = -dV/dx}| | dr| | Gravitational potential energy U of a mass m at a point in the gravitational field of another mass M, is the work done in bringing that mass m {NOT: unit mass, or a mass} from infinity to that point. ; U = m ? = -GMm / r Change in GPE, ? U = mgh only if g is constant over the distance h; {; h;; radius of planet} otherwise, must use: ? U = m? f-m? i | Aspects| Electric Field| Gravitational Field| 1. | Quantity interacting with or producing the field| Charge Q| Mass M| 2. Definition of Field Strength| Force per unit positive charge E = F / q| Force per unit mass g = F / M| 3. | Force between two Point Charges or Masses| Coulomb's Law: Fe = Q1Q2 / 4 or2| Newton's Law of Gravitation: Fg = G (GMm / r2)| 4. | Field Strength of isolated Point Charge or Mass| E = Q / 4 or2| g = G (G M / r2)| 5. | Definition of Potential| Work done in bringing a unit positive charge from infinity to the point; V = W /Q| Work done in bringing a unit mass from infinity to the point; ? = W / M| 6. | Potential of isolated Point Charge or Mass| V = Q / 4 or| ? -G (M / r)| 7. | Change in Potential Energy| ? U = q ? V| ? U = m | Total Energy of a Satellite = GPE + KE = (-GMm / r) + ? (GMm / r) Escape Speed of a Satellite By Conservation of Energy, Initial KE| +| Initial GPE| =| Final KE| +| Final GPE| (? mvE2)| +| (-GMm / r)| =| (0)| +| (0)| Thus escape speed, vE = v(2GM / R) Note : Escape speed of an object is independent of its mass For a satellite in circular orbit, â€Å"the centripetal force is provided by the gravitational force† {Must always state what force is providing the centripetal force before following eqn is used! Hence GMm / r2 = mv2 / r = mr? 2 = mr (2? / T)2 A satellite does not move in the direction of the gravitational force {ie it stays in its circular orbi t} because: the gravitational force exerted by the Earth on the satellite is just sufficient to cause the centripetal acceleration but not enough to also pull it down towards the Earth. {This explains also why the Moon does not fall towards the Earth} Geostationary satellite is one which is always above a certain point on the Earth (as the Earth rotates about its axis. For a geostationary orbit: T = 24 hrs, orbital radius (; height) are fixed values from the centre of the Earth, ang velocity w is also a fixed value; rotates fr west to east. However, the mass of the satellite is NOT a particular value ; hence the ke, gpe, ; the centripetal force are also not fixed values {ie their values depend on the mass of the geostationary satellite. } A geostationary orbit must lie in the equatorial plane of the earth because it must accelerate in a plane where the centre of Earth lies since the net orce exerted on the satellite is the Earth's gravitational force, which is directed towards the c entre of Earth. {Alternatively, may explain by showing why it's impossible for a satellite in a non-equatorial plane to be geostationary. } Thermal Physics Internal Energy: is the sum of the kinetic energy of the molecules due to its random motion ; the potential energy of the molecules due to the intermolecular forces. Internal energy is determined by the values of the current state and is independent of how the state is arrived at. You can read also Thin Film Solar CellThus if a system undergoes a series of changes from one state A to another state B, its change in internal energy is the same, regardless of which path {the changes in the p ; V} it has taken to get from A to B. Since Kinetic Energy proportional to temp, and internal energy of the system = sum of its Kinetic Energy and Potential Energy, a rise in temperature will cause a rise in Kinetic Energy and thus an increase in internal energy. If two bodies are in thermal equilibrium, there is no net flow of heat energy between them and they have the same temperature. NB: this does not imply they must have the same internal energy as internal energy depends also on the number of molecules in the 2 bodies, which is unknown here} Thermodynamic (Kelvin) scale of temperature: theoretical scale that is independent of the properties of any particular substance. An absolute scale of temp is a temp scale which does not depend on the property of any particular subs tance (ie the thermodynamic scale) Absolute zero: Temperature at which all substances have a minimum internal energy {NOT: zero internal energy. } T/K = T/ °C + 273. 15, by definition of the Celsius scale.Specific heat capacity is defined as the amount of heat energy needed to produce unit temperature change {NOT: by 1 K} for unit mass {NOT: 1 kg} of a substance, without causing a change in state. c = Q / m? T Specific latent heat of vaporisation is defined as the amount of heat energy needed to change unit mass of a substance from liquid phase to gaseous phase without a change of temperature. Specific latent heat of fusion is defined as the amount of heat energy needed to change unit mass of a substance from solid phase to liquid phase without a change of temperature L = Q / m {for both cases of vaporisation ; melting}The specific latent heat of vaporisation is greater than the specific latent heat of fusion for a given substance because * During vaporisation, there is a greater increase in volume than in fusion, * Thus more work is done against atmospheric pressure during vaporisation, * The increase in vol also means the INCREASE IN THE (MOLECULAR) POTENTIAL ENERGY, ; hence, internal energy, during vaporisation more than that during melting, * Hence by 1st Law of Thermodynamics, heat supplied during vaporisation more than that during melting; hence lv ; lf {since Q = ml = ?U – W}. Note: 1. the use of comparative terms: greater, more, and; 2. the increase in internal energy is due to an increase in the PE, NOT KE of molecules 3. the system here is NOT to be considered as an ideal gas system Similarly, you need to explain why, when a liq is boiling, thermal energy is being supplied, and yet, the temp of the liq does not change. | Melting| Boiling| Evaporation| Occurrence| Throughout the substance, at fixed temperature and pressure| On the surface, at all temperatures|Spacing(vol) ; PE of molecules| Increase slightly| Increase significantly| | Tempera ture ; hence KE of molecules| Remains constant during process| Decrease for remaining liquid| First Law of Thermodynamics: The increase in internal energy of a system is equal to the sum of the heat supplied to the system and the work done on the system. ?U = W + Q| ? U: Increase in internal energy of the system Q: Heat supplied to the system W: work done on the system| {Need to recall the sign convention for all 3 terms} Work is done by a gas when it expands; work is done on a gas when it is ompressed. W = area under pressure – volume graph. For constant pressure {isobaric process}, Work done = pressure x ? Volume Isothermal process: a process where T = const {? U = 0 for ideal gas} ? U for a cycle = 0 {since U ? T, ; ? T = 0 for a cycle } Equation of state for an ideal gas: p V = n R T, where T is in Kelvin {NOT:  °C}, n: no. of moles. p V = N k T, where N: no. of molecules, k:Boltzmann const Ideal Gas: a gas which obeys the ideal gas equation pV = nRT FOR ALL VALUES OF P , V ; T Avogadro constant: defined as the number of atoms in 12g of carbon-12.It is thus the number of particles (atoms or molecules) in one mole of substance. For an ideal gas, internal energy U = Sum of the KE of the molecules only {since PE = 0 for ideal gas} U = N x? m ;c2; = N x (3/2)kT {for monatomic gas} * U depends on T and number of molecules N * U ? T for a given number of molecules Ave KE of a molecule, ? m ;c2; ? T {T in K: not  °C} Dynamics Newton's laws of motion: Newton's First Law Every body continues in a state of rest or uniform motion in a straight line unless a net (external) force acts on it. Newton's Second LawThe rate of change of momentum of a body is directly proportional to the net force acting on the body, and the momentum change takes place in the direction of the net force. Newton's Third Law When object X exerts a force on object Y, object Y exerts a force of the same type that is equal in magnitude and opposite in direction on object X. The two force s ALWAYS act on different objects and they form an action-reaction pair. Linear momentum and its conservation: Mass: is a measure of the amount of matter in a body, ; is the property of a body which resists change in motion.Weight: is the force of gravitational attraction (exerted by the Earth) on a body. Linear momentum: of a body is defined as the product of its mass and velocity ie p = m v Impulse of a force (I): is defined as the product of the force and the time ? t during which it acts ie I = F x ? t {for force which is const over the duration ? t} For a variable force, the impulse I = Area under the F-t graph { ? Fdt; may need to â€Å"count squares†} Impulse is equal in magnitude to the change in momentum of the body acted on by the force.Hence the change in momentum of the body is equal in mag to the area under a (net) force-time graph. {Incorrect to define impulse as change in momentum} Force: is defined as the rate of change of momentum, ie F = [ m (v – u) ] / t = ma or F = v dm / dt The {one} Newton: is defined as the force needed to accelerate a mass of 1 kg by 1 m s-2. Principle of Conservation of Linear Momentum: When objects of a system interact, their total momentum before and after interaction are equal if no net (external) force acts on the system. * The total momentum of an isolated system is constant m1 u1 + m2 u2 = m1 v1 + m2 v2 if net F = 0 {for all collisions } NB: Total momentum DURING the interaction/collision is also conserved. (Perfectly) elastic collision: Both momentum ; kinetic energy of the system are conserved. Inelastic collision: Only momentum is conserved, total kinetic energy is not conserved. Perfectly inelastic collision: Only momentum is conserved, and the particles stick together after collision. (i. e. move with the same velocity. ) For all elastic collisions, u1 – u2 = v2 – v1 ie. relative speed of approach = relative speed of separation or, ? m1u12 + ? m2u22 = ? m1v12 + ? 