Course: PHYS 5426 — Quantum Statistical Physics Assignment #1 Instructor: Gennady Y. Chitov Date Assigned: January 15, 2014 Due Date: January 29, 2014 Problem 1. Prove [a; f(a†)] = @f(a†) @a† (1) [a†; f(a)] = −@f(a) @a (2) for arbitrary function f of operator which admits a series expansion. The Bose creation/ annihilation operators satisfy the standard commutation relations [a; a†] ≡ aa† − a†a = 1 (3) Hint: From Eqs.(1,2) one can figure out the corresponding commutation relations for the powers of creation/annihilation operators and then prove them by the method of mathematical induction. Note that for an arbitrary operator Aˆ: @A^n @A^ = nAˆn−1. Problem 2. In the presence of a constant external force acting on a one-dimensional oscillating particle its Hamiltonian becomes that of the so-called displaced oscillator, and the Schr¨odinger equation ˆH (q) = E (q) of the problem (cf. lecture notes) can be written in terms of dimensionless variables as ( − 1 2 d2 d2 + 1 2 2 − √ 2  ) () = ” () ; (4) where q = √ ~ m! and E = ~!”. a). Write the Schr¨odinger equation (4) in terms of the creation/annihilation operators of the harmonic oscillator ( = 0)  = √1 2 (a + a†) (5) d d = √1 2 (a − a†) (6) 1 Via a linear transformation to the new creation/annihilation operators ˜a†; ˜a preserving the bosonic commutation relations for ˜a†; ˜a map the problem (4) of the displaced oscillator onto that of a simple harmonic oscillator with new operators (˜a†; ˜a). b). Find the spectrum (eigenvalues) ” (E) of the displaced oscillator. c). Write the normalized eigenstates |n⟩ of the displaced Hamiltonian (4) via a† and the vacuum state |Θ◦⟩ of the new operators, i.e. ˜a|Θ◦⟩ = 0 (7) d). As follows from the completeness of the oscillator’s eigenstates, the vacuum state of the displaced oscillator |Θ◦⟩ can be related to the simple oscillator’s vacuum |0⟩ (i.e., a|0⟩ = 0) as |Θ◦⟩ = Ω(a†)|0⟩ (8) Find (up to a normalization factor) the operator function Ω(a†) relating two vacua. Hint: in working out Eqs.(7,8), employ Eqs.(1,2). Problem 3. Prove from the standard commutation relations ([ai; a † j ]∓ = ij , etc) that ⟨0|aiaja † ka † l |0⟩ = jkil ± ikjl (9) the sign depending on the statistics. Also calculate the vacuum expectation value ⟨0|ahaiaja † ka † l a† m |0⟩. Problem 4. In the formalism of second quantization the two-particle interaction term of the Hamiltonian for spinless fermions is given by ˆ V = 1 2 ∫ ∫ dxdy ˆ †(x) ˆ †(y)V(x; y) ˆ (y) ˆ (x) (10) For the short-ranged interaction V(x; y) = V(|x−y|) ≡ V(r) = e2 exp(−r)=r find ˆ V in the momentum representation. The field operators and the creation/annihilation operators in the momentum representation are related in the usual way, i.e., ˆ †(x) = ∫ dp (2)3 a†(p)e−ipx (11) Note that the limit  → 0 recovers the Coulomb (long-ranged) interaction V(r) = e2=r. What is the Fourier transform V(q) of the Coulomb interaction? 2 Problem 5. The matrix elements of a two-particle interaction from the previous problem can be written as ⟨k3k4|V|k1k2⟩ = (2)3(k1 + k2 − k3 − k4)V(q) (12) where q ≡ k3−k1 is the momentum transfer. Show that the diagonal part of the interaction operator ˆ V found on the previous problem in the k-representation, arises from momentum transfers q = 0 and q = k2−k1. Write down the two interaction terms and identify them as direct (q = 0) and exchange (q = k2 − k1) interactions. Draw the corresponding Feynman diagrams. Problem 6. Find the first correction to the temperature dependence of the chemical potential  of the degenerate ideal electron gas, assuming constant particle concentration ⟨N⟩=V . Express the result in terms of T and the zero-temperature chemical potential ◦. For the calculations the following formula (we set kB = 1) can be used: I ≡ ∫ ∞ 0 f(“)d” e(“−)=T + 1 = ∫  0 f(“)d” + 2 6 T2f′() + O(T4) (13) 3

Course: PHYS 5426 — Quantum Statistical Physics Assignment #1 Instructor: Gennady Y. Chitov Date Assigned: January 15, 2014 Due Date: January 29, 2014 Problem 1. Prove [a; f(a†)] = @f(a†) @a† (1) [a†; f(a)] = −@f(a) @a (2) for arbitrary function f of operator which admits a series expansion. The Bose creation/ annihilation operators satisfy the standard commutation relations [a; a†] ≡ aa† − a†a = 1 (3) Hint: From Eqs.(1,2) one can figure out the corresponding commutation relations for the powers of creation/annihilation operators and then prove them by the method of mathematical induction. Note that for an arbitrary operator Aˆ: @A^n @A^ = nAˆn−1. Problem 2. In the presence of a constant external force acting on a one-dimensional oscillating particle its Hamiltonian becomes that of the so-called displaced oscillator, and the Schr¨odinger equation ˆH (q) = E (q) of the problem (cf. lecture notes) can be written in terms of dimensionless variables as ( − 1 2 d2 d2 + 1 2 2 − √ 2  ) () = ” () ; (4) where q = √ ~ m! and E = ~!”. a). Write the Schr¨odinger equation (4) in terms of the creation/annihilation operators of the harmonic oscillator ( = 0)  = √1 2 (a + a†) (5) d d = √1 2 (a − a†) (6) 1 Via a linear transformation to the new creation/annihilation operators ˜a†; ˜a preserving the bosonic commutation relations for ˜a†; ˜a map the problem (4) of the displaced oscillator onto that of a simple harmonic oscillator with new operators (˜a†; ˜a). b). Find the spectrum (eigenvalues) ” (E) of the displaced oscillator. c). Write the normalized eigenstates |n⟩ of the displaced Hamiltonian (4) via a† and the vacuum state |Θ◦⟩ of the new operators, i.e. ˜a|Θ◦⟩ = 0 (7) d). As follows from the completeness of the oscillator’s eigenstates, the vacuum state of the displaced oscillator |Θ◦⟩ can be related to the simple oscillator’s vacuum |0⟩ (i.e., a|0⟩ = 0) as |Θ◦⟩ = Ω(a†)|0⟩ (8) Find (up to a normalization factor) the operator function Ω(a†) relating two vacua. Hint: in working out Eqs.(7,8), employ Eqs.(1,2). Problem 3. Prove from the standard commutation relations ([ai; a † j ]∓ = ij , etc) that ⟨0|aiaja † ka † l |0⟩ = jkil ± ikjl (9) the sign depending on the statistics. Also calculate the vacuum expectation value ⟨0|ahaiaja † ka † l a† m |0⟩. Problem 4. In the formalism of second quantization the two-particle interaction term of the Hamiltonian for spinless fermions is given by ˆ V = 1 2 ∫ ∫ dxdy ˆ †(x) ˆ †(y)V(x; y) ˆ (y) ˆ (x) (10) For the short-ranged interaction V(x; y) = V(|x−y|) ≡ V(r) = e2 exp(−r)=r find ˆ V in the momentum representation. The field operators and the creation/annihilation operators in the momentum representation are related in the usual way, i.e., ˆ †(x) = ∫ dp (2)3 a†(p)e−ipx (11) Note that the limit  → 0 recovers the Coulomb (long-ranged) interaction V(r) = e2=r. What is the Fourier transform V(q) of the Coulomb interaction? 2 Problem 5. The matrix elements of a two-particle interaction from the previous problem can be written as ⟨k3k4|V|k1k2⟩ = (2)3(k1 + k2 − k3 − k4)V(q) (12) where q ≡ k3−k1 is the momentum transfer. Show that the diagonal part of the interaction operator ˆ V found on the previous problem in the k-representation, arises from momentum transfers q = 0 and q = k2−k1. Write down the two interaction terms and identify them as direct (q = 0) and exchange (q = k2 − k1) interactions. Draw the corresponding Feynman diagrams. Problem 6. Find the first correction to the temperature dependence of the chemical potential  of the degenerate ideal electron gas, assuming constant particle concentration ⟨N⟩=V . Express the result in terms of T and the zero-temperature chemical potential ◦. For the calculations the following formula (we set kB = 1) can be used: I ≡ ∫ ∞ 0 f(“)d” e(“−)=T + 1 = ∫  0 f(“)d” + 2 6 T2f′() + O(T4) (13) 3

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Assignment 1: Coulomb’s Law Due: 8:00am on Wednesday, January 11, 2012 Note: To understand how points are awarded, read your instructor’s Grading Policy. [Switch to Standard Assignment View] Coulomb’s Law Tutorial Learning Goal: To understand how to calculate forces between charged particles, particularly the dependence on the sign of the charges and the distance between them. Coulomb’s law describes the force that two charged particles exert on each other (by Newton’s third law, those two forces must be equal and opposite). The force exerted by particle 2 (with charge ) on particle 1 (with charge ) is proportional to the charge of each particle and inversely proportional to the square of the distance between them: , where and is the unit vector pointing from particle 2 to particle 1. The force vector will be parallel or antiparallel to the direction of , parallel if the product and antiparallel if ; the force is attractive if the charges are of opposite sign and repulsive if the charges are of the same sign. Part A Consider two positively charged particles, one of charge (particle 0) fixed at the origin, and another of charge (particle 1) fixed on the y-axis at . What is the net force on particle 0 due to particle 1? Express your answer (a vector) using any or all of , , , , , , and . ANSWER: = Correct Part B Now add a third, negatively charged, particle, whose charge is (particle 2). Particle 2 fixed on the y-axis at position . What is the new net force on particle 0, from particle 1 and particle 2? Express your answer (a vector) using any or all of , , , , , , , , and . ANSWER: = Correct Part C Particle 0 experiences a repulsion from particle 1 and an attraction toward particle 2. For certain values of and , the repulsion and attraction should balance each other, resulting in no net force. For what ratio is there no net force on particle 0? Express your answer in terms of any or all of the following variables: , , , . ANSWER: = Correct Part D Now add a fourth charged particle, particle 3, with positive charge , fixed in the yz-plane at . What is the net force on particle 0 due solely to this charge? Hint D.1 Find the magnitude of force from particle 3 Hint not displayed Hint D.2 Vector components Hint not displayed Express your answer (a vector) using , , , , , , and . Include only the force caused by particle 3. ANSWER: = Correct Exercise 21.4 You have a pure (24-karat) gold ring with mass . Gold has an atomic mass of and an atomic number of . Part A How many protons are in the ring? ANSWER: = 4.27×1024 Correct Part B What is their total positive charge? ANSWER: = 6.83×105 Correct Part C If the ring carries no net charge, how many electrons are in it? ANSWER: = 4.27×1024 Correct Exercise 21.22 Two point charges are placed on the x-axis as follows: charge = 4.05 is located at 0.197 , and charge = 5.00 is at -0.296 . Part A What is the magnitude of the total force exerted by these two charges on a negative point charge = -6.00 that is placed at the origin? ANSWER: = 2.55×10−6 Correct Part B What is the direction of the total force exerted by these two charges on a negative point charge = -6.00 that is placed at the origin? ANSWER: to the + direction to the – direction perpendicular to the -axis the force is zero Correct Problem 21.66 A charge 4.97 is placed at the origin of an xy-coordinate system, and a charge -1.99 is placed on the positive x-axis at = 3.98 . A third particle, of charge 6.05 is now placed at the point = 3.98 , = 3.01 . Part A Find the x-component of the total force exerted on the third charge by the other two. ANSWER: = 8.66×10−5 Correct Part B Find the y-component of the total force exerted on the third charge by the other two. ANSWER: = −5.40×10−5 Correct Part C Find the magnitude of the total force acting on the third charge. ANSWER: = 1.02×10−4 Correct Part D Find the direction of the total force acting on the third charge. ANSWER: = -0.557 Correct between and +x-axis Problem 21.68 Two identical spheres with mass are hung from silk threads of length , as shown in the figure . Each sphere has the same charge, so . The radius of each sphere is very small compared to the distance between the spheres, so they may be treated as point charges. Part A Suppose that the angle is small, and find the equilibrium separation between the spheres (Hint: If is small, then .) Express your answer in terms of the variables , , and appropriate constants. ANSWER: = Correct

