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You Chapter-19 are expected to: Coulomb's Law 1. Use Coulomb's law to calculate the electric forces between charges. 2. Calculate the E-field due to a discrete charge distribution and simple continuous charge distributions. 3. Know the distinction between the electric force F (see eqs.[1], [2] below) and the E-field 4. Use Gauss' law to calculate the E-field for symmetric continuous charge distributions. 5. Solve problems that contain concepts from this chapter + some simple concepts from PHYS-101. 1. Coulomb's Law According to Coulomb's Law, the magnitude of the electrostatic force between two charged particles with charges Q1 and Q2 and separated by a distance r is given by: Fe = k Q1Q2 r2 ...[1] Where k = 9x109 N.m2/C2 is the Coulomb constant. The unit of charge is taken as a Coulomb (C). The constant k is also written as k = 1/4o where the constant o is called the permittivity of free space o = 8.854x10-12 C2/ N.m2. Since force is a vector quantity, in the vector form Coulomb's law is expressed as: F12 = k Q1Q2 ^ r12 r2 ...[2] r + F21 Q1 ^ r12 + Q2 F12 ^ Where r12 is a unit vector directed from Q1 to Q2. The electric charge is quantized in units of 1.6*10-19 C ( magnitude of the charge of an electron). Problem Solving: 1.1 Finding force on a given charge due to a discrete charge distribution. Break up the problem in three parts: [1] Direction:draw the force vectors at a given charge location due to the other given charges. (Remember: like charges repel, unlike charges attract.) A well-labeled diagram will be very helpful. [2]Magnitude: find the magnitude of various force vectors using eq.[1] [3] after step[2] treat the problem as a vector manipulation problem. The net force F on a given charge due to a discrete charge distribution is simply the vector sum of the forces produced by individual charges in the charge distribution at the location of the charge of your interest. Study problem 2 below to clarify the points mentioned above. 2. The E-field The magnitude of the E-field generated by a charge Q is given by E = kQ/r2. The direction of E at a given location is the direction in which a force would be exerted on a unit positive test charge placed at that location. The E-field due to a discrete charge distribution is simply the vector sum of the E-fields produced by individual charges in the charge distribution. 2.1 Finding the E-field at a given location due to a discrete charge distribution. Break up the problem in three parts: [1] Direction: draw the E-field vector directions at a given location due to the individual charges in the distribution (Remember: the direction of E at a given location is the direction in which a force would be exerted on a unit positive test charge placed at that location). [2]Magnitude: find the magnitude of various E-field vectors using E = kQ/r2. [3] after step [2] treat the problem as a vector manipulation problem Study problem 4 below to clarify the points mentioned above. Problems 1 and 3 are problems that use concepts from Ch. 19 and the conditions of translational equilibrium ( F = ma = 0) we studied last term. You will need to brush up on your free-bodyforce diagram (FBD) drawing abilities. 3. Gauss' Law E = E.ds = GS qenc. 0 (GS Gaussian surface) Read sections 19-8 and 19-9 of SJ ( Serway and Jewett) A crucial aspect of applying Gauss' law to determine the E-field due to a charge distribution is finding the charge enclosed within a Gaussian surface ( Please DO NOT UNDERESTIMATE THIS). Here are a few cases to illustrate this point: 1. A solid conducting sphere of radius R with charge Q. (Remember, all charge will be forced to the surface of the sphere. Why?) qenc. = 0 qenc. = Q for for r<R r>R 2. A solid dielectric (insulator) sphere of radius R with Q distributed uniformly throughout the volume. [i] first determine the volume charge density in terms of Q and R. = 3Q/ 4R3. [ii] determine the charge enclosed by the Gaussian surface. qenc. = (4r3/3) = Qr3/R3 qenc. = Q for r>R for r<R 3. A dielectric (insulator) spherical shell of inner radius a and outer radius b with Q distributed uniformly throughout the volume. The volume charge density, = 3Q/ 4(b3- a3) qenc. = 0 for r<a Q b qenc. =4(r3- a3)/3 =Q(r3- a3)/ (b3- a3) for a< r < b a qenc. = Q for r>b How this information is used with Gauss' law to find the E-field let's determine the E-field at various r-values. Region-1 ( r < a) E1.ds = E1 ds = qenc 0 = 0 (Note: both E1 and ds point radially outward and therefore E1.ds = E1ds, and since E1 is constant over the spherical GS, E1 can be taken out of the integral) E1 = 0 Region-2 ( a< r < b) 2 E2 .ds = E2 ds = 4 r E2 = qenc 0 where qenc. = 4(r3- a3)/3 = Q(r3- a3)/( b3- a3) Therefore E2 = [1/4r2] Q(r3- a3)/ b3- a3) =[ kQ/ r2](r3- a3)/( b3- a3) Region-3 ( r > b) E3 = kQ/r2 Chapter-19 SOLVED EXAMPLES ___________________________________________________________________________ 1. Two identical cork balls each of mass, are m hung from a common point by two insulating threads of negligible mass, each of length L = 50 cm. Each ball has a charge Q = - 0.2C distributed uniformly over its volume. The balls repel each other and assume an equilibrium position as shown. Determine the tension, T in the threads, and the mass m. Tsin60 60 g = 10m/s2 Tcos60 300 300 F mg =10m Solution: T = F/cos60o = 2x9x109x4x10-14/(0.5)2 = 2.88x10-3 N From Tsin60o = 10m, m = Tsin60o/10 = 2.5x 10-4 kg. L m r = 2Lcos60 = 50cm m 2. Three charges are placed at the three vertices of a right-angle triangle as shown. [a] Determine the force exerted on Q3 by charge Q1. Label this force F13 and express it in the usual i, j notation and show it on the diagram. Y Y Q 2= 4.0 C X 53 o Q 1 = - 8.0 C F13 X F23 Q 3 =6.25 C 5.0 cm [b] Determine the force exerted on Q3 by charge Q2. Label this force F23 and express it in the usual i, j notation and show it on the diagram. [c] Determine the magnitude and direction of the net force on Q3. Solution: ( Symbols in bold type are vectors) [a] F13 = - 9x109(8x6.25x10-12)/(5cos53 )2i N = - 500i N [b] F23 = 9x109(4x6.25x10-12)/(5x )2 = 90 N F23 = 90cos53i 90sin53 j = 54i 72 j N [c] FT = F23 +F13= - 446 i 72 j N FT = {(446)2+(72)2}1/2 = 452 N , = tan-1(72/446) = 9.2o 3. A charge Q = 3.0x10-8C is uniformly distributed throughout the volume of a small non-conducting ball of mass, m = 4.0 milligram. The ball hangs, as shown, from an insulating thread of negligible mass in a region of uniform electrostatic Efield produced by a uniformly charged plate, ab. In the diagram, = 37o, and E-field is perpendicular to g and normal to the charged plate. [a] In the space below, draw a clearly labeled free-body force diagram for the ball. [b] Determine the tension, T in the thread and the magnitude of the E-field at the site of the ball. Tcos37 T 37 a + + + + + + + g =10m/s 2 E Q m Tsin37 qE Solution: Tcos37 = mg = 4x10-5N or T = 4x10-5N /cos37 = 5x10-5 N Tsin37 = qE or E = Tsin37/q = 5x10-5x0.6/ 3x10-8 = 103N/C b 4x10-5N 4. Three charges are placed on the three corners of a square as shown. [a] Determine the E-fields produced at the origin, O individually by q1, q2 and q3. E1 = 9*109*3.0*10-6/(0.12)2j N/C = 1.875*106 j N/C E2 = [9*109*8.0*10-6/ 2(0.12)2 ]*0.71( - i j) N/C = - 1.77 *106( i + j) N/C E3 = 9*109*6.0*10-6/(0.12)2i N/C =3.75*106 i N/C [b] Determine the net E-field produced at the origin by the three charges. E = E1+ E2+ E3 = (1.98 i +0.105 j ) 106 N/C [c] Determine the magnitude of the net E-field, and its orientation with respect to the xaxis. E = [ (1.98)2 + (0.105)2]1/2 * 106 N/C = 1.98 * 106 N/C = tan-1[0.105/1.98] =3. 2o [d] If a charge Q = 2.5C is now placed at O, what would be the net force on the charge? F = QE = ( 4.95i +0.26 j) N y q 1 = - 3.0C q2 = 8.0C E1 O 45 0 E2 E3 12.0cm q1 = - 6.0C x For Gauss' Law problems: 1. Read Example 19.10 p. 627 of the Text. 2. Review the case of a conducting sphere discussed in the class. 3. Review the case of a non-conducting sphere discussed in the class. 4. Study the case of a charged dielectric (insulator) spherical shell discussed above. SELF-TEST QUESTIONS 1. Two positive point charges, Q and 4Q are arranged as shown. An electron is released from a point 1.0 cm away from charge Q. Immediately after being released the electron would move: Q 1 .0 cm e le c tro n 4Q X 4.0 cm [a] to the left [b] to the right [c] the electron will be at equilibrium and stay where it is released. 