2v22 In inelastic collisions, total energy is conserved but Kinetic Energy may be converted into other forms of energy such as sound and heat energy. Current of Electricity Electric current is the rate of flow of charge. {NOT: charged particles} Electric charge Q passing a point is defined as the product of the (steady) current at that point and the time for which the current flows, Q = I t One coulomb is defined as the charge flowing per second pass a point at which the current is one ampere. Example 1: An ion beam of singly-charged Na+ and K+ ions is passing through vacuum. If the beam current is 20 ?A, calculate the total number of ions passing any fixed point in the beam per second. (The charge on each ion is 1. 6 x 10-19 C. ) Current, I = Q / t = Ne / t where N is the no. of ions and e is the charge on one ion. No. of ions per second = N / t = I / e = (20 x 10-6) / (1. 6 x 10-19) = 1. 25 x 10-14 Potential difference is defined as the energy transferred from electrical energy to other forms of e nergy when unit charge passes through an electrical device, V = W / Q P. D. = Energy Transferred / Charge = Power / Current or, is the ratio of the power supplied to the device to the current flowing, V = P / IThe volt: is defined as the potential difference between 2 pts in a circuit in which one joule of energy is converted from electrical to non-electrical energy when one coulomb passes from 1 pt to the other, ie 1 volt = One joule per coulomb Difference between Potential and Potential Difference (PD): The potential at a point of the circuit is due to the amount of charge present along with the energy of the charges. Thus, the potential along circuit drops from the positive terminal to negative terminal, and potential differs from points to points. Potential Difference refers to the difference in potential between any given two points.For example, if the potential of point A is 1 V and the potential at point B is 5 V, the PD across AB, or VAB , is 4 V. In addition, when there is no energy loss between two points of the circuit, the potential of these points is same and thus the PD across is 0 V. Example 2: A current of 5 mA passes through a bulb for 1 minute. The potential difference across the bulb is 4 V. Calculate: (a) The amount of charge passing through the bulb in 1 minute. Charge Q = I t = 5 x 10-3 x 60 = 0. 3 C (b) The work done to operate the bulb for 1 minute. Potential difference across the bulb = W / Q 4 = W / 0. Work done to operate the bulb for 1 minute = 0. 3 x 4 = 1. 2 J Electrical Power, P = V I = I2 / R = V2 / R {Brightness of a lamp is determined by the power dissipated, NOT: by V, or I or R alone} Example 3: A high-voltage transmission line with a resistance of 0. 4 ? km-1 carries a current of 500 A. The line is at a potential of 1200 kV at the power station and carries the current to a city located 160 km from the power station. Calculate (a) the power loss in the line. The power loss in the line P = I2 R = 5002 x 0. 4 x 160 = 16 MW (b) the fraction of the transmitted power that is lost.The total power transmitted = I V = 500 x 1200 x 103 = 600 MW The fraction of power loss = 16 / 600 = 0. 267 Resistance is defined as the ratio of the potential difference across a component to the current flowing through it , R = VI {It is NOT defined as the gradient of a V-I graph; however for an ohmic conductor, its resistance equals the gradient of its V-I graph as this graph is a straight line which passes through the origin} The Ohm: is the resistance of a resistor if there is a current of 1 A flowing through it when the pd across it is 1 V, ie, 1 ? = One volt per ampere Example 4:In the circuit below, the voltmeter reading is 8. 00 V and the ammeter reading is 2. 00 A. Calculate the resistance of R. Resistance of R = V / I = 8 / 2 = 4. 0 ? | | Temperature characteristics of thermistors: The resistance (i. e. the ratio V / I) is constant because metallic conductors at constant temperature obey Ohm's Law. | As V increases, the temperature increases, resulting in an increase in the amplitude of vibration of ions and the collision frequency of electrons with the lattice ions. Hence the resistance of the filament increases with V. | A thermistor is made from semi-conductors.As V increases, temperature increases. This releases more charge carriers (electrons and holes) from the lattice, thus reducing the resistance of the thermistor. Hence, resistance decreases as temperature increases. | In forward bias, a diode has low resistance. In reverse bias, the diode has high resistance until the breakdown voltage is reached. | Ohm's law: The current in a component is proportional to the potential difference across it provided physical conditions (eg temp) stay constant. R = ? L / A {for a conductor of length l, uniform x-sect area A and resistivity ? Resistivity is defined as the resistance of a material of unit cross-sectional area and unit length. {From R = ? l / A , ? = RA / L} Example 5: Calculate the resistanc e of a nichrome wire of length 500 mm and diameter 1. 0 mm, given that the resistivity of nichrome is 1. 1 x 10-6 ? m. Resistance, R = ? l / A = [(1. 1 x 10-6)(500 x 10-3)] / ? (1 x 10-3 / 2)2 = 0. 70 ? Electromotive force (Emf) is defined as the energy transferred / converted from non-electrical forms of energy into electrical energy when unit charge is moved round a complete circuit. ie EMF = Energy Transferred per unit charge E = WQEMF refers to the electrical energy generated from non-electrical energy forms, whereas PD refers to electrical energy being changed into non-electrical energy. For example, EMF Sources| Energy Change| PD across| Energy Change| Chemical Cell| Chem ; Elec| Bulb| Elec ; Light| Generator| Mech ; Elec| Fan| Elec ; Mech| Thermocouple| Thermal ; Elec| Door Bell| Elec ; Sound| Solar Cell| Solar ; Elec| Heating element| Elec ; Thermal| Effects of the internal resistance of a source of EMF: Internal resistance is the resistance to current flow within the power source.It reduces the potential difference (not EMF) across the terminal of the power supply when it is delivering a current. Consider the circuit below: The voltage across the resistor, V = IR, The voltage lost to internal resistance = Ir Thus, the EMF of the cell, E = IR + Ir = V + Ir Therefore If I = 0A or if r = 0? , V = E Motion in a Circle Kinematics of uniform circular motion Radian (rad) is the S. I. unit for angle, ? and it can be related to degrees in the following way. In one complete revolution, an object rotates through 360 ° , or 2? rad. As the object moves through an angle ? , with respect to the centre of rotation, this angle ? s known as the angular displacement. Angular velocity (? ) of the object is the rate of change of angular displacement with respect to time. ? = ? / t = 2? / T (for one complete revolution) Linear velocity, v, of an object is its instantaneous velocity at any point in its circular path. v = arc length / time taken = r? / t = r? * The directi on of the linear velocity is at a tangent to the circle described at that point. Hence it is sometimes referred to as the tangential velocity * ? is the same for every point in the rotating object, but the linear velocity v is greater for points further from the axis.A body moving in a circle at a constant speed changes velocity {since its direction changes}. Thus, it always experiences an acceleration, a force and a change in momentum. Centripetal acceleration a = r? 2 = v2 / r {in magnitude} Centripetal force Centripetal force is the resultant of all the forces that act on a system in circular motion. {It is not a particular force; â€Å"centripetal† means â€Å"centre-seeking†. Also, when asked to draw a diagram showing all the forces that act on a system in circular motion, it is wrong to include a force that is labelled as â€Å"centripetal force†. } Centripetal force, F = m r ? 