Assignment 1: Coulomb’s Law Due: 8:00am on Wednesday, January 11, 2012 Note: To understand how points are awarded, read your instructor’s Grading Policy. [Switch to Standard Assignment View] Coulomb’s Law Tutorial Learning Goal: To understand how to calculate forces between charged particles, particularly the dependence on the sign of the charges and the distance between them. Coulomb’s law describes the force that two charged particles exert on each other (by Newton’s third law, those two forces must be equal and opposite). The force exerted by particle 2 (with charge ) on particle 1 (with charge ) is proportional to the charge of each particle and inversely proportional to the square of the distance between them: , where and is the unit vector pointing from particle 2 to particle 1. The force vector will be parallel or antiparallel to the direction of , parallel if the product and antiparallel if ; the force is attractive if the charges are of opposite sign and repulsive if the charges are of the same sign. Part A Consider two positively charged particles, one of charge (particle 0) fixed at the origin, and another of charge (particle 1) fixed on the y-axis at . What is the net force on particle 0 due to particle 1? Express your answer (a vector) using any or all of , , , , , , and . ANSWER: = Correct Part B Now add a third, negatively charged, particle, whose charge is (particle 2). Particle 2 fixed on the y-axis at position . What is the new net force on particle 0, from particle 1 and particle 2? Express your answer (a vector) using any or all of , , , , , , , , and . ANSWER: = Correct Part C Particle 0 experiences a repulsion from particle 1 and an attraction toward particle 2. For certain values of and , the repulsion and attraction should balance each other, resulting in no net force. For what ratio is there no net force on particle 0? Express your answer in terms of any or all of the following variables: , , , . ANSWER: = Correct Part D Now add a fourth charged particle, particle 3, with positive charge , fixed in the yz-plane at . What is the net force on particle 0 due solely to this charge? Hint D.1 Find the magnitude of force from particle 3 Hint not displayed Hint D.2 Vector components Hint not displayed Express your answer (a vector) using , , , , , , and . Include only the force caused by particle 3. ANSWER: = Correct Exercise 21.4 You have a pure (24-karat) gold ring with mass . Gold has an atomic mass of and an atomic number of . Part A How many protons are in the ring? ANSWER: = 4.27×1024 Correct Part B What is their total positive charge? ANSWER: = 6.83×105 Correct Part C If the ring carries no net charge, how many electrons are in it? ANSWER: = 4.27×1024 Correct Exercise 21.22 Two point charges are placed on the x-axis as follows: charge = 4.05 is located at 0.197 , and charge = 5.00 is at -0.296 . Part A What is the magnitude of the total force exerted by these two charges on a negative point charge = -6.00 that is placed at the origin? ANSWER: = 2.55×10−6 Correct Part B What is the direction of the total force exerted by these two charges on a negative point charge = -6.00 that is placed at the origin? ANSWER: to the + direction to the – direction perpendicular to the -axis the force is zero Correct Problem 21.66 A charge 4.97 is placed at the origin of an xy-coordinate system, and a charge -1.99 is placed on the positive x-axis at = 3.98 . A third particle, of charge 6.05 is now placed at the point = 3.98 , = 3.01 . Part A Find the x-component of the total force exerted on the third charge by the other two. ANSWER: = 8.66×10−5 Correct Part B Find the y-component of the total force exerted on the third charge by the other two. ANSWER: = −5.40×10−5 Correct Part C Find the magnitude of the total force acting on the third charge. ANSWER: = 1.02×10−4 Correct Part D Find the direction of the total force acting on the third charge. ANSWER: = -0.557 Correct between and +x-axis Problem 21.68 Two identical spheres with mass are hung from silk threads of length , as shown in the figure . Each sphere has the same charge, so . The radius of each sphere is very small compared to the distance between the spheres, so they may be treated as point charges. Part A Suppose that the angle is small, and find the equilibrium separation between the spheres (Hint: If is small, then .) Express your answer in terms of the variables , , and appropriate constants. ANSWER: = Correct

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HIST 303 Rebels and Renegades Comparative Paper – Conroy & Drakulic In a well-written analysis of about 3 pages, compare and contrast Conroy’s Belfast Diary or Drakulic’s How We Survived Communism and Even Laughed in response to the following question: It can be argued that in the midst of deprivation and hardship, people still exercise considerable agency—or the power to act within one’s particular socio-political context. In fact, living the ordinary can be considered an act of rebellion against an imposing power. That is, people use and experience their lives as resistance to oppression or war. This is sometimes referred to as the “politics of everyday life”. How does this concept of agency play out in these works? In your response, do not simply list examples, but analyze the examples by the authors in relation to the larger themes of the course. A successful assignment will (this is a checklist, so heed it well!!!): * have a solid introduction with an arguable thesis; * be well organized with coherent paragraphs relevant to the thesis; * have a concluding paragraph that concisely and accurately summarizes the paper; * adequately analyze the histories and their connections to each other; * use relevant evidence to substantiate claims; * be analytic, not descriptive; * properly cite and punctuate quotations and evidence; * be paginated; * have an interesting title relevant to the argument (e.g. “Comparative Paper” is unacceptable); * be well written, well edited and well documented. Author Specific Points that discuss everyday activities as resistance Relate to your other Reading (Williams, Hall, Hebdige, etc.) Conroy Drakulic Working Thesis: _____________________________________________________________________ ____________________________________________________________________________________ ****FORMATTING DIRECTIONS: This paper should be 3 – 4 pages (no more), typed, doublespaced, with one-inch margins and 12-point font. This assignment is worth 25% of your grade in this course. You must head your paper with your name and date and include your name and pages (x of x) in a header or footer of each page. At the end of your paper, you must skip four lines then sign with the following: “I attest that the work contained in this document is entirely my own and it numbers x pages.” *****

HIST 303 Rebels and Renegades Comparative Paper – Conroy & Drakulic In a well-written analysis of about 3 pages, compare and contrast Conroy’s Belfast Diary or Drakulic’s How We Survived Communism and Even Laughed in response to the following question: It can be argued that in the midst of deprivation and hardship, people still exercise considerable agency—or the power to act within one’s particular socio-political context. In fact, living the ordinary can be considered an act of rebellion against an imposing power. That is, people use and experience their lives as resistance to oppression or war. This is sometimes referred to as the “politics of everyday life”. How does this concept of agency play out in these works? In your response, do not simply list examples, but analyze the examples by the authors in relation to the larger themes of the course. A successful assignment will (this is a checklist, so heed it well!!!): * have a solid introduction with an arguable thesis; * be well organized with coherent paragraphs relevant to the thesis; * have a concluding paragraph that concisely and accurately summarizes the paper; * adequately analyze the histories and their connections to each other; * use relevant evidence to substantiate claims; * be analytic, not descriptive; * properly cite and punctuate quotations and evidence; * be paginated; * have an interesting title relevant to the argument (e.g. “Comparative Paper” is unacceptable); * be well written, well edited and well documented. Author Specific Points that discuss everyday activities as resistance Relate to your other Reading (Williams, Hall, Hebdige, etc.) Conroy Drakulic Working Thesis: _____________________________________________________________________ ____________________________________________________________________________________ ****FORMATTING DIRECTIONS: This paper should be 3 – 4 pages (no more), typed, doublespaced, with one-inch margins and 12-point font. This assignment is worth 25% of your grade in this course. You must head your paper with your name and date and include your name and pages (x of x) in a header or footer of each page. At the end of your paper, you must skip four lines then sign with the following: “I attest that the work contained in this document is entirely my own and it numbers x pages.” *****

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CHM114: Exam #1 CHM 114, S2015 Exam #1, Version B Instructor: O. Graudejus Points: 100 Print Name Sign Name Student I.D. # 1. You are responsible for the information on this page. Please read it carefully. 2. If you enter your ASU ID incorrectly on the scantron, a 3 point penalty will be assessed. 3. Code your name and 10 digit affiliate identification number on the separate scantron answer sheet. Use only a #2 pencil 4. Do all calculations on the exam pages. Do not make any unnecessary marks on the answer sheet. 5. This exam consists of 25 multiple choice questions worth 4 points each and a periodic table. Make sure you have them all. 6. Choose the best answer to each of the questions and answer it on the computer-graded answer sheet. Read all responses before making a selection. 7. Read the directions carefully for each problem. 8. Avoid even casual glances at other students’ exams. 9. Stop writing and hand in your scantron answer sheet and your test promptly when instructed. LATE EXAMS MAY HAVE POINTS DEDUCTED. 10. You will have 50 minutes to complete the exam. 11. If you leave early, please do so quietly. 12. Work the easiest problems first. 