2. A thin, uniformly charged ring lies in the x-y plane with its center at the origin as shown. The net E-field at point P on the z-axis will point: [a] somewhere in the x-y plane. [b] along the positive z-axis axis. [c] along the negative z-axis axis. [d] E-field at P is zero because of the symmetry of the charge distribution. + + x + + o + z P + + + + + + y 3. An electric dipole is situated along the x-axis with its center at the origin. The net Efield at point P on the y-axis will point: [a] along the positive y-axis. [b] along the positive x-axis. [c] along the negative x-axis [b] The E-field at P is zero due to the opposite but equal contributions from the two charges. y P +q + o -q x 4. Two point charges are situated symmetrically about the origin. The E-field measured at the origin is zero. At point P, the E-field points in the positive x-direction. From this one can conclude that: [a] both charges are positive and equal in magnitude. [b] both charges are negative and equal in magnitude. [c] the charges are of opposite polarity but of equal magnitude. [d] none of the above, we don't have sufficient information. y q1 0 q2 P E x 5. The E-field inside a uniformly charged conducting shell is determined to be zero. When a positive charge Q is brought near the shell, the E-field at the center of the shell would: [a] still be zero [b] be non- zero and point radially away from Q [c] be non- zero and point radially toward Q + + + + O + + q + + Q
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Path: American University of Sharjah >> MECHANICAL >> 223,224,22 Spring, 2008
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Path: American University of Sharjah >> MECHANICAL >> 223,224,22 Spring, 2008
Description: CHAPTER 13 KEY EQUATIONS Equation Number Key Equation 13.1 v iE = I ES exp BE V T iE = iC + iB 13.2 - 1 13.3 13.6 13.9 = iC iE 13.10 13.20 13.21 13.23 13.24 13.35 13.38 13.39 13.40 13.43 13.44 13.45 13.46 v iC I s exp BE V T i ...
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Path: American University of Sharjah >> MECHANICAL >> 223,224,22 Spring, 2008
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Path: American University of Sharjah >> MECHANICAL >> 223,224,22 Spring, 2008
Description: MCE 230 L Materials Science Corrosion Test Gagan Gururaj ID: 8526 Group 2 Date of Experiment: 9/11/03 2 Table of Contents 1) Abstract.3 2) Part A: Introduction..3 3) Theory.3 4) Experimental procedure.4 5) Data..5 6) Calculations.6 7) Part B: Intr...
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Path: American University of Sharjah >> MECHANICAL >> 223,224,22 Spring, 2008
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Path: American University of Sharjah >> MCE >> 240 Spring, 2008
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Path: American University of Sharjah >> MCE >> 240 Spring, 2008
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Path: American University of Sharjah >> MCE >> 240 Spring, 2008
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Path: American University of Sharjah >> MCE >> 240 Spring, 2008
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Path: American University of Sharjah >> MCE >> 240 Spring, 2008
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Path: American University of Sharjah >> MECHANICAL >> 223,224,22 Spring, 2008
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Path: American University of Sharjah >> MCE >> 240 Spring, 2008
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Path: American University of Sharjah >> MECHANICAL >> 223,224,22 Spring, 2008
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Path: American University of Sharjah >> MECHANICAL >> 223,224,22 Spring, 2008
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Path: American University of Sharjah >> MECHANICAL >> 223,224,22 Spring, 2008
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Path: American University of Sharjah >> MECHANICAL >> 223,224,22 Spring, 2008
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Path: American University of Sharjah >> ARA >> 101,102 Spring, 2008
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Path: American University of Sharjah >> MCE >> 240 Spring, 2008
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Path: American University of Sharjah >> ARA >> 101,102 Spring, 2008
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Path: American University of Sharjah >> MECHANICAL >> 223,224,22 Spring, 2008
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Path: American University of Sharjah >> MCE >> 240 Spring, 2008
Description: American University of Sharjah College of Engineering Mechanical Engineering Department Spring 2008 Due Date: Sunday, April 20th, 2008. Statics MCE 220 Assignment # 13 Solve the following problems from the textbook (Engineering Mechanics: Statics ...