2 = mv2 / r {in magnitude}A person in a satellite orbiting the Earth experience s â€Å"weightlessness† although the gravi field strength at that height is not zero because the person and the satellite would both have the same acceleration; hence the contact force between man ; satellite / normal reaction on the person is zero {Not because the field strength is negligible}. D. C. Circuits Circuit Symbols: Open Switch| Closed Switch| Lamp| Cell| Battery| Voltmeter| Resistor| Fuse| Ammeter| Variable resistor| Thermistor| Light dependent resistor (LDR)| Resistors in Series: R = R1 + R2 + †¦ Resistors in Parallel: 1/R = 1/R1 + 1/R2 + †¦ Example 1:Three resistors of resistance 2 ? , 3 ? and 4 ? respectively are used to make the combinations X, Y and Z shown in the diagrams. List the combinations in order of increasing resistance. Resistance for X = [1/2 + 1/(4+3)]-1 = 1. 56 ? Resistance for Y = 2 + (1/4 + 1/3)-1 = 3. 71 ? Resistance for Z = (1/3 + 1/2 + 1/4)-1 = 0. 923 ? Therefore, the combination of resistors in order of increasing resistance is Z X Y. Example: Referring to the circuit drawn, determine the value of I1, I and R, the combined resistance in the circuit. E = I1 (160) = I2 (4000) = I3 (32000) I1 = 2 / 160 = 0. 0125 A I2 = 2 / 4000 = 5 x 10-4 AI3 = 2 / 32000 = 6. 25 x 10-5 ASince I = I1 + I2 + I3, I = 13. 1 mAApplying Ohm’s Law, R = 213. 1 x 10-3 = 153 ? | | Example: A battery with an EMF of 20 V and an internal resistance of 2. 0 ? is connected to resistors R1 and R2 as shown in the diagram. A total current of 4. 0 A is supplied by the battery and R2 has a resistance of 12 ?. Calculate the resistance of R1 and the power supplied to each circuit component. E – I r = I2 R2 20 – 4 (2) = I2 (12) I2 = 1A Therefore, I1 = 4 – 1 = 3 AE – I r = I1 R1 12 = 3 R1 Therefore, R1 = 4Power supplied to R1 = (I1)2 R1 = 36 W Power supplied to R2 = (I2)2 R2 = 12 W| |For potential divider with 2 resistors in series, Potential drop across R1, V1 = R1 / (R1 + R2) x PD across R1 ; R2 Potential drop acro ss R2, V1 = R2 / (R1 + R2) x PD across R1 ; R2 Example: Two resistors, of resistance 300 k? and 500 k? respectively, form a potential divider with outer junctions maintained at potentials of +3 V and -15 V. Determine the potential at the junction X between the resistors. The potential difference across the 300 k? resistor = 300 / (300 + 500) [3 – (-15)] = 6. 75 V The potential at X = 3 – 6. 75 = -3. 75 V A thermistor is a resistor whose resistance varies greatly with temperature.Its resistance decreases with increasing temperature. It can be used in potential divider circuits to monitor and control temperatures. Example: In the figure on the right, the thermistor has a resistance of 800 ? when hot, and a resistance of 5000 ? when cold. Determine the potential at W when the temperature is hot. When thermistor is hot, potential difference across it = [800 / (800 + 1700)] x (7 – 2) = 1. 6 VThe potential at W = 2 + 1. 6 V = 3. 6 V| | A Light dependent resistor (LDR) is a resistor whose resistance varies with the intensity of light falling on it. Its resistance decreases with increasing light intensity.It can be used in a potential divider circuit to monitor light intensity. Example: In the figure below, the resistance of the LDR is 6. 0 M in the dark but then drops to 2. 0 k in the light Determine the potential at point P when the LDR is in the light. In the light the potential difference across the LDR= [2k / (3k + 2k)] x (18 – 3) = 6 VThe potential at P = 18 – 6= 12 V| | The potential difference along the wire is proportional to the length of the wire. The sliding contact will move along wire AB until it finds a point along the wire such that the galvanometer shows a zero reading.When the galvanometer shows a zero reading, the current through the galvanometer (and the device that is being tested) is zero and the potentiometer is said to be â€Å"balanced†. If the cell has negligible internal resistance, and if the potent iometer is balanced, EMF / PD of the unknown source, V = [L1 / (L1 + L2)] x E Example: In the circuit shown, the potentiometer wire has a resistance of 60 ?. Determine the EMF of the unknown cell if the balanced point is at B. Resistance of wire AB= [0. 65 / (0. 65 + 0. 35)] x 60 = 39 ? EMF of the test cell= [39 / (60 + 20)] x 12| Work, Energy and PowerWork Done by a force is defined as the product of the force and displacement (of its point of application) in the direction of the force W = F s cos ? Negative work is said to be done by F if x or its compo. is anti-parallel to F If a variable force F produces a displacement in the direction of F, the work done is determined from the area under F-x graph. {May need to find area by â€Å"counting the squares†. } By Principle of Conservation of Energy, Work Done on a system = KE gain + GPE gain + Work done against friction} Consider a rigid object of mass m that is initially at rest.To accelerate it uniformly to a speed v, a cons tant net force F is exerted on it, parallel to its motion over a displacement s. Since F is constant, acceleration is constant, Therefore, using the equation: v2 = u2 +2as, as = 12 (v2 – u2) Since kinetic energy is equal to the work done on the mass to bring it from rest to a speed v, The kinetic energy, EK| = Work done by the force F = Fs = mas = ? m (v2 – u2)| Gravitational potential energy: this arises in a system of masses where there are attractive gravitational forces between them.The gravitational potential energy of an object is the energy it possesses by virtue of its position in a gravitational field. Elastic potential energy: this arises in a system of atoms where there are either attractive or repulsive short-range inter-atomic forces between them. Electric potential energy: this arises in a system of charges where there are either attractive or repulsive electric forces between them. The potential energy, U, of a body in a force field {whether gravitationa l or electric field} is related to the force F it experiences by: F = – dU / dx.Consider an object of mass m being lifted vertically by a force F, without acceleration, from a certain height h1 to a height h2. Since the object moves up at a constant speed, F is equal to mg. The change in potential energy of the mass| = Work done by the force F = F s = F h = m g h| Efficiency: The ratio of (useful) output energy of a machine to the input energy. ie =| Useful Output Energy| x100% =| Useful Output Power| x100%| | Input Energy| | Input Power| | Power {instantaneous} is defined as the work done per unit time. P =| Total Work Done| =| W| | Total Time| | t|Since work done W = F x s, P =| F x s| =| Fv| | t| | | * for object moving at const speed: F = Total resistive force {equilibrium condition} * for object beginning to accelerate: F = Total resistive force + ma Forces Hooke's Law: Within the limit of proportionality, the extension produced in a material is directly proportional to the force/load applied F = kx Force constant k = force per unit extension (F/x) Elastic potential energy/strain energy = Area under the F-x graph {May need to â€Å"count the squares†} For a material that obeys Hooke? s law, Elastic Potential Energy, E = ? F x = ? x2 Forces on Masses in Gravitational Fields: A region of space in which a mass experiences an (attractive) force due to the presence of another mass. Forces on Charge in Electric Fields: A region of space where a charge experiences an (attractive or repulsive) force due to the presence of another charge. Hydrostatic Pressure p = ? gh {or, pressure difference between 2 points separated by a vertical distance of h } Upthrust: An upward force exerted by a fluid on a submerged or floating object; arises because of the difference in pressure between the upper and lower surfaces of the object.Archimedes' Principle: Upthrust = weight of the fluid displaced by submerged object. ie Upthrust = Volsubmerged x ? fluid x g Frict ional Forces: * The contact force between two surfaces = (friction2 + normal reaction2)? * The component along the surface of the contact force is called friction * Friction between 2 surfaces always opposes relative motion {or attempted motion}, and * Its value varies up to a maximum value {called the static friction} Viscous Forces: * A force that opposes the motion of an object in a fluid * Only exists when there is (relative) motion Magnitude of viscous force increases with the speed of the object Centre of Gravity of an object is defined as that pt through which the entire weight of the object may be considered to act. A couple is a pair of forces which tends to produce rotation only. Moment of a Force: The product of the force and the perpendicular distance of its line of action to the pivot Torque of a Couple: The produce of one of the forces of the couple and the perpendicular distance between the lines of action of the forces. (WARNING: NOT an action-reaction pair as they a ct on the same body. ) Conditions for Equilibrium (of an extended object): 1.The resultant force acting on it in any direction equals