13. A periodic table is attached as the last page to this exam. 14. Answers will be posted online this afternoon. Potentially useful information: K = ºC + 273.15 Avogadro’s Number = 6.022 × 1023 particles/mole 1amu = 1.66·10-24 g 1 cal=4.184 J \ -2- CHM 114: Exam #1 1) What volume (mL) of a concentrated solution of sodium hydroxide (6.00 M) must be diluted to 200.0 mL to make a 0.880 M solution of sodium hydroxide? A) 2.64 B) 176 C) 29.3 D) 26.4 E) 50.0 2) Sulfur and fluorine react in a combination reaction to produce sulfur hexafluoride: S (s) + 3 F2 (g)  SF6 (g) The maximum amount of SF6 that can be produced from the reaction of 3.5 g of sulfur with 4.5 g of fluorine is __________ g. A) 5.8 B) 3.2 C) 12 D) 16 E) 8.0 3) Of the reactions below, only __________ is not spontaneous. A) 2 2 Mg (s) 2HCl + (aq)®MgCl (aq) + H (g) B) 2 4 2 4 2 2Ni (s) + H SO (aq) ®Ni SO (aq) + H (g) C) 3 2 2Al (s) + 6HBr (aq)®2AlBr (aq) + 3H (g) D) 3 3 2 2Ag (s) + 2HNO (aq) ®2AgNO (aq) + H (g) E) 2 2 Zn (s) + 2HI (aq) ®ZnI (aq) + H (g) 4) Which solution has the same number of moles of NaOH as 40.00 mL of 0.100M solution of NaOH? A) 20.00 mL of 0.200M solution of NaOH B) 25.00 mL of 0.175M solution of NaOH C) 30.00 mL of 0.145M solution of NaOH D) 50.00 mL of 0.125M solution of NaOH E) 100.00 mL of 0.0500M solution of NaOH 5) What is the concentration (M) of a NaCl solution prepared by dissolving 9.3 g of NaCl in sufficient water to give 450 mL of solution? A) 0.35 B) 0.16 C) 0.45 D) 27 E) -2 2.7×10 -3- CHM 114: Exam #1 6) In which reaction does the oxidation number of hydrogen change? A) 2 HCl (aq) NaOH (+ aq)® NaCl (aq) + H O (l) B) 2 2 CaO (s) + H O (l) ®Ca(OH) (s) C) 4 3 4 2 2 2 2 HClO (aq) + CaCO (s) ® Ca(ClO ) (aq) + H O (l) +CO (g) D) 2 2 2 3 SO (g) + H O (l)®H SO (aq) E) 2 2 2 Na (s) + 2H O (l) ® 2 NaOH (aq) + H (g) 7) Which atom has the smallest number of neutrons? A) phosphorus-30 B) chlorine-37 C) potassium-39 D) argon-40 E) calcium-40 8) The change in the internal energy of a system that absorbs 2,500 J of heat and that has received 7,655 J of work by the surroundings is __________ J. A) -10,155 B) -5,155 C) 7 −1.91×10 D) 10,155 E) 5,155 9) When a metal and a nonmetal react, the __________ tends to lose electrons and the __________ tends to gain electrons. A) metal, metal B) nonmetal, nonmetal C) metal, nonmetal D) nonmetal, metal E) None of the above, these elements share electrons. 10) What is the oxidation number of nitrogen in HNO2? A) -5 B) -3 C) 0 D) +3 E) +5 -4- CHM 114: Exam #1 11) Elements in Group 7A are known as the __________. A) chalcogens B) alkaline earth metals C) alkali metals D) halogens E) noble gases 12) The concentration of iodide ions in a 0.193 M solution of sodium iodide is __________. A) 0.193 M B) 0.386 M C) 0.0965 M D) 0.579 M E) 0.0643 M 13) Lithium and nitrogen react to produce lithium nitride: 6Li (s) + N2 (g)  2Li3N (s) How many moles of N2 are needed to react with 1.422 mol of lithium? A) 4.26 B) 0.710 C) 0.237 D) 2.13 E) 0.118 14) The balanced equation for the decomposition of sodium azide is __________. A) 2NaN3 (s)  Na2 (s) + 3 N2 (g) B) NaN3 (s)  Na (s) + N2 (g) C) 2NaN3 (s)  2Na (s) + 3 N2 (g) D) NaN3 (s)  Na (s) + N2 (g) + N (g) E) 2NaN3 (s)  2Na (s) + 2 N2 (g) 15) A sample of CH2F2 with a mass of 9.5 g contains __________ atoms of F. A) 2.2 × 1023 B) 38 C) 3.3 × 1024 D) 4.4 × 1023 E) 9.5 -5- CHM 114: Exam #1 16) An unknown element is found to have three naturally occurring isotopes with atomic masses of 35.9675 (0.337%), 37.9627 (0.063%), and 39.9624 (99.600%). Which of the following is the unknown element? A) Ar B) K C) Cl D) Ca E) None of the above could be the unknown element. 17) The value of DH° for the reaction below is -482 kJ. Calculate the heat (kJ) released to the surroundings when 24.0 g of CO (g) reacts completely. 2 2 2CO(g) +O (g)®2CO (g) A) 3 2.89×10 B) 207 C) 103 D) 65.7 E) -482 18) Lead (II) carbonate decomposes to give lead (II) oxide and carbon dioxide: PbCO3 (s)  PbO (s) + CO2 (g) __________ grams of carbondioxide will be produced by the decomposition of 7.50 g of lead (II) carbonate? A) 1.23 B) 2.50 C) 0.00936 D) 6.26 E) 7.83 19) Combining aqueous solutions of BaCl2 and K2SO4 affords a precipitate of 4 BaSO . Which ion(s) is/are spectator ions in the reaction? A) 2 Ba only + B) K+ only C) 2 2 Ba and SO4 + − D) SO4 2- and Cl- E) K+ and Cl- 20) Which combination will produce a precipitate? A) Pb(NO3)2 (aq) and HCl (aq) B) Cu(NO3)2 (aq) and KCl (aq) C) KOH (aq) and HNO3 (aq) D) AgNO3 (aq) and HNO3 (aq) E) NaOH (aq) and Sr(NO3)2 (aq) -6- CHM 114: Exam #1 21) There are __________ sulfur atoms in 50 molecules of C4H4S2. A) 1.5 × 1025 B) 100 C) 3.0 × 1025 D) 50 E) 6.02 × 1023 22) A compound contains 38.7% K, 13.9% N, and 47.4% O by mass. What is the empirical formula of the compound? A) K2N2O3 B) KNO2 C) KNO3 D) K2NO3 E) K4NO5 23) Predict the empirical formula of the ionic compound that forms from sodium and fluorine. A) 2 Na F B) 2 NaF C) 2 3 Na F D) NaF E) 3 2 Na F 24) The mass % of Krypton in the binary compound KrF2 is __________. A) 18.48 B) 45.38 C) 68.80 D) 81.52 E) 31.20 25) The correct name for K2SO3 is __________. A) potassium sulfate B) potassium disulfide C) potassium sulfite D) potassium sulfide E) dipotassium sulfate -7- CHM 114: Exam #1

CHM114: Exam #1 CHM 114, S2015 Exam #1, Version B Instructor: O. Graudejus Points: 100 Print Name Sign Name Student I.D. # 1. You are responsible for the information on this page. Please read it carefully. 2. If you enter your ASU ID incorrectly on the scantron, a 3 point penalty will be assessed. 3. Code your name and 10 digit affiliate identification number on the separate scantron answer sheet. Use only a #2 pencil 4. Do all calculations on the exam pages. Do not make any unnecessary marks on the answer sheet. 5. This exam consists of 25 multiple choice questions worth 4 points each and a periodic table. Make sure you have them all. 6. Choose the best answer to each of the questions and answer it on the computer-graded answer sheet. Read all responses before making a selection. 7. Read the directions carefully for each problem. 8. Avoid even casual glances at other students’ exams. 9. Stop writing and hand in your scantron answer sheet and your test promptly when instructed. LATE EXAMS MAY HAVE POINTS DEDUCTED. 10. You will have 50 minutes to complete the exam. 11. If you leave early, please do so quietly. 12. Work the easiest problems first. 13. A periodic table is attached as the last page to this exam. 14. Answers will be posted online this afternoon. Potentially useful information: K = ºC + 273.15 Avogadro’s Number = 6.022 × 1023 particles/mole 1amu = 1.66·10-24 g 1 cal=4.184 J \ -2- CHM 114: Exam #1 1) What volume (mL) of a concentrated solution of sodium hydroxide (6.00 M) must be diluted to 200.0 mL to make a 0.880 M solution of sodium hydroxide? A) 2.64 B) 176 C) 29.3 D) 26.4 E) 50.0 2) Sulfur and fluorine react in a combination reaction to produce sulfur hexafluoride: S (s) + 3 F2 (g)  SF6 (g) The maximum amount of SF6 that can be produced from the reaction of 3.5 g of sulfur with 4.5 g of fluorine is __________ g. A) 5.8 B) 3.2 C) 12 D) 16 E) 8.0 3) Of the reactions below, only __________ is not spontaneous. A) 2 2 Mg (s) 2HCl + (aq)®MgCl (aq) + H (g) B) 2 4 2 4 2 2Ni (s) + H SO (aq) ®Ni SO (aq) + H (g) C) 3 2 2Al (s) + 6HBr (aq)®2AlBr (aq) + 3H (g) D) 3 3 2 2Ag (s) + 2HNO (aq) ®2AgNO (aq) + H (g) E) 2 2 Zn (s) + 2HI (aq) ®ZnI (aq) + H (g) 4) Which solution has the same number of moles of NaOH as 40.00 mL of 0.100M solution of NaOH? A) 20.00 mL of 0.200M solution of NaOH B) 25.00 mL of 0.175M solution of NaOH C) 30.00 mL of 0.145M solution of NaOH D) 50.00 mL of 0.125M solution of NaOH E) 100.00 mL of 0.0500M solution of NaOH 5) What is the concentration (M) of a NaCl solution prepared by dissolving 9.3 g of NaCl in sufficient water to give 450 mL of solution? A) 0.35 B) 0.16 C) 0.45 D) 27 E) -2 2.7×10 -3- CHM 114: Exam #1 6) In which reaction does the oxidation number of hydrogen change? A) 2 HCl (aq) NaOH (+ aq)® NaCl (aq) + H O (l) B) 2 2 CaO (s) + H O (l) ®Ca(OH) (s) C) 4 3 4 2 2 2 2 HClO (aq) + CaCO (s) ® Ca(ClO ) (aq) + H O (l) +CO (g) D) 2 2 2 3 SO (g) + H O (l)®H SO (aq) E) 2 2 2 Na (s) + 2H O (l) ® 2 NaOH (aq) + H (g) 7) Which atom has the smallest number of neutrons? A) phosphorus-30 B) chlorine-37 C) potassium-39 D) argon-40 E) calcium-40 8) The change in the internal energy of a system that absorbs 2,500 J of heat and that has received 7,655 J of work by the surroundings is __________ J. A) -10,155 B) -5,155 C) 7 −1.91×10 D) 10,155 E) 5,155 9) When a metal and a nonmetal react, the __________ tends to lose electrons and the __________ tends to gain electrons. A) metal, metal B) nonmetal, nonmetal C) metal, nonmetal D) nonmetal, metal E) None of the above, these elements share electrons. 10) What is the oxidation number of nitrogen in HNO2? A) -5 B) -3 C) 0 D) +3 E) +5 -4- CHM 114: Exam #1 11) Elements in Group 7A are known as the __________. A) chalcogens B) alkaline earth metals C) alkali metals D) halogens E) noble gases 12) The concentration of iodide ions in a 0.193 M solution of sodium iodide is __________. A) 0.193 M B) 0.386 M C) 0.0965 M D) 0.579 M E) 0.0643 M 13) Lithium and nitrogen react to produce lithium nitride: 6Li (s) + N2 (g)  2Li3N (s) How many moles of N2 are needed to react with 1.422 mol of lithium? A) 4.26 B) 0.710 C) 0.237 D) 2.13 E) 0.118 14) The balanced equation for the decomposition of sodium azide is __________. A) 2NaN3 (s)  Na2 (s) + 3 N2 (g) B) NaN3 (s)  Na (s) + N2 (g) C) 2NaN3 (s)  2Na (s) + 3 N2 (g) D) NaN3 (s)  Na (s) + N2 (g) + N (g) E) 2NaN3 (s)  2Na (s) + 2 N2 (g) 15) A sample of CH2F2 with a mass of 9.5 g contains __________ atoms of F. A) 2.2 × 1023 B) 38 C) 3.3 × 1024 D) 4.4 × 1023 E) 9.5 -5- CHM 114: Exam #1 16) An unknown element is found to have three naturally occurring isotopes with atomic masses of 35.9675 (0.337%), 37.9627 (0.063%), and 39.9624 (99.600%). Which of the following is the unknown element? A) Ar B) K C) Cl D) Ca E) None of the above could be the unknown element. 17) The value of DH° for the reaction below is -482 kJ. Calculate the heat (kJ) released to the surroundings when 24.0 g of CO (g) reacts completely. 2 2 2CO(g) +O (g)®2CO (g) A) 3 2.89×10 B) 207 C) 103 D) 65.7 E) -482 18) Lead (II) carbonate decomposes to give lead (II) oxide and carbon dioxide: PbCO3 (s)  PbO (s) + CO2 (g) __________ grams of carbondioxide will be produced by the decomposition of 7.50 g of lead (II) carbonate? A) 1.23 B) 2.50 C) 0.00936 D) 6.26 E) 7.83 19) Combining aqueous solutions of BaCl2 and K2SO4 affords a precipitate of 4 BaSO . Which ion(s) is/are spectator ions in the reaction? A) 2 Ba only + B) K+ only C) 2 2 Ba and SO4 + − D) SO4 2- and Cl- E) K+ and Cl- 20) Which combination will produce a precipitate? A) Pb(NO3)2 (aq) and HCl (aq) B) Cu(NO3)2 (aq) and KCl (aq) C) KOH (aq) and HNO3 (aq) D) AgNO3 (aq) and HNO3 (aq) E) NaOH (aq) and Sr(NO3)2 (aq) -6- CHM 114: Exam #1 21) There are __________ sulfur atoms in 50 molecules of C4H4S2. A) 1.5 × 1025 B) 100 C) 3.0 × 1025 D) 50 E) 6.02 × 1023 22) A compound contains 38.7% K, 13.9% N, and 47.4% O by mass. What is the empirical formula of the compound? A) K2N2O3 B) KNO2 C) KNO3 D) K2NO3 E) K4NO5 23) Predict the empirical formula of the ionic compound that forms from sodium and fluorine. A) 2 Na F B) 2 NaF C) 2 3 Na F D) NaF E) 3 2 Na F 24) The mass % of Krypton in the binary compound KrF2 is __________. A) 18.48 B) 45.38 C) 68.80 D) 81.52 E) 31.20 25) The correct name for K2SO3 is __________. A) potassium sulfate B) potassium disulfide C) potassium sulfite D) potassium sulfide E) dipotassium sulfate -7- CHM 114: Exam #1