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Path: American University of Sharjah >> MECHANICAL >> 223,224,22 Spring, 2008
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Path: American University of Sharjah >> MECHANICAL >> 223,224,22 Spring, 2008
Description: MCE 230 L Materials Science Static Bending Test Gagan Gururaj ID: 8526 Group 2 Date of Experiment: 16/11/03 2 Table of Contents 1) Discussion.3 2) Introduction..3 3) Theoretical Background.3 4) Theory.3 5) Experimental Procedure.4 6) Experimental...
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Path: American University of Sharjah >> MECHANICAL >> 223,224,22 Spring, 2008
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Path: American University of Sharjah >> MECHANICAL >> 223,224,22 Spring, 2008
Description: Test Type Name: Company: Lab name: Test date: Geometry: Specimen Specimen name: Width: Thickness: Support span: Fixture type: Comment: Static Bending Fall 2003 Gourp 2 AUS Materials Science 11/16/2003 Rectangular 1 Wood 25 25 360 3-point Without Scr...
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Path: American University of Sharjah >> ARA >> 101,102 Spring, 2008
Description: Caliphal Succession: The `Abbasid Caliphate The `Abbasid Caliphate The `Abbasid period in its entirety covers approximately half a millennium spanning the years 132/750 to 656/1258. Consequently, historians have divided the period into three sub-per...
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Path: American University of Sharjah >> MECHANICAL >> 223,224,22 Spring, 2008
Description: SUMMARY: Fatigue is a form of failure that occurs in structures subjected to dynamic and fluctuating stresses (e.g., bridges, aircraft, and machine component); in this experiment we see that four different metals aluminum, copper, brass and steel, wh...
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Path: American University of Sharjah >> MECHANICAL >> 223,224,22 Spring, 2008
Description: Specimen Aluminum Aluminum Brass Brass Aluminum Aluminum Aluminum Notch type V U V U V V V Temperature (degrees celsius) 25 25 25 25 100 200 300 Width (cm) 0.5 0.49 0.5 0.49 0.5 0.5 0.5 Depth (cm) 0.49 0.41 0.49 0.41 0.49 0.49 0.49 Net Impact Wo...
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Path: American University of Sharjah >> MECHANICAL >> 223,224,22 Spring, 2008
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Path: American University of Sharjah >> MECHANICAL >> 223,224,22 Spring, 2008
Description: MCE 230 L Materials Science Hardness Test Gagan Gururaj ID: 8526 Group 2 Date of Experiment: 26/10/03 2 Table of Contents 1) Abstract.3 2) Introduction..3 3) Theory.3 4) Experimental procedure.3 5) Data..4 6) Calculations.4 7) Discussion.5 8) Refe...
Statics HW _12, Spring 2008
Path: American University of Sharjah >> MCE >> 240 Spring, 2008
Description: American University of Sharjah College of Engineering Mechanical Engineering Department Spring 2008 Due Date: Sunday, April 13th, 2008. Statics MCE 220 Assignment # 12 Solve the following problems from the textbook (Engineering Mechanics: Statics ...
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Path: American University of Sharjah >> MECHANICAL >> 223,224,22 Spring, 2008
Description: MCE 230 Materials Science Gagan Gururaj ID: 8526 Email: b00008526@aus.ac.ae Instructor: Dr. Hany El-Kadi Date due: 14/12/03 Problems: Ch.4 4.4 4.11 4.18 4.23 4.34 Ch.5 5.3 5.6 5.11 5.25 ...
MCE 230 - Fatigue Test
Path: American University of Sharjah >> MECHANICAL >> 223,224,22 Spring, 2008
Description: Abstract: Three samples of unpolished aluminum and three samples of unpolished copper were used in the fatigue test. Under an applied load of 80N, the first sample of aluminum fractured after 13892 load cycles. Similarly, the second sample of aluminu...
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Path: American University of Sharjah >> MECHANICAL >> 223,224,22 Spring, 2008
Description: Stress (Pa) Primary parallel Secondary parallel Perpendicular Strain Stress Strain stress Strain Stress 0 6.05E+01 0 492.917 0 5803.364 0.000209 8.94E+04 0.000413 91217.01 6.26E-05 95780.96 0.000417 1.78E+05 0.000832 223763 0.000108 196940.9 0.00062...