zero 2. The resultant moment about any point is zero If a mass is acted upon by 3 forces only and remains in equilibrium, then 1. The lines of action of the 3 forces must pass through a common point 2. When a vector diagram of the three forces is drawn, the forces will form a closed triangle (vector triangle), with the 3 vectors pointing in the same orientation around the triangle. Principle of Moments: For a body to be in equilibrium, the sum of all the anticlockwise moments about any point must be equal to the sum of all the clockwise moments about that same point.Measurement Base quantities and their units; mass (kg), length (m), time (s), current (A), temperature (K), amount of substance (mol): Base Quantities| SI Units| | Name| Symbol| Length| metre| m| Mass| kilogram| kg| Time| second| s| Amount of substance| mole| mol| Temperature| Kelvin| K| C urrent| ampere| A| Luminous intensity| candela| cd| Derived units as products or quotients of the base units: Derived| Quantities Equation| Derived Units| Area (A)| A = L2| m2| Volume (V)| V = L3| m3| Density (? )| ? = m / V| kg m-3| Velocity (v)| v = L / t| ms-1| Acceleration (a)| a = ? v / t| ms-1 / s = ms-2|Momentum (p)| p = m x v| (kg)(ms-1) = kg m s-1| Derived Quantities| Equation| Derived Unit| Derived Units| | | Special Name| Symbol| | Force (F)| F = ? p / t| Newton| N| [(kg m s-1) / s = kg m s-2| Pressure (p)| p = F / A| Pascal| Pa| (kg m s-2) / m2 = kg m-1 s-2| Energy (E)| E = F x d| joule| J| (kg m s-2)(m) = kg m2 s-2| Power (P)| P = E / t| watt| W| (kg m2 s-2) / s = kg m2 s-3| Frequency (f)| f = 1 / t| hertz| Hz| 1 / s = s-1| Charge (Q)| Q = I x t| coulomb| C| A s| Potential Difference (V)| V = E / Q| volt| V| (kg m2 s-2) / A s = kg m2 s-3 A-1| Resistance (R)| R = V / I| ohm| ? (kg m2 s-3 A-1) / A = kg m2 s-3 A-2| Prefixes and their symbols to indicate decimal sub-multipl es or multiples of both base and derived units: Multiplying Factor| Prefix| Symbol| 10-12| pico| p| 10-9| nano| n| 10-6| micro| ? | 10-3| milli| m| 10-2| centi| c| 10-1| decid| d| 103| kilo| k| 106| mega| M| 109| giga| G| 1012| tera| T| Estimates of physical quantities: When making an estimate, it is only reasonable to give the figure to 1 or at most 2 significant figures since an estimate is not very precise. Physical Quantity| Reasonable Estimate| Mass of 3 cans (330 ml) of Coke| 1 kg|Mass of a medium-sized car| 1000 kg| Length of a football field| 100 m| Reaction time of a young man| 0. 2 s| * Occasionally, students are asked to estimate the area under a graph. The usual method of counting squares within the enclosed area is used. (eg. Topic 3 (Dynamics), N94P2Q1c) * Often, when making an estimate, a formula and a simple calculation may be involved. EXAMPLE 1: Estimate the average running speed of a typical 17-year-old? s 2. 4-km run. velocity = distance / time = 2400 / (12. 5 x 60) = 3. 2 ? 3 ms-1 EXAMPLE 2: Which estimate is realistic? | Option| Explanation|A| The kinetic energy of a bus travelling on an expressway is 30000J| A bus of mass m travelling on an expressway will travel between 50 to 80 kmh-1, which is 13. 8 to 22. 2 ms-1. Thus, its KE will be approximately ? m(182) = 162m. Thus, for its KE to be 30000J: 162m = 30000. Thus, m = 185kg, which is an absurd weight for a bus; ie. This is not a realistic estimate. | B| The power of a domestic light is 300W. | A single light bulb in the house usually runs at about 20W to 60W. Thus, a domestic light is unlikely to run at more than 200W; this estimate is rather high. | C| The temperature of a hot oven is 300 K. 300K = 27 0C. Not very hot. | D| The volume of air in a car tyre is 0. 03 m3. | | Estimating the width of a tyre, t, is 15 cm or 0. 15 m, and estimating R to be 40 cm and r to be 30 cm,volume of air in a car tyre is = ? (R2 – r2)t = ? (0. 42 – 0. 32)(0. 15) = 0. 033 m3 ? 0. 03 m3 (t o one sig. fig. )| Distinction between systematic errors (including zero errors) and random errors and between precision and accuracy: Random error: is the type of error which causes readings to scatter about the true value. Systematic error: is the type of error which causes readings to deviate in one direction from the true value.Precision: refers to the degree of agreement (scatter, spread) of repeated measurements of the same quantity. {NB: regardless of whether or not they are correct. } Accuracy: refers to the degree of agreement between the result of a measurement and the true value of the quantity. | ; ; R Error Higher ; ; ; ; ; ; Less Precise ; ; ;| v v vS Error HigherLess Accuratev v v| | | | | | Assess the uncertainty in a derived quantity by simple addition of actual, fractional or percentage uncertainties (a rigorous statistical treatment is not required). For a quantity x = (2. 0  ± 0. 1) mm,Actual/ Absolute uncertainty, ? x =  ± 0. 1 mm Fractional uncertainty, ? x x = 0. 05 Percentage uncertainty, ? xx 100% = 5 % If p = (2x + y) / 3 or p = (2x – y) / 3, ? p = (2? x + ? y) / 3 If r = 2xy3 or r = 2x / y3, ? r / r = ? x / x + 3? y / y Actual error must be recorded to only 1 significant figure, ; The number of decimal places a calculated quantity should have is determined by its actual error. For eg, suppose g has been initially calculated to be 9. 80645 ms-2 ; ? g has been initially calculated to be 0. 04848 ms-2. The final value of ? g must be recorded as 0. 5 ms-2 {1 sf }, and the appropriate recording of g is (9. 81  ± 0. 05) ms-2. Distinction between scalar and vector quantities: | Scalar| Vector| Definition| A scalar quantity has a magnitude only. It is completely described by a certain number and a unit. | A vector quantity has both magnitude and direction. It can be described by an arrow whose length represents the magnitude of the vector and the arrow-head represents the direction of the vector. | Examples| Distance, speed, mass , time, temperature, work done, kinetic energy, pressure, power, electric charge etc. Common Error:Students tend to associate kinetic energy and pressure with vectors because of the vector components involved. However, such considerations have no bearings on whether the quantity is a vector or scalar. | Displacement, velocity, moments (or torque), momentum, force, electric field etc. | Representation of vector as two perpendicular components: In the diagram below, XY represents a flat kite of weight 4. 0 N. At a certain instant, XY is inclined at 30 ° to the horizontal and the wind exerts a steady force of 6. 0 N at right angles to XY so that the kite flies freely.By accurate scale drawing| By calculations using sine and cosine rules, or Pythagoras? theorem| Draw a scale diagram to find the magnitude and direction of the resultant force acting on the kite. R = 3. 2 N (? 3. 2 cm) at ? = 112 ° to the 4 N vector. | Using cosine rule, a2 = b2 + c2 – 2bc cos A R2 = 42 + 62 -2( 4)(6)(cos 30 °) R = 3. 23 NUsing sine rule: a / sin A = b / sin B 6 / sin ? = 3. 23 / sin 30 ° ? = 68 ° or 112 ° = 112 ° to the 4 N vector| Summing Vector Components| | Fx = – 6 sin 30 ° = – 3 NFy = 6 cos 30 ° – 4 = 1. 2 NR = v(-32 + 1. 22) = 3. 23 Ntan ? = 1. 2 / 3 = 22 °R is at an angle 112 ° to the 4 N vector. (90 ° + 22 °)|Kinematics Displacement, speed, velocity and acceleration: Distance: Total length covered irrespective of the direction of motion. Displacement: Distance moved in a certain direction. Speed: Distance travelled per unit time. Velocity: is defined as the rate of change of displacement, or, displacement per unit time {NOT: displacement over time, nor, displacement per second, nor, rate of change of displacement per unit time} Acceleration: is defined as the rate of change of velocity. Using graphs to find displacement, velocity and acceleration: * The area under a velocity-time graph is the change in displacement. The gr adient of a displacement-time graph is the {instantaneous} velocity. * The gradient of a velocity-time graph is the acceleration. The ‘SUVAT' Equations of Motion The most important word for this chapter is SUVAT, which stands for: * S (displacement), * U (initial velocity), * V (final velocity), * A (acceleration) and * T (time) of a particle that is in motion. Below is a list of the equations you MUST memorise, even if they are in the formula book, memorise them anyway, to ensure you can implement them quickly. 1. v = u +at| derived from definition of acceleration: a = (v – u) / t| 2. | s = ? (u + v) t| derived from the area under the v-t graph| 3. | v2 = u2 + 2as| derived from equations (1) and (2)| 4. | s = ut + ? at2| derived from equations (1) and (2)| These equations apply only if the motion takes place along a straight line and the acceleration is constant; {hence, for eg. , air resistance must be negligible. } Motion of bodies falling in a uniform gravitational field with air resistance: Consider a body moving in a uniform gravitational field under 2 different conditions: Without Air Resistance:Assuming negligible air resistance, whether the body is moving up, or at the highest point or moving down, the weight of the body, W, is the only force acting on it, causing it to experience a constant acceleration. Thus, the gradient of the v-t graph is constant throughout its rise and fall. The body is said to undergo free fall. With Air Resistance: If air resistance is NOT negligible and if it is projected upwards with the same initial velocity, as the body moves upwards, both air resistance and weight act downwards. Thus its speed will decrease at a rate greater than . 