Extra Credit Due: 11:59pm on Thursday, May 15, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy A Man Running to Catch a Bus A man is running at speed (much less than the speed of light) to catch a bus already at a stop. At , when he is a distance from the door to the bus, the bus starts moving with the positive acceleration . Use a coordinate system with at the door of the stopped bus. Part A What is , the position of the man as a function of time? Answer symbolically in terms of the variables , , and . Hint 1. Which equation should you use for the man’s speed? Because the man’s speed is constant, you may use . ANSWER: c t = 0 b a x = 0 xman(t) b c t x(t) = x(0) + vt xman(t) = −b + ct Correct Part B What is , the position of the bus as a function of time? Answer symbolically in terms of and . Hint 1. Which equation should you use for the bus’s acceleration? Because the bus has constant acceleration, you may use . Recall that . ANSWER: Correct Part C What condition is necessary for the man to catch the bus? Assume he catches it at time . Hint 1. How to approach this problem If the man is to catch the bus, then at some moment in time , the man must arrive at the position of the door of the bus. How would you express this condition mathematically? ANSWER: xbus(t) a t x(t) = x(0) + v(0)t + (1/2)at2 vbus(0) = 0 xbus = 1 a 2 t2 tcatch tcatch Typesetting math: 15% Correct Part D Inserting the formulas you found for and into the condition , you obtain the following: , or . Intuitively, the man will not catch the bus unless he is running fast enough. In mathematical terms, there is a constraint on the man’s speed so that the equation above gives a solution for that is a real positive number. Find , the minimum value of for which the man will catch the bus. Express the minimum value for the man’s speed in terms of and . Hint 1. Consider the discriminant Use the quadratic equation to solve: . What is the discriminant (the part under the radical) of the solution for ? xman(tcatch) > xbus(tcatch) xman(tcatch) = xbus(tcatch) xman(tcatch) < xbus(tcatch) c = a  tcatch xman(t) xbus(t) xman(tcatch) = xbus(tcatch) −b+ct = a catch 1 2 t2 catch 1 a −c +b = 0 2 t2 catch tcatch c tcatch cmin c a b 1 a − c + b = 0 2 t2 catch tcatch tcatch Typesetting math: 15% Hint 1. The quadratic formula Recall: If then ANSWER: Hint 2. What is the constraint? To get a real value for , the discriminant must be greater then or equal to zero. This condition yields a constraint that exceed . ANSWER: Correct Part E Assume that the man misses getting aboard when he first meets up with the bus. Does he get a second chance if he continues to run at the constant speed ? Hint 1. What is the general quadratic equation? The general quadratic equation is , where , \texttip{B}{B}, and \texttip{C}{C} are constants. Depending on the value of the discriminant, \Delta = c^2-2ab, the equation may have Ax2 + Bx + C = 0 x = −B±B2−4AC 2A  = cc − 2ab tcatch c cmin cmin = (2ab) −−−−  c > cmin Ax2 + Bx + C = 0 A Typesetting math: 15% two real valued solutions 1. if \Delta > 0, 2. one real valued solution if \Delta = 0, or 3. two complex valued solutions if \Delta < 0. In this case, every real valued solution corresponds to a time at which the man is at the same position as the door of the bus. ANSWER: Correct Adding and Subtracting Vectors Conceptual Question Six vectors (A to F) have the magnitudes and directions indicated in the figure. Part A No; there is no chance he is going to get aboard. Yes; he will get a second chance Typesetting math: 15% Which two vectors, when added, will have the largest (positive) x component? Hint 1. Largest x component The two vectors with the largest x components will, when combined, give the resultant with the largest x component. Keep in mind that positive x components are larger than negative x components. ANSWER: Correct Part B Which two vectors, when added, will have the largest (positive) y component? Hint 1. Largest y component The two vectors with the largest y components will, when combined, give the resultant with the largest y component. Keep in mind that positive y components are larger than negative y components. ANSWER: C and E E and F A and F C and D B and D Typesetting math: 15% Correct Part C Which two vectors, when subtracted (i.e., when one vector is subtracted from the other), will have the largest magnitude? Hint 1. Subtracting vectors To subtract two vectors, add a vector with the same magnitude but opposite direction of one of the vectors to the other vector. ANSWER: Correct Tactics Box 3.1 Determining the Components of a Vector Learning Goal: C and D A and F E and F A and B E and D A and F A and E D and B C and D E and F Typesetting math: 15% To practice Tactics Box 3.1 Determining the Components of a Vector. When a vector \texttip{\vec{A}}{A_vec} is decomposed into component vectors \texttip{\vec{A}_{\mit x}}{A_vec_x} and \texttip{\vec{A}_{\mit y}}{A_vec_y} parallel to the coordinate axes, we can describe each component vector with a single number (a scalar) called the component. This tactics box describes how to determine the x component and y component of vector \texttip{\vec{A}}{A_vec}, denoted \texttip{A_{\mit x}}{A_x} and \texttip{A_{\mit y}}{A_y}. TACTICS BOX 3.1 Determining the components of a vector The absolute value |A_x| of the x component \texttip{A_{\mit x}}{A_x} is the magnitude of the component vector \texttip{\vec{A}_{\1. mit x}}{A_vec_x}. The sign of \texttip{A_{\mit x}}{A_x} is positive if \texttip{\vec{A}_{\mit x}}{A_vec_x} points in the positive x direction; it is negative if \texttip{\vec{A}_{\mit x}}{A_vec_x} points in the negative x direction. 2. 3. The y component \texttip{A_{\mit y}}{A_y} is determined similarly. Part A What is the magnitude of the component vector \texttip{\vec{A}_{\mit x}}{A_vec_x} shown in the figure? Express your answer in meters to one significant figure. ANSWER: Correct |A_x| = 5 \rm m Typesetting math: 15% Part B What is the sign of the y component \texttip{A_{\mit y}}{A_y} of vector \texttip{\vec{A}}{A_vec} shown in the figure? ANSWER: Correct Part C Now, combine the information given in the tactics box above to find the x and y components, \texttip{B_{\mit x}}{B_x} and \texttip{B_{\mit y}}{B_y}, of vector \texttip{\vec{B}}{B_vec} shown in the figure. Express your answers, separated by a comma, in meters to one significant figure. positive negative Typesetting math: 15% ANSWER: Correct Conceptual Problem about Projectile Motion Learning Goal: To understand projectile motion by considering horizontal constant velocity motion and vertical constant acceleration motion independently. Projectile motion refers to the motion of unpowered objects (called projectiles) such as balls or stones moving near the surface of the earth under the influence of the earth's gravity alone. In this analysis we assume that air resistance can be neglected. An object undergoing projectile motion near the surface of the earth obeys the following rules: An object undergoing projectile motion travels horizontally at a constant rate. That is, the x component of its velocity, \texttip{v_{\mit x}}{1. v_x}, is constant. An object undergoing projectile motion moves vertically with a constant downward acceleration whose magnitude, denoted by \texttip{g}{g}, is equal to 9.80 \rm{m/s^2} near the surface of the earth. Hence, the y component of its velocity, \texttip{v_{\mit y}}{v_y}, changes continuously. 2. An object undergoing projectile motion will undergo the horizontal and vertical motions described above from the instant it is launched until the instant it strikes the ground again. Even though the horizontal and vertical motions can be treated independently, they are related by the fact that they occur for exactly the same amount of time, namely the time \texttip{t}{t} the projectile is in the air. 3. The figure shows the trajectory (i.e., the path) of a ball undergoing projectile motion over level ground. The time t_0 = 0\;\rm{s} corresponds to the moment just after the ball is launched from position x_0 = 0\;\rm{m} and y_0 = 0\;\rm{m}. Its launch velocity, also called the initial velocity, is \texttip{\vec{v}_{\rm 0}}{v_vec_0}. Two other points along the trajectory are indicated in the figure. One is the moment the ball reaches the peak of its trajectory, at time \texttip{t_{\rm 1}}{t_1} with velocity \texttip{\vec{v}_{\rm 1}}{v_1_vec}. Its position at this moment is denoted by (x_1, y_1) or (x_1, y_{\max}) since it is at its maximum \texttip{B_{\mit x}}{B_x}, \texttip{B_{\mit y}}{B_y} = -2,-5 \rm m, \rm m Typesetting math: 15% The other point, at time \texttip{t_{\rm 2}}{t_2} with velocity \texttip{\vec{v}_{\rm 2}}{v_2_vec}, corresponds to the moment just before the ball strikes the ground on the way back down. At this time its position is (x_2, y_2), also known as (x_{\max}, y_2) since it is at its maximum horizontal range. Projectile motion is symmetric about the peak, provided the object lands at the same vertical height from which is was launched, as is the case here. Hence y_2 = y_0 = 0\;\rm{m}. Part A How do the speeds \texttip{v_{\rm 0}}{v_0}, \texttip{v_{\rm 1}}{v_1}, and \texttip{v_{\rm 2}}{v_2} (at times \texttip{t_{\rm 0}}{t_0}, \texttip{t_{\rm 1}}{t_1}, and \texttip{t_{\rm 2}}{t_2}) compare? ANSWER: Correct Here \texttip{v_{\rm 0}}{v_0} equals \texttip{v_{\rm 2}}{v_2} by symmetry and both exceed \texttip{v_{\rm 1}}{v_1}. This is because \texttip{v_{\rm 0}}{v_0} and \texttip{v_{\rm 2}}{v_2} include vertical speed as well as the constant horizontal speed. Consider a diagram of the ball at time \texttip{t_{\rm 0}}{t_0}. Recall that \texttip{t_{\rm 0}}{t_0} refers to the instant just after the ball has been launched, so it is still at ground level (x_0 = y_0= 0\;\rm{m}). However, it is already moving with initial velocity \texttip{\vec{v}_{\rm 0}}{v_0_vec}, whose magnitude is v_0 = 30.0\;{\rm m/s} and direction is \theta = 60.0\;{\rm degrees} counterclockwise from the positive x direction. \texttip{v_{\rm 0}}{v_0} = \texttip{v_{\rm 1}}{v_1} = \texttip{v_{\rm 2}}{v_2} > 0 \texttip{v_{\rm 0}}{v_0} = \texttip{v_{\rm 2}}{v_2} > \texttip{v_{\rm 1}}{v_1} = 0 \texttip{v_{\rm 0}}{v_0} = \texttip{v_{\rm 2}}{v_2} > \texttip{v_{\rm 1}}{v_1} > 0 \texttip{v_{\rm 0}}{v_0} > \texttip{v_{\rm 1}}{v_1} > \texttip{v_{\rm 2}}{v_2} > 0 \texttip{v_{\rm 0}}{v_0} > \texttip{v_{\rm 2}}{v_2} > \texttip{v_{\rm 1}}{v_1} = 0 Typesetting math: 15% Part B What are the values of the intial velocity vector components \texttip{v_{0,x}}{v_0, x} and \texttip{v_{0,y}}{v_0, y} (both in \rm{m/s}) as well as the acceleration vector components \texttip{a_{0,x}}{a_0, x} and \texttip{a_{0,y}}{a_0, y} (both in \rm{m/s^2})? Here the subscript 0 means “at time \texttip{t_{\rm 0}}{t_0}.” Hint 1. Determining components of a vector that is aligned with an axis If a vector points along a single axis direction, such as in the positive x direction, its x component will be its full magnitude, whereas its y component will be zero since the vector is perpendicular to the y direction. If the vector points in the negative x direction, its x component will be the negative of its full magnitude. Hint 2. Calculating the components of the initial velocity Notice that the vector \texttip{\vec{v}_{\rm 0}}{v_0_vec} points up and to the right. Since “up” is the positive y axis direction and “to the right” is the positive x axis direction, \texttip{v_{0,x}}{v_0, x} and \texttip{v_{0,y}}{v_0, y} will both be positive. As shown in the figure, \texttip{v_{0,x}}{v_0, x}, \texttip{v_{0,y}}{v_0, y}, and \texttip{v_{\rm 0}}{v_0} are three sides of a right triangle, one angle of which is \texttip{\theta }{theta}. Thus \texttip{v_{0,x}}{v_0, x} and \texttip{v_{0,y}}{v_0, y} can be found using the definition of the sine and cosine functions given below. Recall that v_0 = 30.0\;\rm{m/s} and \theta = 60.0\;\rm{degrees} and note that \large{\sin(\theta) = \frac{\rm{length\;of\;opposite\;side}}{\rm{length\;of\;hypotenuse}}} \large{= \frac{v_{0, y}}{v_0}}, \large{\cos(\theta) = \frac{\rm{length\;of\;adjacent\;side}}{\rm{length\;of\;hypotenuse}}} \large{= \frac{v_{0, x}}{v_0}.