NaḳÄ'id EI [1]
Path: American University of Sharjah >> ARA >> 101,102 Spring, 2008
Description: Na i Meaning \"contradicting poems, flytings\", pl. of na a (from the verb na a a \"to destroy, undo, rebut, oppose\"), synonymous with mun a t (from the verbal form III n a a): a form of poetic duelling in which tribal or personal insults are exchange...
Jahiliyya EI [1]
Path: American University of Sharjah >> ARA >> 101,102 Spring, 2008
Description: hilliya A term used, in almost all its occurrences, as the opposite of the word islm , and which refers to the state of affairs in Arabia before the mission of the Prophet, to paganism (sometimes even that of non-Arab lands), the pre-Islamic perio...
ARA 101 Essay Questions [1]
Path: American University of Sharjah >> ARA >> 101,102 Spring, 2008
Description: AMERICAN UNIVESITY OF SHARJAH COLLEGE OF ARTS AND SCIENCES Department of Arabic Studies ARA 101 Readings in Arabic Heritage Essay Questions for Fall 2007 To be submitted by 16.00 on the 5th of December 2007. The essays should be submitted in soft co...
Introduction ARA 101E (1)
Path: American University of Sharjah >> ARA >> 101,102 Spring, 2008
Description: ARA 101 E Readings in Arabic Heritage (English Sections) Dr. Gavin Picken Office: NAB 222 Office Tel: ext. 2873 Office Hours: Sunday 11-12, Monday 11-12, Tuesday 3-4 and Wednesday 3-4. E-mail: gpicken@aus.edu B. Sc. Biological Sciences University ...
al-Akhtal EI [1]
Path: American University of Sharjah >> ARA >> 101,102 Spring, 2008
Description: - al b. al- alt, who died probably before 92/710. He belonged to the great tribe of the lib [q.v.] of northern Syria, which remained entirely Christian, of the Monophysite persuasion. By his mother Layla he was connected to another Christian tribe...
Presentation ARA 101 Umayyad Poetry [1]
Path: American University of Sharjah >> ARA >> 101,102 Spring, 2008
Description: Poetry in the Umayyad Period: Al-Farazdaq, Jarir and al-Akhtal Poetry in the Umayyad Period Tammm b. Ghalib (Ab Firs) al- Farazdaq \"the lump of dough\", famous Arab satirist and panegyrist, died at Basra about 110/728 or 112/730. Born in Yamma on a ...
al-Farazdaq EI [1]
Path: American University of Sharjah >> ARA >> 101,102 Spring, 2008
Description: al- Farazda \"the lump of dough\", properly Tammm b. lib (Ab Firs), famous Arab satirist and panegyrist, died at Ba ra about 110/728 or 112/730. Born in Yamma (Eastern Arabia) on a date which is uncertain (probably after 20/640), this poet i, of the Dr...
ḤassÄn b. Thabit EI [1]
Path: American University of Sharjah >> ARA >> 101,102 Spring, 2008
Description: bit - ir b. arm Of the tribe of rib (later Medna), traditionally known as the \"poet laureate\" of the Prophet, is more correctly the most prominent of several poets who were associated with the rise of Islam , and one who already had an establis...
Ḳaṣīda EI [1]
Path: American University of Sharjah >> ARA >> 101,102 Spring, 2008
Description: a da 1. In Arabic. a da collective a d is the name given in Arabic to some poems of a certain length. It is derived from the root a ada, \"to aim at\", for the primitive a da was intended to eulogize the tribe of the poet and denigrate the opposi...
Ḳabīla EI [1]
Path: American University of Sharjah >> ARA >> 101,102 Spring, 2008
Description: abla Denotes a large agnatic group, the members of which claim to be descended from one common ancestor; this word is generally understood in the sense of tribe. It derives from the Arabic root -b-l, of which the form bala signifies to meet, to be...
Jarir EI [1]
Path: American University of Sharjah >> ARA >> 101,102 Spring, 2008
Description: arr b. A iyya b. al- a ayfa) b. Badr Was among the most important -writers of the Umayyad period (the other two were his rivals al and al-Farazda [qq.v.], and may be considered one of the greatest Islamic-Arabic poets of all time. He belonged...