81 ms-2 . This causes the time taken to reach its maximum height reached to be lower than in the case with no air resistance. The max height reached is also reduced. At the highest point, the body is momentarily at rest; air resistance becomes zero and hence the only force acting on it is the weight. The acceleration is thus 9. 81 ms-2 at this point. As a body falls, air resistance opposes its weight. The downward acceleration is thus less than 9. 81 ms-2. As air resistance increases with speed, it eventually equals its weight (but in opposite direction).From then there will be no resultant force acting on the body and it will fall with a constant speed, called the terminal velocity. Equations for the horizontal and vertical motion: | x direction (horizontal – axis)| y direction (vertical – axis)| s (displacement)| sx = ux t sx = ux t + ? ax t2| sy = uy t + ? ay t2 (Note: If projectile ends at same level as the start, then sy = 0)| u (initial velocity)| ux| uy| v (final velocity)| vx = ux + axt (Note: At max height, vx = 0)| vy = uy + at vy2 = uy2 + 2asy| a (acceleration)| ax (Note: Exists when a force in x direction present)| ay (Note: If object is falling, then ay = -g)| (time)| t| t| Parabolic Motion: tan ? = vy / vx ?: direction of tangenti al velocity {NOT: tan ? = sy / sx } Forces Hooke's Law: Within the limit of proportionality, the extension produced in a material is directly proportional to the force/load applied F = kx Force constant k = force per unit extension (F/x) Elastic potential energy/strain energy = Area under the F-x graph {May need to â€Å"count the squares†} For a material that obeys Hooke? s law, Elastic Potential Energy, E = ? F x = ? k x2 Forces on Masses in Gravitational Fields: A region of space in which a mass experiences an (attractive) force due to the presence of another mass.Forces on Charge in Electric Fields: A region of space where a charge experiences an (attractive or repulsive) force due to the presence of another charge. Hydrostatic Pressure p = ? gh {or, pressure difference between 2 points separated by a vertical distance of h } Upthrust: An upward force exerted by a fluid on a submerged or floating object; arises because of the difference in pressure between the upper and l ower surfaces of the object. Archimedes' Principle: Upthrust = weight of the fluid displaced by submerged object. ie Upthrust = Volsubmerged x ? fluid x g Frictional Forces: The contact force between two surfaces = (friction2 + normal reaction2)? * The component along the surface of the contact force is called friction * Friction between 2 surfaces always opposes relative motion {or attempted motion}, and * Its value varies up to a maximum value {called the static friction} Viscous Forces: * A force that opposes the motion of an object in a fluid * Only exists when there is (relative) motion * Magnitude of viscous force increases with the speed of the object Centre of Gravity of an object is defined as that pt through which the entire weight of the object may be considered to act.A couple is a pair of forces which tends to produce rotation only. Moment of a Force: The product of the force and the perpendicular distance of its line of action to the pivot Torque of a Couple: The produ ce of one of the forces of the couple and the perpendicular distance between the lines of action of the forces. (WARNING: NOT an action-reaction pair as they act on the same body. ) Conditions for Equilibrium (of an extended object): 1. The resultant force acting on it in any direction equals zero 2. The resultant moment about any point is zero If a mass is acted upon by 3 forces only and remains in equilibrium, then 1.The lines of action of the 3 forces must pass through a common point 2. When a vector diagram of the three forces is drawn, the forces will form a closed triangle (vector triangle), with the 3 vectors pointing in the same orientation around the triangle. Principle of Moments: For a body to be in equilibrium, the sum of all the anticlockwise moments about any point must be equal to the sum of all the clockwise moments about that same point. Work, Energy and Power Work Done by a force is defined as the product of the force and displacement (of its point of application) in the direction of the force W = F s cos ?Negative work is said to be done by F if x or its compo. is anti-parallel to F If a variable force F produces a displacement in the direction of F, the work done is determined from the area under F-x graph. {May need to find area by â€Å"counting the squares†. } By Principle of Conservation of Energy, Work Done on a system = KE gain + GPE gain + Work done against friction} Consider a rigid object of mass m that is initially at rest. To accelerate it uniformly to a speed v, a constant net force F is exerted on it, parallel to its motion over a displacement s. Since F is constant, acceleration is constant, Therefore, using the equation: 2 = u2 +2as, as = 12 (v2 – u2) Since kinetic energy is equal to the work done on the mass to bring it from rest to a speed v, The kinetic energy, EK| = Work done by the force F = Fs = mas = ? m (v2 – u2)| Gravitational potential energy: this arises in a system of masses where there are at tractive gravitational forces between them. The gravitational potential energy of an object is the energy it possesses by virtue of its position in a gravitational field. Elastic potential energy: this arises in a system of atoms where there are either attractive or repulsive short-range inter-atomic forces between them.Electric potential energy: this arises in a system of charges where there are either attractive or repulsive electric forces between them. The potential energy, U, of a body in a force field {whether gravitational or electric field} is related to the force F it experiences by: F = – dU / dx. Consider an object of mass m being lifted vertically by a force F, without acceleration, from a certain height h1 to a height h2. Since the object moves up at a constant speed, F is equal to mg. The change in potential energy of the mass| = Work done by the force F = F s = F h = m g h|Efficiency: The ratio of (useful) output energy of a machine to the input energy. ie =| U seful Output Energy| x100% =| Useful Output Power| x100%| | Input Energy| | Input Power| | Power {instantaneous} is defined as the work done per unit time. P =| Total Work Done| =| W| | Total Time| | t| Since work done W = F x s, P =| F x s| =| Fv| | t| | | * for object moving at const speed: F = Total resistive force {equilibrium condition} * for object beginning to accelerate: F = Total resistive force + ma Wave Motion Displacement (y): Position of an oscillating particle from its equilibrium position.Amplitude (y0 or A): The maximum magnitude of the displacement of an oscillating particle from its equilibrium position. Period (T): Time taken for a particle to undergo one complete cycle of oscillation. Frequency (f): Number of oscillations performed by a particle per unit time. Wavelength (? ): For a progressive wave, it is the distance between any two successive particles that are in phase, e. g. it is the distance between 2 consecutive crests or 2 troughs. Wave speed (v): The sp eed at which the waveform travels in the direction of the propagation of the wave.Wave front: A line or surface joining points which are at the same state of oscillation, i. e. in phase, e. g. a line joining crest to crest in a wave. Ray: The path taken by the wave. This is used to indicate the direction of wave propagation. Rays are always at right angles to the wave fronts (i. e. wave fronts are always perpendicular to the direction of propagation). From the definition of speed, Speed = Distance / Time A wave travels a distance of one wavelength, ? , in a time interval of one period, T. The frequency, f, of a wave is equal to 1 / T Therefore, speed, v = ? / T = (1 / T)? f? v = f? Example 1: A wave travelling in the positive x direction is showed in the figure. Find the amplitude, wavelength, period, and speed of the wave if it has a frequency of 8. 0 Hz. Amplitude (A) = 0. 15 mWavelength (? ) = 0. 40 mPeriod (T) = 1f = 18. 0 ? 0. 125 sSpeed (v) =f? = 8. 0 x 0. 40 = 3. 