} What are the values of \texttip{v_{0,x}}{v_0, x} and \texttip{v_{0,y}}{v_0, y}? Enter your answers numerically in meters per second separated by a comma. ANSWER: ANSWER: 15.0,26.0 \rm{m/s} Typesetting math: 15% Correct Also notice that at time \texttip{t_{\rm 2}}{t_2}, just before the ball lands, its velocity components are v_{2, x} = 15\;\rm{m/s} (the same as always) and v_{2, y} = – 26.0\;\rm{m/s} (the same size but opposite sign from \texttip{v_{0,y}}{v_0, y} by symmetry). The acceleration at time \texttip{t_{\rm 2}}{t_2} will have components (0, -9.80 \rm{m/s^2}), exactly the same as at \texttip{t_{\rm 0}}{t_0}, as required by Rule 2. The peak of the trajectory occurs at time \texttip{t_{\rm 1}}{t_1}. This is the point where the ball reaches its maximum height \texttip{y_{\rm max}}{y_max}. At the peak the ball switches from moving up to moving down, even as it continues to travel horizontally at a constant rate. Part C What are the values of the velocity vector components \texttip{v_{1,x}}{v_1, x} and \texttip{v_{1,y}}{v_1, y} (both in \rm{m/s}) as well as the acceleration vector components \texttip{a_{1,x}}{a_1, x} and \texttip{a_{1,y}}{a_1, y} (both in \rm{m/s^2})? Here the subscript 1 means that these are all at time \texttip{t_{\rm 1}}{t_1}. ANSWER: 30.0, 0, 0, 0 0, 30.0, 0, 0 15.0, 26.0, 0, 0 30.0, 0, 0, -9.80 0, 30.0, 0, -9.80 15.0, 26.0, 0, -9.80 15.0, 26.0, 0, +9.80 Typesetting math: 15% Correct At the peak of its trajectory the ball continues traveling horizontally at a constant rate. However, at this moment it stops moving up and is about to move back down. This constitutes a downward-directed change in velocity, so the ball is accelerating downward even at the peak. The flight time refers to the total amount of time the ball is in the air, from just after it is launched (\texttip{t_{\rm 0}}{t_0}) until just before it lands (\texttip{t_{\rm 2}}{t_2}). Hence the flight time can be calculated as t_2 – t_0, or just \texttip{t_{\rm 2}}{t_2} in this particular situation since t_0 = 0. Because the ball lands at the same height from which it was launched, by symmetry it spends half its flight time traveling up to the peak and the other half traveling back down. The flight time is determined by the initial vertical component of the velocity and by the acceleration. The flight time does not depend on whether the object is moving horizontally while it is in the air. Part D If a second ball were dropped from rest from height \texttip{y_{\rm max}}{y_max}, how long would it take to reach the ground? Ignore air resistance. Check all that apply. Hint 1. Kicking a ball of cliff; a related problem Consider two balls, one of which is dropped from rest off the edge of a cliff at the same moment that the other is kicked horizontally off the edge of the cliff. Which ball reaches the level ground at the base of the cliff first? Ignore air resistance. Hint 1. Comparing position, velocity, and acceleration of the two balls Both balls start at the same height and have the same initial y velocity (v_{0,y} = 0) as well as the same acceleration (\vec a = g downward). They differ only in their x velocity (one is 0, 0, 0, 0 0, 0, 0, -9.80 15.0, 0, 0, 0 15.0, 0, 0, -9.80 0, 26.0, 0, 0 0, 26.0, 0, -9.80 15.0, 26.0, 0, 0 15.0, 26.0, 0, -9.80 Typesetting math: 15% zero, the other nonzero). This difference will affect their x motion but not their y motion. ANSWER: ANSWER: Correct In projectile motion over level ground, it takes an object just as long to rise from the ground to the peak as it takes for it to fall from the peak back to the ground. The range \texttip{R}{R} of the ball refers to how far it moves horizontally, from just after it is launched until just before it lands. Range is defined as x_2 – x_0, or just \texttip{x_{\rm 2}}{x_2} in this particular situation since x_0 = 0. Range can be calculated as the product of the flight time \texttip{t_{\rm 2}}{t_2} and the x component of the velocity \texttip{v_{\mit x}}{v_x} (which is the same at all times, so v_x = v_{0,x}). The value of \texttip{v_{\mit x}}{v_x} can be found from the launch speed \texttip{v_{\rm 0}}{v_0} and the launch angle \texttip{\theta }{theta} using trigonometric functions, as was done in Part B. The flight time is related to the initial y component of the velocity, which may also be found from \texttip{v_{\rm 0}}{v_0} and \texttip{\theta }{theta} using trig functions. The following equations may be useful in solving projectile motion problems, but these equations apply only to a projectile launched over level ground from position (x_0 = y_0 = 0) at time t_0 = 0 with initial speed \texttip{v_{\rm 0}}{v_0} and launch angle \texttip{\theta }{theta} measured from the horizontal. As was the case above, \texttip{t_{\rm 2}}{t_2} refers to the flight time and \texttip{R}{R} refers to the range of the projectile. flight time: \large{t_2 = \frac{2 v_{0, y}}{g} = \frac{2 v_0 \sin(\theta)}{g}} range: \large{R = v_x t_2 = \frac{v_0^2 \sin(2\theta)}{g}} The ball that falls straight down strikes the ground first. The ball that was kicked so it moves horizontally as it falls strikes the ground first. Both balls strike the ground at the same time. \texttip{t_{\rm 0}}{t_0} t_1 – t_0 \texttip{t_{\rm 2}}{t_2} t_2 – t_1 \large{\frac{t_2 – t_0}{2}} Typesetting math: 15% In general, a high launch angle yields a long flight time but a small horizontal speed and hence little range. A low launch angle gives a larger horizontal speed, but less flight time in which to accumulate range. The launch angle that achieves the maximum range for projectile motion over level ground is 45 degrees. Part E Which of the following changes would increase the range of the ball shown in the original figure? Check all that apply. ANSWER: Correct A solid understanding of the concepts of projectile motion will take you far, including giving you additional insight into the solution of projectile motion problems numerically. Even when the object does not land at the same height from which is was launched, the rules given in the introduction will still be useful. Recall that air resistance is assumed to be negligible here, so this projectile motion analysis may not be the best choice for describing things like frisbees or feathers, whose motion is strongly influenced by air. The value of the gravitational free-fall acceleration \texttip{g}{g} is also assumed to be constant, which may not be appropriate for objects that move vertically through distances of hundreds of kilometers, like rockets or missiles. However, for problems that involve relatively dense projectiles moving close to the surface of the earth, these assumptions are reasonable. A World-Class Sprinter World-class sprinters can accelerate out of the starting blocks with an acceleration that is nearly horizontal and has magnitude 15 \;{\rm m}/{\rm s}^{2}. Part A How much horizontal force \texttip{F}{F} must a sprinter of mass 64{\rm kg} exert on the starting blocks to produce this acceleration? Express your answer in newtons using two significant figures. Increase \texttip{v_{\rm 0}}{v_0} above 30 \rm{m/s}. Reduce \texttip{v_{\rm 0}}{v_0} below 30 \rm{m/s}. Reduce \texttip{\theta }{theta} from 60 \rm{degrees} to 45 \rm{degrees}. Reduce \texttip{\theta }{theta} from 60 \rm{degrees} to less than 30 \rm{degrees}. Increase \texttip{\theta }{theta} from 60 \rm{degrees} up toward 90 \rm{degrees}. Typesetting math: 15% Hint 1. Newton’s 2nd law of motion According to Newton’s 2nd law of motion, if a net external force \texttip{F_{\rm net}}{F_net} acts on a body, the body accelerates, and the net force is equal to the mass \texttip{m}{m} of the body times the acceleration \texttip{a}{a} of the body: F_{\rm net} = ma. ANSWER: Co

Extra Credit Due: 11:59pm on Thursday, May 15, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy A Man Running to Catch a Bus A man is running at speed (much less than the speed of light) to catch a bus already at a stop. At , when he is a distance from the door to the bus, the bus starts moving with the positive acceleration . Use a coordinate system with at the door of the stopped bus. Part A What is , the position of the man as a function of time? Answer symbolically in terms of the variables , , and . Hint 1. Which equation should you use for the man’s speed? Because the man’s speed is constant, you may use . ANSWER: c t = 0 b a x = 0 xman(t) b c t x(t) = x(0) + vt xman(t) = −b + ct Correct Part B What is , the position of the bus as a function of time? Answer symbolically in terms of and . Hint 1. Which equation should you use for the bus’s acceleration? Because the bus has constant acceleration, you may use . Recall that . ANSWER: Correct Part C What condition is necessary for the man to catch the bus? Assume he catches it at time . Hint 1. How to approach this problem If the man is to catch the bus, then at some moment in time , the man must arrive at the position of the door of the bus. How would you express this condition mathematically? ANSWER: xbus(t) a t x(t) = x(0) + v(0)t + (1/2)at2 vbus(0) = 0 xbus = 1 a 2 t2 tcatch tcatch Typesetting math: 15% Correct Part D Inserting the formulas you found for and into the condition , you obtain the following: , or . Intuitively, the man will not catch the bus unless he is running fast enough. In mathematical terms, there is a constraint on the man’s speed so that the equation above gives a solution for that is a real positive number. Find , the minimum value of for which the man will catch the bus. Express the minimum value for the man’s speed in terms of and . Hint 1. Consider the discriminant Use the quadratic equation to solve: . What is the discriminant (the part under the radical) of the solution for ? xman(tcatch) > xbus(tcatch) xman(tcatch) = xbus(tcatch) xman(tcatch) < xbus(tcatch) c = a  tcatch xman(t) xbus(t) xman(tcatch) = xbus(tcatch) −b+ct = a catch 1 2 t2 catch 1 a −c +b = 0 2 t2 catch tcatch c tcatch cmin c a b 1 a − c + b = 0 2 t2 catch tcatch tcatch Typesetting math: 15% Hint 1. The quadratic formula Recall: If then ANSWER: Hint 2. What is the constraint? To get a real value for , the discriminant must be greater then or equal to zero. This condition yields a constraint that exceed . ANSWER: Correct Part E Assume that the man misses getting aboard when he first meets up with the bus. Does he get a second chance if he continues to run at the constant speed ? Hint 1. What is the general quadratic equation? The general quadratic equation is , where , \texttip{B}{B}, and \texttip{C}{C} are constants. Depending on the value of the discriminant, \Delta = c^2-2ab, the equation may have Ax2 + Bx + C = 0 x = −B±B2−4AC 2A  = cc − 2ab tcatch c cmin cmin = (2ab) −−−−  c > cmin Ax2 + Bx + C = 0 A Typesetting math: 15% two real valued solutions 1. if \Delta > 0, 2. one real valued solution if \Delta = 0, or 3. two complex valued solutions if \Delta < 0. In this case, every real valued solution corresponds to a time at which the man is at the same position as the door of the bus. ANSWER: Correct Adding and Subtracting Vectors Conceptual Question Six vectors (A to F) have the magnitudes and directions indicated in the figure. Part A No; there is no chance he is going to get aboard. Yes; he will get a second chance Typesetting math: 15% Which two vectors, when added, will have the largest (positive) x component? Hint 1. Largest x component The two vectors with