Hasan%20b.%20Thabit%20EAL%20%5b1%5d
Path: American University of Sharjah >> ARA >> 101,102 Spring, 2008
Description: ...
al-Farazdaq [1]
Path: American University of Sharjah >> ARA >> 101,102 Spring, 2008
Description: From the wafayat al-a`yan of Ibn Khallikan Abu-l ,Abbas Ahmad b. Khallikan (1211-1282 CE) was born at Arbela, Iraq. By his talents and his writings he received the title of the most learned man and the ablest historian of that city. He studied jurisp...
Statics HW _6 Spring 2008
Path: American University of Sharjah >> MCE >> 240 Spring, 2008
Description: American University of Sharjah College of Engineering Mechanical Engineering Department Spring 2008 Due Date: Sunday, February 24th, 2008. Statics MCE 220 Assignment # 6 Solve the following problems from the textbook (Engineering Mechanics: Static...
Statics HW _5 Spring 2008
Path: American University of Sharjah >> MCE >> 240 Spring, 2008
Description: American University of Sharjah College of Engineering Mechanical Engineering Department Spring 2008 Due Date: Tuesday, February 19th, 2008. Statics MCE 220 Assignment # 5 Solve the following problems from the textbook (Engineering Mechanics: Stati...
Statics HW _3 Springr 2008
Path: American University of Sharjah >> MCE >> 240 Spring, 2008
Description: American University of Sharjah College of Engineering Mechanical Engineering Department Spring 2008 Due Date: Tuesday, February 12th, 2008. Statics MCE 220 Assignment # 3 Solve the following problems from the textbook (Engineering Mechanics: Stati...
Statics HW _1 Spring 2008
Path: American University of Sharjah >> MCE >> 240 Spring, 2008
Description: American University of Sharjah College of Engineering Mechanical Engineering Department Spring 2008 Due Date: Sunday, February 3rd, 2008. Solve the following problems 1. Round off the following numbers to three significant figures: (a) 4.65735 m, (b...
Statics HW _2 Spring 2008
Path: American University of Sharjah >> MCE >> 240 Spring, 2008
Description: American University of Sharjah College of Engineering Mechanical Engineering Department Spring 2008 Due Date: Sunday, February 10, 2008. Statics MCE 220 Assignment # 2 Solve the following problems from the textbook (Engineering Mechanics: Statics ...
Statics HW _7, Spring 2008
Path: American University of Sharjah >> MCE >> 240 Spring, 2008
Description: American University of Sharjah College of Engineering Mechanical Engineering Department Spring 2008 Due Date: Sunday, March 2nd, 2008. Statics MCE 220 Assignment # 7 Solve the following problems from the textbook (Engineering Mechanics: Statics by...
Tensile Test - Al 2
Path: American University of Sharjah >> MECHANICAL >> 223,224,22 Spring, 2008
Description: Test Type Name: Company: Lab name: Test date: Geometry: Specimen Specimen name: Length: Diameter: Tensile Test for Metallic Materials With Extensometer Group 2 AUS Material Sc. Lab 9/28/2003 Circular 1 aluminum 95 6.2 Extension mm Load N Strain Stre...
Tensile Test - steel
Path: American University of Sharjah >> MECHANICAL >> 223,224,22 Spring, 2008
Description: Test Type Name: Company: Lab name: Test date: Geometry: Specimen Specimen name: Length: Diameter: Tensile Test Group 2 AUS Material Sc. Lab 9/28/2003 Circular 1 Steel 95 mm 5.9 mm Extension mm 0 0.01147958 0.02062737 0.0307318 0.0409558 0.05207665 0...
Tensile Test Exp.
Path: American University of Sharjah >> MECHANICAL >> 223,224,22 Spring, 2008
Description: MCE 230 L Materials Science Tensile Test Gagan Gururaj ID: 8526 Group 2 Date of Experiment: 28/9/03 Abstract: Two samples of aluminum and a sample of steel were used in the Tensile Test Experiment. The mechanical properties of these three materials...
Chapter 01
Path: American University of Sharjah >> MECHANICAL >> 223,224,22 Spring, 2008
Description: CHAPTER 1 KEY EQUATIONS Equation Number Key Equation dq (t ) 1.1 i (t ) = 1.2 1.6 1.7 q (t ) = i (t )dt + q (t 0 ) p (t ) = v (t )i (t ) t0 t dt = t2 t1 p (t )dt 1 v = iR v ab = iab R 1.8 G = 1.9 1.10 1.12 1.13 R i = Gv L R= A p = Ri 2 v...