20 m s-1A wa ve which results in a net transfer of energy from one place to another is known as a progressive wave. | | Intensity {of a wave}: is defined as the rate of energy flow per unit time {power} per unit cross-sectional area perpendicular to the direction of wave propagation.Intensity = Power / Area = Energy / (Time x Area) For a point source (which would emit spherical wavefronts), Intensity = (? m? 2xo2) / (t x 4? r2) where x0: amplitude ; r: distance from the point source. Therefore, I ? xo2 / r2 (Pt Source) For all wave sources, I ? (Amplitude)2 Transverse wave: A wave in which the oscillations of the wave particles {NOT: movement} are perpendicular to the direction of the propagation of the wave. Longitudinal wave: A wave in which the oscillations of the wave particles are parallel to the direction of the propagation of the wave.Polarisation is said to occur when oscillations are in one direction in a plane, {NOT just â€Å"in one direction†} normal to the direction of propag ation. {Only transverse waves can be polarized; longitudinal waves can’t. }Example 2: The following stationary wave pattern is obtained using a C. R. O. whose screen is graduated in centimetre squares. Given that the time-base is adjusted such that 1 unit on the horizontal axis of the screen corresponds to a time of 1. 0 ms, find the period and frequency of the wave. Period, T = (4 units) x 1. 0 = 4. 0 ms = 4. 0 x 10-3 sf = 1 / T = 14 x 10-3 250 Hz| | Superposition Principle of Superposition: When two or more waves of the same type meet at a point, the resultant displacement of the waves is equal to the vector sum of their individual displacements at that point. Stretched String A horizontal rope with one end fixed and another attached to a vertical oscillator. Stationary waves will be produced by the direct and reflected waves in the string. Or we can have the string stopped at one end with a pulley as shown below. Microwaves A microwave emitter placed a distance away from a metal plate that reflects the emitted wave.By moving a detector along the path of the wave, the nodes and antinodes could be detected. Air column A tuning fork held at the mouth of a open tube projects a sound wave into the column of air in the tube. The length of the tube can be changed by varying the water level. At certain lengths of the tube, the air column resonates with the tuning fork. This is due to the formation of stationary waves by the incident and reflected sound waves at the water surface. Stationary (Standing) Wave) is one * whose waveform/wave profile does not advance {move}, where there is no net transport of energy, and * where the positions of antinodes and nodes do not change (with time). A stationary wave is formed when two progressive waves of the same frequency, amplitude and speed, travelling in opposite directions are superposed. {Assume boundary conditions are met} | Stationary waves| Stationary Waves Progressive Waves| Amplitude| Varies from maximum at th e anti-nodes to zero at the nodes. | Same for all particles in the wave (provided no energy is lost). | Wavelength| Twice the distance between a pair of adjacent nodes or anti-nodes. The distance between two consecutive points on a wave, that are in phase. | Phase| Particles in the same segment/ between 2 adjacent nodes, are in phase. Particles in adjacent segments are in anti-phase. | All particles within one wavelength have different phases. | Wave Profile| The wave profile does not advance. | The wave profile advances. | Energy| No energy is transported by the wave. | Energy is transported in the direction of the wave. | Node is a region of destructive superposition where the waves always meet out of phase by ? radians. Hence displacement here is permanently zero {or minimum}.Antinode is a region of constructive superposition where the waves always meet in phase. Hence a particle here vibrates with maximum amplitude {but it is NOT a pt with a permanent large displacement! } Dist between 2 successive nodes / antinodes = ? / 2 Max pressure change occurs at the nodes {NOT the antinodes} because every node changes fr being a pt of compression to become a pt of rarefaction {half a period later} Diffraction: refers to the spreading {or bending} of waves when they pass through an opening {gap}, or round an obstacle (into the â€Å"shadow† region). Illustrate with diag} For significant diffraction to occur, the size of the gap ? ? of the wave For a diffraction grating, d sin ? = n ? , d = dist between successive slits {grating spacing} = reciprocal of number of lines per metre When a â€Å"white light† passes through a diffraction grating, for each order of diffraction, a longer wavelength {red} diffracts more than a shorter wavelength {violet} {as sin ? ? ? }. Diffraction refers to the spreading of waves as they pass through a narrow slit or near an obstacle. For diffraction to occur, the size of the gap should approximately be equal to the wavelengt h of the wave.Coherent waves: Waves having a constant phase difference {not: zero phase difference / in phase} Interference may be described as the superposition of waves from 2 coherent sources. For an observable / well-defined interference pattern, the waves must be coherent, have about the same amplitude, be unpolarised or polarised in the same direction, ; be of the same type. Two-source interference using: 1. Water Waves Interference patterns could be observed when two dippers are attached to the vibrator of the ripple tank.The ripples produce constructive and destructive interference. The dippers are coherent sources because they are fixed to the same vibrator. 2. Microwaves Microwave emitted from a transmitter through 2 slits on a metal plate would also produce interference patterns. By moving a detector on the opposite side of the metal plate, a series of rise and fall in amplitude of the wave would be registered. 3. Light Waves (Young? s double slit experiment) Since light is emitted from a bulb randomly, the way to obtain two coherent light sources is by splitting light from a single slit.The 2 beams from the double slit would then interfere with each other, creating a pattern of alternate bright and dark fringes (or high and low intensities) at regular intervals, which is also known as our interference pattern. Condition for Constructive Interference at a pt P: Phase difference of the 2 waves at P = 0 {or 2? , 4? , etc} Thus, with 2 in-phase sources, * implies path difference = n? ; with 2 antiphase sources: path difference = (n + ? )? Condition for Destructive Interference at a pt P: Phase difference of the 2 waves at P = ? { or 3? , 5? , etc } With 2 in-phase sources, + implies path difference = (n+ ? ), with 2 antiphase sources: path difference = n ? Fringe separation x = ? D / a, if a;;D {applies only to Young's Double Slit interference of light, ie, NOT for microwaves, sound waves, water waves} Phase difference betw the 2 waves at any pt X {be tw the central & 1st maxima) is (approx) proportional to the dist of X from the central maxima. Using 2 sources of equal amplitude x0, the resultant amplitude of a bright fringe would be doubled {2Ãâ€"0}, & the resultant intensity increases by 4 times {not 2 times}. { IResultant ? (2 x0)2 } Electric FieldsElectric field strength / intensity at a point is defined as the force per unit positive charge acting at that point {a vector; Unit: N C-1 or V m-1} E = F / q > F = qE * The electric force on a positive charge in an electric field is in the direction of E, while * The electric force on a negative charge is opposite to the direction of E. * Hence a +ve charge placed in an electric field will accelerate in the direction of E and gain KE {& simultaneously lose EPE}, while a negative charge caused to move (projected) in the direction of E will decelerate, ie lose KE, { & gain EPE}. Representation of electric fields by field lines | | | | | Coulomb's law: The (mutual) electric force F acting between 2 point charges Q1 and Q2 separated by a distance r is given by: F = Q1Q2 / 4 or2 where ? 0: permittivity of free space or, the (mutual) electric force between two point charges is proportional to the product of their charges ; inversely proportional to the square of their separation. Example 1: Two positive charges, each 4. 18 ? C, and a negative charge, -6. 36 ? C, are fixed at the vertices of an equilateral triangle of side 13. 0 cm. Find the electrostatic force on the negative charge. | F = Q1Q2 / 4 or2= (8. 99 x 109) [(4. 18 x 10-6)(6. 6 x 10-6) / (13. 0 x 10-2)2]= 14. 1 N (Note: negative sign for -6. 36 ? C has been ignored in the calculation)FR = 2 x Fcos300= 24. 4 N, vertically upwards| Electric field strength due to a Point Charge Q : E = Q / 4 or2 {NB: Do NOT substitute a negative Q with its negative sign in calculations! } Example 2: In the figure below, determine the point (other than at infinity) at which the total electric field strength is zero. From t he diagram, it can be observed that the point where E is zero lies on a straight line where the charges lie, to the left of the -2. 5 ? C charge. Let this point be a distance r from the left charge.Since the total electric field strength is zero, E6? = E-2? [6? / (1 + r)2] / 4 or2 = [2. 5? / r2] / 4 or2 (Note: negative sign for -2. 5 ? C has been ignored here) 6 / (1 + r)2 = 2. 5 / r2 v(6r) = 2. 5 (1 + r) r = 1. 82 m The point lies on a straight line where the charges lie, 1. 