the largest x components will, when combined, give the resultant with the largest x component. Keep in mind that positive x components are larger than negative x components. ANSWER: Correct Part B Which two vectors, when added, will have the largest (positive) y component? Hint 1. Largest y component The two vectors with the largest y components will, when combined, give the resultant with the largest y component. Keep in mind that positive y components are larger than negative y components. ANSWER: C and E E and F A and F C and D B and D Typesetting math: 15% Correct Part C Which two vectors, when subtracted (i.e., when one vector is subtracted from the other), will have the largest magnitude? Hint 1. Subtracting vectors To subtract two vectors, add a vector with the same magnitude but opposite direction of one of the vectors to the other vector. ANSWER: Correct Tactics Box 3.1 Determining the Components of a Vector Learning Goal: C and D A and F E and F A and B E and D A and F A and E D and B C and D E and F Typesetting math: 15% To practice Tactics Box 3.1 Determining the Components of a Vector. When a vector \texttip{\vec{A}}{A_vec} is decomposed into component vectors \texttip{\vec{A}_{\mit x}}{A_vec_x} and \texttip{\vec{A}_{\mit y}}{A_vec_y} parallel to the coordinate axes, we can describe each component vector with a single number (a scalar) called the component. This tactics box describes how to determine the x component and y component of vector \texttip{\vec{A}}{A_vec}, denoted \texttip{A_{\mit x}}{A_x} and \texttip{A_{\mit y}}{A_y}. TACTICS BOX 3.1 Determining the components of a vector The absolute value |A_x| of the x component \texttip{A_{\mit x}}{A_x} is the magnitude of the component vector \texttip{\vec{A}_{\1. mit x}}{A_vec_x}. The sign of \texttip{A_{\mit x}}{A_x} is positive if \texttip{\vec{A}_{\mit x}}{A_vec_x} points in the positive x direction; it is negative if \texttip{\vec{A}_{\mit x}}{A_vec_x} points in the negative x direction. 2. 3. The y component \texttip{A_{\mit y}}{A_y} is determined similarly. Part A What is the magnitude of the component vector \texttip{\vec{A}_{\mit x}}{A_vec_x} shown in the figure? Express your answer in meters to one significant figure. ANSWER: Correct |A_x| = 5 \rm m Typesetting math: 15% Part B What is the sign of the y component \texttip{A_{\mit y}}{A_y} of vector \texttip{\vec{A}}{A_vec} shown in the figure? ANSWER: Correct Part C Now, combine the information given in the tactics box above to find the x and y components, \texttip{B_{\mit x}}{B_x} and \texttip{B_{\mit y}}{B_y}, of vector \texttip{\vec{B}}{B_vec} shown in the figure. Express your answers, separated by a comma, in meters to one significant figure. positive negative Typesetting math: 15% ANSWER: Correct Conceptual Problem about Projectile Motion Learning Goal: To understand projectile motion by considering horizontal constant velocity motion and vertical constant acceleration motion independently. Projectile motion refers to the motion of unpowered objects (called projectiles) such as balls or stones moving near the surface of the earth under the influence of the earth's gravity alone. In this analysis we assume that air resistance can be neglected. An object undergoing projectile motion near the surface of the earth obeys the following rules: An object undergoing projectile motion travels horizontally at a constant rate. That is, the x component of its velocity, \texttip{v_{\mit x}}{1. v_x}, is constant. An object undergoing projectile motion moves vertically with a constant downward acceleration whose magnitude, denoted by \texttip{g}{g}, is equal to 9.80 \rm{m/s^2} near the surface of the earth. Hence, the y component of its velocity, \texttip{v_{\mit y}}{v_y}, changes continuously. 2. An object undergoing projectile motion will undergo the horizontal and vertical motions described above from the instant it is launched until the instant it strikes the ground again. Even though the horizontal and vertical motions can be treated independently, they are related by the fact that they occur for exactly the same amount of time, namely the time \texttip{t}{t} the projectile is in the air. 3. The figure shows the trajectory (i.e., the path) of a ball undergoing projectile motion over level ground. The time t_0 = 0\;\rm{s} corresponds to the moment just after the ball is launched from position x_0 = 0\;\rm{m} and y_0 = 0\;\rm{m}. Its launch velocity, also called the initial velocity, is \texttip{\vec{v}_{\rm 0}}{v_vec_0}. Two other points along the trajectory are indicated in the figure. One is the moment the ball reaches the peak of its trajectory, at time \texttip{t_{\rm 1}}{t_1} with velocity \texttip{\vec{v}_{\rm 1}}{v_1_vec}. Its position at this moment is denoted by (x_1, y_1) or (x_1, y_{\max}) since it is at its maximum \texttip{B_{\mit x}}{B_x}, \texttip{B_{\mit y}}{B_y} = -2,-5 \rm m, \rm m Typesetting math: 15% The other point, at time \texttip{t_{\rm 2}}{t_2} with velocity \texttip{\vec{v}_{\rm 2}}{v_2_vec}, corresponds to the moment just before the ball strikes the ground on the way back down. At this time its position is (x_2, y_2), also known as (x_{\max}, y_2) since it is at its maximum horizontal range. Projectile motion is symmetric about the peak, provided the object lands at the same vertical height from which is was launched, as is the case here. Hence y_2 = y_0 = 0\;\rm{m}. Part A How do the speeds \texttip{v_{\rm 0}}{v_0}, \texttip{v_{\rm 1}}{v_1}, and \texttip{v_{\rm 2}}{v_2} (at times \texttip{t_{\rm 0}}{t_0}, \texttip{t_{\rm 1}}{t_1}, and \texttip{t_{\rm 2}}{t_2}) compare? ANSWER: Correct Here \texttip{v_{\rm 0}}{v_0} equals \texttip{v_{\rm 2}}{v_2} by symmetry and both exceed \texttip{v_{\rm 1}}{v_1}. This is because \texttip{v_{\rm 0}}{v_0} and \texttip{v_{\rm 2}}{v_2} include vertical speed as well as the constant horizontal speed. Consider a diagram of the ball at time \texttip{t_{\rm 0}}{t_0}. Recall that \texttip{t_{\rm 0}}{t_0} refers to the instant just after the ball has been launched, so it is still at ground level (x_0 = y_0= 0\;\rm{m}). However, it is already moving with initial velocity \texttip{\vec{v}_{\rm 0}}{v_0_vec}, whose magnitude is v_0 = 30.0\;{\rm m/s} and direction is \theta = 60.0\;{\rm degrees} counterclockwise from the positive x direction. \texttip{v_{\rm 0}}{v_0} = \texttip{v_{\rm 1}}{v_1} = \texttip{v_{\rm 2}}{v_2} > 0 \texttip{v_{\rm 0}}{v_0} = \texttip{v_{\rm 2}}{v_2} > \texttip{v_{\rm 1}}{v_1} = 0 \texttip{v_{\rm 0}}{v_0} = \texttip{v_{\rm 2}}{v_2} > \texttip{v_{\rm 1}}{v_1} > 0 \texttip{v_{\rm 0}}{v_0} > \texttip{v_{\rm 1}}{v_1} > \texttip{v_{\rm 2}}{v_2} > 0 \texttip{v_{\rm 0}}{v_0} > \texttip{v_{\rm 2}}{v_2} > \texttip{v_{\rm 1}}{v_1} = 0 Typesetting math: 15% Part B What are the values of the intial velocity vector components \texttip{v_{0,x}}{v_0, x} and \texttip{v_{0,y}}{v_0, y} (both in \rm{m/s}) as well as the acceleration vector components \texttip{a_{0,x}}{a_0, x} and \texttip{a_{0,y}}{a_0, y} (both in \rm{m/s^2})? Here the subscript 0 means “at time \texttip{t_{\rm 0}}{t_0}.” Hint 1. Determining components of a vector that is aligned with an axis If a vector points along a single axis direction, such as in the positive x direction, its x component will be its full magnitude, whereas its y component will be zero since the vector is perpendicular to the y direction. If the vector points in the negative x direction, its x component will be the negative of its full magnitude. Hint 2. Calculating the components of the initial velocity Notice that the vector \texttip{\vec{v}_{\rm 0}}{v_0_vec} points up and to the right. Since “up” is the positive y axis direction and “to the right” is the positive x axis direction, \texttip{v_{0,x}}{v_0, x} and \texttip{v_{0,y}}{v_0, y} will both be positive. As shown in the figure, \texttip{v_{0,x}}{v_0, x}, \texttip{v_{0,y}}{v_0, y}, and \texttip{v_{\rm 0}}{v_0} are three sides of a right triangle, one angle of which is \texttip{\theta }{theta}. Thus \texttip{v_{0,x}}{v_0, x} and \texttip{v_{0,y}}{v_0, y} can be found using the definition of the sine and cosine functions given below. Recall that v_0 = 30.0\;\rm{m/s} and \theta = 60.0\;\rm{degrees} and note that \large{\sin(\theta) = \frac{\rm{length\;of\;opposite\;side}}{\rm{length\;of\;hypotenuse}}} \large{= \frac{v_{0, y}}{v_0}}, \large{\cos(\theta) = \frac{\rm{length\;of\;adjacent\;side}}{\rm{length\;of\;hypotenuse}}} \large{= \frac{v_{0, x}}{v_0}.} What are the values of \texttip{v_{0,x}}{v_0, x} and \texttip{v_{0,y}}{v_0, y}? Enter your answers numerically in meters per second separated by a comma. ANSWER: ANSWER: 15.0,26.0 \rm{m/s} Typesetting math: 15% Correct Also notice that at time \texttip{t_{\rm 2}}{t_2}, just before the ball lands, its velocity components are v_{2, x} = 15\;\rm{m/s} (the same as always) and v_{2, y} = – 26.0\;\rm{m/s} (the same size but opposite sign from \texttip{v_{0,y}}{v_0, y} by symmetry). The acceleration at time \texttip{t_{\rm 2}}{t_2} will have components (0, -9.80 \rm{m/s^2}), exactly the same as at \texttip{t_{\rm 0}}{t_0}, as required by Rule 2. The peak of the trajectory occurs at time \texttip{t_{\rm 1}}{t_1}. This is the point where the ball reaches its maximum height \texttip{y_{\rm max}}{y_max}. At the peak the ball switches from moving up to moving down, even as it continues to travel horizontally at a constant rate. Part C What are the values of the velocity vector components \texttip{v_{1,x}}{v_1, x} and \texttip{v_{1,y}}{v_1, y} (both in \rm{m/s}) as well as the acceleration vector components \texttip{a_{1,x}}{a_1, x} and \texttip{a_{1,y}}{a_1, y} (both in \rm{m/s^2})? Here the subscript 1 means that these are all at time \texttip{t_{\rm 1}}{t_1}. ANSWER: 30.0, 0, 0, 0 0, 30.0, 0, 0 15.0, 26.0, 0, 0 30.0, 0, 0, -9.80 0, 30.0, 0, -9.80 15.0, 26.0, 0, -9.80 15.0, 26.0, 0, +9.80 Typesetting math: 15% Correct At the peak of its trajectory the ball continues traveling horizontally at a constant rate. However, at this moment it stops moving up and is about to move back down. This constitutes a downward-directed change in velocity, so the ball is accelerating downward even at the peak. The flight time refers to the total amount of time the ball is in the air, from just after it is launched (\texttip{t_{\rm 0}}{t_0}) until just before it lands (\texttip{t_{\rm 2}}{t_2}). Hence the flight time can be calculated as t_2 – t_0, or just \texttip{t_{\rm 2}}{t_2} in this particular situation since t_0 = 0. Because the ball lands at the same height from which it was launched, by symmetry it spends half its flight time traveling up to the peak and the other half traveling back down. The flight time is determined by the initial vertical component of the velocity and by the acceleration. The flight time does not depend on whether the object is moving horizontally while it is in the air. Part D If a second ball were dropped from rest from height \texttip{y_{\rm max}}{y_max}, how long would it take to reach the ground? Ignore air resistance. Check all that apply. Hint 1. Kicking a ball of cliff; a related problem Consider two balls, one of which is dropped from rest off the edge of a cliff at the same moment that the other is kicked horizontally off the edge of the cliff. Which ball reaches the level ground at the base of the cliff first? Ignore air resistance. Hint 1. Comparing position, velocity, and acceleration of the two balls Both balls start at the same height and have the same initial y velocity (v_{0,y} = 0) as well as the same acceleration (\vec a = g downward). They differ only in their x velocity (one is 0, 0, 0, 0 0, 0, 0, -9.80 15.0, 0, 0, 0 15.0, 0, 0, -9.80 0, 26.0, 0, 0 0, 26.0, 0, -9.80 15.0, 26.0, 0, 0 15.0, 26.0, 0, -9.80 Typesetting math: 15% zero, the other nonzero). This difference will affect their x motion but not their y motion. ANSWER: ANSWER: Correct In projectile motion over level ground, it takes an object just as long to rise from the ground to the peak as it takes for it to fall from the peak back to the ground. The range \texttip{R}{R} of the ball refers to how far it moves horizontally, from just after it is launched until just before it lands. Range is defined as x_2 – x_0, or just \texttip{x_{\rm 2}}{x_2} in this particular situation since x_0 = 0. Range can be calculated as the product of the flight time \texttip{t_{\rm 2}}{t_2} and the x component of the velocity \texttip{v_{\mit x}}{v_x} (which is the same at all times, so v_x = v_{0,x}). The value of \texttip{v_{\mit x}}{v_x} can be found from the launch speed \texttip{v_{\rm 0}}{v_0} and the launch angle \texttip{\theta }{theta} using trigonometric functions, as was done in Part B. The flight time is related to the initial y component of the velocity, which may also be found from \texttip{v_{\rm 0}}{v_0} and \texttip{\theta }{theta} using trig functions. The following equations may be useful in solving projectile motion problems, but these equations apply only to a projectile launched over level ground from position (x_0 = y_0 = 0) at time t_0 = 0 with initial speed \texttip{v_{\rm 0}}{v_0} and launch angle \texttip{\theta }{theta} measured from the horizontal. As was the case above, \texttip{t_{\rm 2}}{t_2} refers to the flight time and \texttip{R}{R} refers to the range of the projectile. flight time: \large{t_2 = \frac{2 v_{0, y}}{g} = \frac{2 v_0 \sin(\theta)}{g}} range: \large{R = v_x t_2 = \frac{v_0^2 \sin(2\theta)}{g}} The ball that falls straight down strikes the ground first. The ball that was kicked so it moves horizontally as it falls strikes the ground first. Both balls strike the ground at the same time. \texttip{t_{\rm 0}}{t_0} t_1 – t_0 \texttip{t_{\rm 2}}{t_2} t_2 – t_1 \large{\frac{t_2 – t_0}{2}} Typesetting math: 15% In general, a high launch angle yields a long flight time but a small horizontal speed and hence little range. A low launch angle gives a larger horizontal speed, but less flight time in which to accumulate range. The launch angle that achieves the maximum range for projectile motion over level ground is 45 degrees. Part E Which of the following changes would increase the range of the ball shown in the original figure? Check all that apply. ANSWER: Correct A solid understanding of the concepts of projectile motion will take you far, including giving you additional insight into the solution of projectile motion problems numerically. Even when the object does not land at the same height from which is was launched, the rules given in the introduction will still be useful. Recall that air resistance is assumed to be negligible here, so this projectile motion analysis may not be the best choice for describing things like frisbees or feathers, whose motion is strongly influenced by air. The value of the gravitational free-fall acceleration \texttip{g}{g} is also assumed to be constant, which may not be appropriate for objects that move vertically through distances of hundreds of kilometers, like rockets or missiles. However, for problems that involve relatively dense projectiles moving close to the surface of the earth, these assumptions are reasonable. A World-Class Sprinter World-class sprinters can accelerate out of the starting blocks with an acceleration that is nearly horizontal and has magnitude 15 \;{\rm m}/{\rm s}^{2}. Part A How much horizontal force \texttip{F}{F} must a sprinter of mass 64{\rm kg} exert on the starting blocks to produce this acceleration? Express your answer in newtons using two significant figures. Increase \texttip{v_{\rm 0}}{v_0} above 30 \rm{m/s}. Reduce \texttip{v_{\rm 0}}{v_0} below 30 \rm{m/s}. Reduce \texttip{\theta }{theta} from 60 \rm{degrees} to 45 \rm{degrees}. Reduce \texttip{\theta }{theta} from 60 \rm{degrees} to less than 30 \rm{degrees}. Increase \texttip{\theta }{theta} from 60 \rm{degrees} up toward 90 \rm{degrees}. Typesetting math: 15% Hint 1. Newton’s 2nd law of motion According to Newton’s 2nd law of motion, if a net external force \texttip{F_{\rm net}}{F_net} acts on a body, the body accelerates, and the net force is equal to the mass \texttip{m}{m} of the body times the acceleration \texttip{a}{a} of the body: F_{\rm net} = ma. ANSWER: Co

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Excel Review Assignment #1 – ISM3011 Ask before/after/during class or come into office/online hours if you have questions on any of this. Refer to the syllabus on Academic Dishonesty and group/individual work and allowable help for all projects – also remember it’s your responsibility to protect your work. Before you start — read this whole assignment and use your optional text and/or review the tutorials as necessary on Canvas or www.bwarner.org/tips. A project overview for each project is also available. Part 1 – Create / Download / Parts • Create a blank workbook. Name it using your Last name followed by your initials and _ 1EX (underscore then 1EX). For Example: WarnerBL_1EX .xlsx. Either extension is fine. • Download the Word file Ex1 Data1-F15.docx and copy/paste Word table from the file into the 2nd worksheet in your workbook. Name the tab ‘2014 Sales’. • Download the Word file Ex1 Data2-F15.docx and copy/paste Word table from the file into the 3rd worksheet in your workbook. Name the tab ‘2015 Sales’. • Adjust the column widths of both Sales worksheets so that no data is cut off. • Do not add any formulas or cells to the Sales worksheets Part 2 – Summary Worksheet • Create a summary sheet from the Sales worksheets. Name the worksheet ‘Summary’. Build two summaries on this worksheet. Summary 1: Comparison of Sales by Month and Summary 2: Comparison of Sales by Store ID. • Use the project overview as a guide for the format. Use colors, borders and backgrounds to make the worksheet look professional. o Include the following:  Month and Store ID headings that reference the 2014 Sales worksheet. This means if ‘January’ is changed to ‘Jan’ in the 2014 Sales worksheet, the summary worksheet heading will also change. Do the same with the Store ID and 2014 Sales worksheet.  Formulas that reference the 2014 and 2015 Sales worksheets. If the Sales worksheets change, the summary worksheet should also adjust automatically.  Correct format for all book totals (commas, no decimal places)  Correct % change formulas in both tables. This is how much the totals have changed compared to the 2014 totals.  Correct format for all % change (% sign, 1 decimal place).  Use borders and background colors on the column & row headings for both tables of data • On the summary worksheet, use conditional formatting to highlight any % change cell that greater than zero with a bright color background. If the % change is negative, display the value with a red font and no background color. o There should be only two conditional formats set on each cell. o **Note – to do the conditional formatting steps, you can set the conditional formatting for one cell and then use the format painter to apply to other appropriate cells. If the values are all changed, the conditional formatting should still work. Once you have it working, check by changing some values & see if the conditional formatting changes correctly. Return to the original values/formulas in the cell before you submit. If you don’t use the format painter for this be sure you still try it out & understand how it works. Part 3 – Chart • Create 2 column graphs displaying Totals by Month and Totals by Store ID. Include: • Titles on both chart as well as labeling on the x and the y axis. • Color fonts for the title and axis labels (not dark blue or black) • Large font for the title (at least 16 point) • Include a legend • Format the background (chart area/walls) of the graph with a texture – use one that is easy to see. • Be sure that if any headings or numbers in the worksheets change, these changes are automatically reflected in your chart. • Add a star or banner shape between the two charts and add your name. Be sure the text is part of the shape (not a shape and a separate text box). Part 4 – Finishing Up • Be sure your worksheet tabs are named correctly and if possible, make each worksheet tab a distinctly different color. If your version of Excel doesn’t allow this, don’t worry about it. But do delete any additional worksheets in the workbook. • Create a title in the first row of your summary worksheet. Use the merge and center feature (across all columns with data) and a larger font & different font color (not blue or black). Also add a background color. Add a comment with your email address and the date your spreadsheet was created. • Below the title, add a row with the current date (use the today or now formula) so it is updated whenever the spreadsheet is opened). • Check your formulas, be sure they are correct and make sense. For example, if you are subtracting 2 numbers don’t use the SUM formulas (sum is for adding). Excel may figure out what you mean, but we want the formulas to be used correctly (show that you understand how to use them). • Check your worksheet for errors! Potential errors in cells show up as small green triangles in the top left corner of each cell. Do a little Googling on error checking for your version of Excel and be sure you have error checking turned on and that you reconcile each error so they don’t display when we open your project for grading. Sample: Project Submission Instructions / Notes: • Office/online hours get busy as deadlines approach. If you procrastinate and wait until the last days to work on your project, you may not be able to get all the help you want. • The only way we can fairly grade the projects is if we check for each requirement. Please go through the instructions before you submit & be sure you have done each one correctly so you don’t miss out on points. Compare your solution to the project overview. • Submitting: o Remember to leave all of the internal file properties intact for your project, if they are modified or deleted, you project won’t be accepted (see syllabus for more on this). o Read and follow the instructions in the Assignments section of Canvas on uploading and checking your upload. If you follow these instructions you can ensure that your project is uploaded correctly (and is the correct project). Be sure that Access / Excel are closed before you try to upload your project files. o If your project doesn’t upload correctly before the due date, it will be considered late and be assessed the late penalty – even it was finished on time. This is the only way we can ensure that students check their Canvas submissions. • Technology problems relating to your home computer (Windows based or Mac), internet connection or slow Canvas access are not valid excuses for late/missing work, unless Canvas is down for 6+ hours on the due date. Computers at USF computer labs and the library are available; leave enough time to access them as needed. Also give yourself enough time that if a TA can’t answer a question, you’ll have time to contact me & I can either help you or make an allowance in your grade. If you wait until the last days, I may not be able to do either.