82 m to the left of the -2. 5 ? C charge. Uniform electric field between 2 Charged Parallel Plates: E = Vd, d: perpendicular dist between the plates, V: potential difference between plates Path of charge moving at 90 ° to electric field: parabolic. Beyond the pt where it exits the field, the path is a straight line, at a tangent to the parabola at exit.Example 3: An electron (m = 9. 11 x 10-31 kg; q = -1. 6 x 10-19 C) moving with a speed of 1. 5 x 107 ms-1, enters a region between 2 parallel plates, which are 20 mm apart and 60 mm long. The top plate is at a potential of 80 V relative to the lower plate. Determine the angle through which the electron has been deflected as a result of passing through the plates. Time taken for the electron to travel 60 mm horizontally = Distance / Speed = 60 x 10-3 / 1. 5 x 107 = 4 x 10-9 s E = V / d = 80 / 20 x 10-3 = 4000 V m-1 a = F / m = eE / m = (1. 6 x 10-19)(4000) / (9. 1 x 10-31) = 7. 0 x 1014 ms-2 vy = uy + at = 0 + (7. x 1014)( 4 x 10-9) = 2. 8 x 106 ms-1 tan ? = vy / vx = 2. 8 x 106 / 1. 5 x 107 = 0. 187 Therefore ? = 10. 6 ° Effect of a uniform electric field on the motion of charged particles * Equipotential surface: a surface where the electric potential is constant * Potential gradient = 0, ie E along surface = 0 } * Hence no work is done when a charge is moved along this surface. { W=QV, V=0 } * Electric field lines must meet this surface at right angles. * {If the field lines are not at 90 ° to it, it would imply that there is a non- zero component of E along the surface. This would contradict the fact that E along an equipotential = 0. Electric potential at a point: is defined as the work done in moving a unit positive charge from infinity to that point, { a scalar; unit: V } ie V = W / Q The electric potential at infinity is defined as zero. At any other point, it may be positive or negative depending on the sign of Q that sets up the field. {Contrast gravitational potential. } Relation between E and V: E = – dV / dr i. e. The electric field strength at a pt is numerically equal to the potential gradient at that pt. NB: Electric field lines point in direction of decreasing potential {ie from high to low pot}.Electric potential energy U of a charge Q at a pt where the potential is V: U = QV Work done W on a charge Q in moving it across a pd ? V: W = Q ? V Electric Potential due to a point charge Q : V = Q / 4 or {NB: Substitute Q with its sign} Electromagnetism When a conductor carrying a current is plac ed in a magnetic field, it experiences a magnetic force. The figure above shows a wire of length L carrying a current I and lying in a magnetic field of flux density B. Suppose the angle between the current I and the field B is ? , the magnitude of the force F on the conductor is iven by F = BILsin? The direction of the force can be found using Fleming? s Left Hand Rule (see figure above). Note that the force is always perpendicular to the plane containing both the current I and the magnetic field B. * If the wire is parallel to the field lines, then ? = 0 °, and F = 0. (No magnetic force acts on the wire) * If the wire is at right angles to the field lines, then ? = 90 °, and the magnetic force acting on the wire would be maximum (F = BIL) Example The 3 diagrams below each show a magnetic field of flux density 2 T that lies in the plane of the page.In each case, a current I of 10 A is directed as shown. Use Fleming's Left Hand Rule to predict the directions of the forces and wo rk out the magnitude of the forces on a 0. 5 m length of wire that carries the current. (Assume the horizontal is the current) | | | F = BIL sin? = 2 x 10 x 0. 5 x sin90 = 10 N| F = BIL sin? = 2 x 10 x 0. 5 x sin60 = 8. 66 N| F = BIL sin ? = 2 x 10 x 0. 5 x sin180 = 0 N| Magnetic flux density B is defined as the force acting per unit current in a wire of unit length at right-angles to the field B = F / ILsin ? > F = B I L sin ? {? Angle between the B and L} {NB: write down the above defining equation & define each symbol if you're not able to give the â€Å"statement form†. } Direction of the magnetic force is always perpendicular to the plane containing the current I and B {even if ? ? 0} The Tesla is defined as the magnetic flux density of a magnetic field that causes a force of one newton to act on a current of one ampere in a wire of length one metre which is perpendicular to the magnetic field. By the Principle of moments, Clockwise moments = Anticlockwise moments mg â⠂¬ ¢ x = F †¢ y = BILsin90 †¢ yB = mgx / ILy Example A 100-turn rectangular coil 6. 0 cm by 4. 0 cm is pivoted about a horizontal axis as shown below. A horizontal uniform magnetic field of direction perpendicular to the axis of the coil passes through the coil. Initially, no mass is placed on the pan and the arm is kept horizontal by adjusting the counter-weight. When a current of 0. 50 A flows through the coil, equilibrium is restored by placing a 50 mg mass on the pan, 8. 0 cm from the pivot. Determine the magnitude of the magnetic flux density and the direction of the current in the coil.Taking moments about the pivot, sum of Anti-clockwise moments = Clockwise moment (2 x n)(FB) x P = W x Q (2 x n)(B I L) x P = m g x Q, where n: no. of wires on each side of the coil (2 x 100)(B x 0. 5 x 0. 06) x 0. 02 = 50 x 10

Compare curanderismo, espiritualismo, with Afro-Caribbean Santeria, Essay

Compare curanderismo, espiritualismo, with Afro-Caribbean Santeria, Pentecostalism - Essay Example Moreover, there are several objects that are used by the practitioners. They include the holy water, crucifixes, lemons, eggs, candles, saints, incense, candles, spices, eggs, limes, and oils. Evidently, curanderismo originated from the Mexican culture following its colonization by Mexico. It derives its meaning from the word curar which is Spanish for ‘to heal.’ Incidentally, curanderismo is a combination of the indigenous Latin American folk medicine and Catholicism. Presently, curanderismo is practiced in a number of Latin American countries and also in the United States. To this end, it has retained its popularity among certain Mexican-American people as an alternative mode of medicine. Its popularity is largely due to the belief that it offers spiritual alleviation from ailments that are beyond conventional medicine. Espiritualismo involves the practice of spiritualism. Evidently its practice is based on the belief that the spirit world can offer intervention within the human world. To this end, it is practised by a majority of Caribbean’s and also by some citizens from Latin America. However, it is different from Santeria since there are rituals c haracterized by animal sacrifices. Espiritualismo is further regarded as a philosophical movement that is based on reverence to God and the soul, the spiritual and moral principles, and the immortality of being. Moreover, espiritualismo believes in reincarnation, survival ideals of the soul, and the relation between the disembodied and embodied. The general principles of espiritualismo include the belief in God, his helpers and angels; spiritual adoration and worship; the original root of religion and other manifestations of religion; and the divine reverence of the Great Spirit known as ‘God.’ Moreover, mineral, plants, oils, prayers, trees, candles, flowers, and music equally play a pertinent role in the belief of espiritualismo. Evidently, the doctrines of espiritualismo espouse that when a person is born, he or she is a constituent of two bodies. The first body is the physical and visible entity which is earthly and temporary. The second body is the spiritual entity which is eternal and invisible. Furthermore, after death the physical body ceases to exist but the spiritual body continues in an eternal existence under the control of God. On the other hand, Santeria is a combination of religious beliefs and traditions that constitutes a similar African traditional religion. Evidently, its origin can be traced back to Brazil and Cuba. It is characterized by a combination of the worship elements of Catholicism and the traditional Yoruba faith. The Santeria religion is based on creating relationships between the human beings and mortal spirits which are powerful and known as the Orishas. Evidently, the Orisha is a reflection of the god also known as Olodumare. In this regard, the adherents of Santeria believed that the spirits provided them with the gift of life when they performed satisfactory rituals. This consequently enabled them to be blessed with the destiny bestowed upon them before their birth. Interestingly, the Santeria religion exhibits a relation with the Roman Catholic church through the association between Orishas and the Catholic Saints. For example, Our Lady of Charity was known as Ochun in the Santeria religion. She is the Yoruba goddess in charge of the river. The goddess was equally associated with love, sweets, water, love and yellow. Saint Lazarus was the alternate version of Babalu-Aye in Santeria religion.

Jews and Race in the United States Essay Example | Topics and Well Written Essays - 1000 words

Jews and Race in the United States - Essay Example History has it that Jews entered America years earlier than 1700s (Pattai and Pattai 27). They mainly immigrated to the Southern States of the US, where they were slave masters, big economists, planters and slave traders. As they continued to stay in America alongside increased immigration of other races into America, Jews related and liquidated with the new races as well as the original ones. These interrelations led to complication in identification of the Jews and to an extent tell whether Jews have a race or not. With reference to Marcus, before 1790, American Constitution did not allow room for naturalization of impure white race(s) into America (3). Fascinatingly, by that time Jews who immigrated to America were white and thus got naturalized as citizens of the US. Today, determining Jews is a big problem that may require expertise of doctors to determine genetic makeup of the suspected Jews. Steinsaltz and Henegbi mention that in the 19th century, Jews were considered merely a s religious group and not people belonging to any special race (1). Jews were most known to be anti-Christian though they lived and originated from Israel believed to be birth place of Christ. The recruits into Judaism or Jews have to learn and adhere to the strict commandments of Torah. Jews constitute of diversity of races among them Africans, Asians and Europeans and as religion, every individual who join Judaism becomes an automatic Jew. From the prior review, Jews therefore disqualifies to be a race but rather a people sharing common beliefs. Unlike other races whose physical makeup changes when they mingle and live long with other races, Jews at all times despite the color variations are identical when certain physical characteristics are carefully speculated (Pattai and Pattai 30). Jews are naturally promiscuous group who in the early 18th centuries when they dominated as slave masters in the US, copulated with Negros in the Southern part of America to produce intermediary ra ces or just Negro. The Jews also intermarried with the some of the European races like the Irish, Celts, and Anglo-Saxons among others. The intermarriages produce individuals of varied races depending on the Jew’s intermarrying partner. Among the characteristics used to determine Jews is the self-hatred psychology. As observed by Goldstein, Jews will easily be identified from their motives towards the Semites, they are always anti-Semites and this is a common attitude in every descendant of Jew in spite of color (10). Goldstein indicates that the facial appearance of the Jews that makes them easily identified, resemble that of a black African (5). First, Jews are characterized by muzzled-shaped mouth that does not resemble any race. Second, Jews have small chins, projected mouth and closely packed eyes. Jews are also at times in America, viewed as cultural people who share certain cultural and social beliefs. Jews are like a family believing in the same orders and rules. This aspect was also dominant in the American history when the slave masters taught and influenced the slaves with their cultural practices and finally converting the slave Negros to adapt Jews concepts. Fishberg dictates that the spread and contamination of the original Jewish race was due to their capabilities of mixing and fitting in any environment despite of weather, culture and language differences

Single slit diffraction & double slit interference Lab Report

Single slit diffraction & double slit interference - Lab Report Example Hence, diffraction patterns usually have a series of maxima and minima. The slit must satisfy two conditions in order the diffraction occur: first, the slit should has dimensions of infinitely length to width and second, the width of the slit is on the order of the wavelength of light being used. The wavefront from a light source will form secondary waves. The one located at the top edge of the slit interferes destructively with other secondary wave located at the middle of the slit, when the path difference between them is equal to '/2. Similarly, the secondary wave just below the top of the slit will interfere destructively with the secondary wave located just below the middle of the slit. Thus we can conclude that the condition for destructive interference for the entire slit is the same as the condition for destructive interference between double slits with distance equal to half the width of the slit. The path difference is given by: When monochromatic light illuminates a double slit aperture having dimensions of the order of the wavelength of light, diffraction of light occurs if the slits width much narrower than there lengths. The incident wavefront will divided into two point sources of light which can interfere with each other to produce an interference pattern 1. Constructive Interference - When the path difference between the two beams in an integral multiplication of the wavelength. The result is brighter illumination in these regions when a crest of a wave meets a crest from another wave 2. Destructive Interference - When the path difference between the two beams in an odd multiplication of half a wavelength. The result is dark bands in these regions when a crest of a wave meets a trough from another wave Constructive interference occurs when: (3.5) Where: ' is the wavelength of the light, d is the separation of the slits, the distance between (b) and (c) in (Fig.3.1) n is the order of maximum observed (central maximum is n = 0), x is the fringe distance, the distance between the bands of light and the central maximum. L is the distance from the slits to the screen. This is only an approximation and depends on certain conditions. It is possible to work out the wavelength of the used light using this equation and the above apparatus. If (d) and (L) are known and (x) is observed, then ' can be easily calculated. Objectives: Examine the diffraction pattern formed by laser light passing through single and double slits. Verify that the positions of the minima in the diffraction pattern match the positions predicted by the theory To compare

Conflict of Interest Becomes Key Issue in Public Sector Research Paper

Conflict of Interest Becomes Key Issue in Public Sector - Research Paper Example Conflict of Interest becomes a key issue in Public Sector. Chapter 7 Title 59 of the Idaho State’s Code specifically states the conflict of interest occurs when any official or administrative action, decision or recommendation by any person in relation to ones’ official duty as a public officer that would generate economic gain of the person or member of the public officer’s family members, or a business owned, whether partially or wholly, by the public officer. The code specifically states that the public officer shall not use one’s office to enrich oneself. For example, the police officer shall not receive money in exchange for not giving a parking ticket. The judge shall not receive gifts in exchange for winning a case filed under the judge’s courtroom. In addition, the fireman shall not receive cash in exchange for prioritizing the saving of one’s home over the other homes in the community. Likewise, the government construction engineer s hall not receive cash or other gifts from the suppliers in exchange for winning a government contract. (http://www.boisestate.edu/policy/policy_docs/7080_ethicsingovernmentconflictofinterest.pdf) Exceptions to the Conflict of Interest Rule. However, there are exceptions that would prevent the public officer’s action or inaction from being classified as conflict of Interest. One example is when the law requires the public officer to pursue the action or inaction. ... ic officer’s legal salaries, wages, and other benefits) on the public officer as that of a substantial group of persons engaging in the same profession, trade, or occupation. Further, the public officer can act or not act on any transaction if the public officer or any member of his family is a director, owner, officer, or partner employee owns stocks in the benefiting organization amounting to $ 5,000 or less. Lastly, another example is when the public officer’s action or inaction in relation tax imposition will have the same effect on the public officer and the general public. (http://www.boisestate.edu/policy/policy_docs/7080_ethicsingovernmentconflictofinterest.pdf) Ethics in Government. All government employees must comply with government ethics policies. The †¦ states that a public officer who is a noncareer officer or employee working on a government position with the rank of GS-15 or the General Schedule, or if not found under the General Schedule, has a ba sic salary rate equal to or more than 120 percent of the minimum rate of basic pay for a GS- 15 of the General Schedule, in any one accounting year, should not receive outside remuneration exceeding fifteen percent of the annual basic pay for level II of the Executive Schedule under Section 5313 Title 5 of the United States Code starting January 1, 1978. Likewise, the law allows the public’s giving of charitable institution on behalf of the public officer provided the amount is equal to $2,000 or less in any given accounting year. However, the public’s giving of charitable contributions to any charitable organization where the public officer or any of his family members will have economic gain, whether directly or indirectly. (http://www.library.ca.gov/crb/98/02/98002.pdf) Further, the same website

Sample Statistic, p-value, Confidence interval Assignment

Sample Statistic, p-value, Confidence interval - Assignment Example 1) What is the null hypothesis (H0) tested? H0: Ï€ ≠¤ 0.5 2) What is the alternative hypothesis (H1)? H1: Ï€ > 0.5 3) Sample statistic: a. What is the meaning of the sample statistic? A sample statistic is calculated numerical value that characterizes some aspect of sample set of data, often meant to estimate the real value of the corresponding parameter in an underlying population. What is its value? 0.05 4) Test statistic: a. What is the meaning of the test statistic? The test stat is the distance of the sample proportion from the population proportion in standard errors of the distribution of the test statistic b. What is its value? 0.8944 5) Critical values: a. What is the meaning of critical value? Critical value(s) is a factor used to compute the margin of error. Critical value(s) of the test statistic bounds the rejection region(s) of probability alpha = the risk we are willing to take of rejecting H0 when H0 is true b. What is (are) the critical value(s)? Critical lower value is 1.6449

TPA6 Essay Example | Topics and Well Written Essays - 750 words

TPA6 - Essay Example The recent past has seen the failure of major IT projects like the Queensland Department of Health Payroll System and the US Combat Support System. Among the reasons that cause such failures, is the exclusion of a project Champion in such projects. IT projects are associated with a substantial level of complexities in terms of complex system interfaces, scarcity of IT resources like machines that need to be shared, data conversion to compatible formats, and the ever changing technology that calls for the need to upgrade systems. Most Project Managers do not have a clear understanding of such needs or if they do, only try to solve them in a tight timeframe, and when everything has gone out of control. Thus, a Project Champion is essential at this point to develop the project’s scope, define the objectives and metrics of the project and provide an accurate specification of resources like hardware and software. In addition, a Project Champion actively supports the system’s architecture to stakeholders in an effort to provide a clear understanding of the various states the project is supposed to undergo. For instance, in case there is a change in the project’s implementation, or the hardware and software that were initially stated, most stakeholders and project managers end up being confused and filled with fear. In fact, they tend to understand change in what can be called a fragmented format, in that the change is not uniformly understood. The end results are inconsistent compliance, agitation and failure of the project. Thus, a Project Champion is needed, primarily to play a critical role in ensuring a swift transformation of changes through clarifying each and every step taken to avoid any misconceptions that might arise from the project managers, project team or the customer (Chakrabart, 1974). Most IT projects fail due to technological complexities and over-optimistic habit of project managers without having a clear