Excel Review Assignment #1 – ISM3011 Ask before/after/during class or come into office/online hours if you have questions on any of this. Refer to the syllabus on Academic Dishonesty and group/individual work and allowable help for all projects – also remember it’s your responsibility to protect your work. Before you start — read this whole assignment and use your optional text and/or review the tutorials as necessary on Canvas or www.bwarner.org/tips. A project overview for each project is also available. Part 1 – Create / Download / Parts • Create a blank workbook. Name it using your Last name followed by your initials and _ 1EX (underscore then 1EX). For Example: WarnerBL_1EX .xlsx. Either extension is fine. • Download the Word file Ex1 Data1-F15.docx and copy/paste Word table from the file into the 2nd worksheet in your workbook. Name the tab ‘2014 Sales’. • Download the Word file Ex1 Data2-F15.docx and copy/paste Word table from the file into the 3rd worksheet in your workbook. Name the tab ‘2015 Sales’. • Adjust the column widths of both Sales worksheets so that no data is cut off. • Do not add any formulas or cells to the Sales worksheets Part 2 – Summary Worksheet • Create a summary sheet from the Sales worksheets. Name the worksheet ‘Summary’. Build two summaries on this worksheet. Summary 1: Comparison of Sales by Month and Summary 2: Comparison of Sales by Store ID. • Use the project overview as a guide for the format. Use colors, borders and backgrounds to make the worksheet look professional. o Include the following:  Month and Store ID headings that reference the 2014 Sales worksheet. This means if ‘January’ is changed to ‘Jan’ in the 2014 Sales worksheet, the summary worksheet heading will also change. Do the same with the Store ID and 2014 Sales worksheet.  Formulas that reference the 2014 and 2015 Sales worksheets. If the Sales worksheets change, the summary worksheet should also adjust automatically.  Correct format for all book totals (commas, no decimal places)  Correct % change formulas in both tables. This is how much the totals have changed compared to the 2014 totals.  Correct format for all % change (% sign, 1 decimal place).  Use borders and background colors on the column & row headings for both tables of data • On the summary worksheet, use conditional formatting to highlight any % change cell that greater than zero with a bright color background. If the % change is negative, display the value with a red font and no background color. o There should be only two conditional formats set on each cell. o **Note – to do the conditional formatting steps, you can set the conditional formatting for one cell and then use the format painter to apply to other appropriate cells. If the values are all changed, the conditional formatting should still work. Once you have it working, check by changing some values & see if the conditional formatting changes correctly. Return to the original values/formulas in the cell before you submit. If you don’t use the format painter for this be sure you still try it out & understand how it works. Part 3 – Chart • Create 2 column graphs displaying Totals by Month and Totals by Store ID. Include: • Titles on both chart as well as labeling on the x and the y axis. • Color fonts for the title and axis labels (not dark blue or black) • Large font for the title (at least 16 point) • Include a legend • Format the background (chart area/walls) of the graph with a texture – use one that is easy to see. • Be sure that if any headings or numbers in the worksheets change, these changes are automatically reflected in your chart. • Add a star or banner shape between the two charts and add your name. Be sure the text is part of the shape (not a shape and a separate text box). Part 4 – Finishing Up • Be sure your worksheet tabs are named correctly and if possible, make each worksheet tab a distinctly different color. If your version of Excel doesn’t allow this, don’t worry about it. But do delete any additional worksheets in the workbook. • Create a title in the first row of your summary worksheet. Use the merge and center feature (across all columns with data) and a larger font & different font color (not blue or black). Also add a background color. Add a comment with your email address and the date your spreadsheet was created. • Below the title, add a row with the current date (use the today or now formula) so it is updated whenever the spreadsheet is opened). • Check your formulas, be sure they are correct and make sense. For example, if you are subtracting 2 numbers don’t use the SUM formulas (sum is for adding). Excel may figure out what you mean, but we want the formulas to be used correctly (show that you understand how to use them). • Check your worksheet for errors! Potential errors in cells show up as small green triangles in the top left corner of each cell. Do a little Googling on error checking for your version of Excel and be sure you have error checking turned on and that you reconcile each error so they don’t display when we open your project for grading. Sample: Project Submission Instructions / Notes: • Office/online hours get busy as deadlines approach. If you procrastinate and wait until the last days to work on your project, you may not be able to get all the help you want. • The only way we can fairly grade the projects is if we check for each requirement. Please go through the instructions before you submit & be sure you have done each one correctly so you don’t miss out on points. Compare your solution to the project overview. • Submitting: o Remember to leave all of the internal file properties intact for your project, if they are modified or deleted, you project won’t be accepted (see syllabus for more on this). o Read and follow the instructions in the Assignments section of Canvas on uploading and checking your upload. If you follow these instructions you can ensure that your project is uploaded correctly (and is the correct project). Be sure that Access / Excel are closed before you try to upload your project files. o If your project doesn’t upload correctly before the due date, it will be considered late and be assessed the late penalty – even it was finished on time. This is the only way we can ensure that students check their Canvas submissions. • Technology problems relating to your home computer (Windows based or Mac), internet connection or slow Canvas access are not valid excuses for late/missing work, unless Canvas is down for 6+ hours on the due date. Computers at USF computer labs and the library are available; leave enough time to access them as needed. Also give yourself enough time that if a TA can’t answer a question, you’ll have time to contact me & I can either help you or make an allowance in your grade. If you wait until the last days, I may not be able to do either.

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CHM114: Exam #2 CHM 114, S2015 Exam #2, Version C 16 March 2015 Instructor: O. Graudejus Points: 100 Print Name Sign Name Student I.D. # 1. You are responsible for the information on this page. Please read it carefully. 2. Code your name and 10 digit affiliate identification number on the separate scantron answer sheet. Use only a #2 pencil 3. If you enter your ASU ID incorrectly on the scantron, a 3 point penalty will be assessed. 4. Do all calculations on the exam pages. Do not make any unnecessary marks on the answer sheet. 5. This exam consists of 25 multiple choice questions worth 4 points each and a periodic table. Make sure you have them all. 6. Choose the best answer to each of the questions and answer it on the computer-graded answer sheet. Read all responses before making a selection. 7. Read the directions carefully for each problem. 8. Avoid even casual glances at other students’ exams. 9. Stop writing and hand in your scantron answer sheet and your test promptly when instructed. LATE EXAMS MAY HAVE POINTS DEDUCTED. 10. You will have 50 minutes to complete the exam. 11. If you leave early, please do so quietly. 12. Work the easiest problems first. 13. A periodic table is attached as the last page to this exam. 14. Answers will be posted online this afternoon. Potentially useful information: K = ºC + 273.15 RH=2.18·10-18 J R=8.314 J·K-1·mol-1 1Å=10-10 m c=3·108 m/s Ephoton=h·n=h·c/l h=6.626·10-34 Js Avogadro’s Number = 6.022 × 1023 particles/mole DH°rxn =  n DHf° (products) –  n DHf° (reactants) ) 1 1 ( 2 2 f i H n n DE = R − \ -2- CHM114: Exam #2 1) Which one of the following is an incorrect orbital notation? A) 2s B) 2p C) 3f D) 3d E) 4s 2) The energy of a photon that has a frequency of 8.21 1015s 1 − × is __________ J. A) 8.08 10 50 − × B) 1.99 10 25 − × C) 5.44 10 18 − × D) 1.24×1049 E) 1.26 10 19 − × 3) The ground state electron configuration of Ga is __________. A) 1s22s23s23p64s23d104p1 B) 1s22s22p63s23p64s24d104p1 C) 1s22s22p63s23p64s23d104p1 D) 1s22s22p63s23p64s23d104d1 E) [Ar]4s23d11 4) Of the bonds N–N, N=N, and NN, the N-N bond is __________. A) strongest/shortest B) weakest/longest C) strongest/longest D) weakest/shortest E) intermediate in both strength and length 5) Of the atoms below, __________ is the most electronegative. A) Br B) O C) Cl D) N E) F 6) Of the following, __________ cannot accommodate more than an octet of electrons. A) P B) O C) S D) Cl E) I -3- CHM 114: Exam #2 7) Which electron configuration represents a violation of Hund’s Rule? A) B) C) D) E) 8) A tin atom has 50 electrons. Electrons in the _____ subshell experience the highest effective nuclear charge. A) 1s B) 3p C) 3d D) 5s E) 5p 9) In ionic compounds, the lattice energy_____ as the magnitude of the ion charges _____ and the radii _____. A) increases, decrease, increase B) increases, increase, increase C) decreases, increase, increase D) increases, increase, decrease E) increases, decrease, decrease 10) Which of the following ionic compounds has the highest lattice energy? A) LiF B) MgO C) CsF D) CsI E) LiI -4- CHM 114: Exam #2 11) For which one of the following reactions is the value of H°rxn equal to Hf° for the product? A) 2 C (s, graphite) + 2 H2 (g)  C2H4 (g) B) N2 (g) + O2 (g)  2 NO (g) C) 2 H2 (g) + O2 (g)  2 H2O (l) D) 2 H2 (g) + O2 (g)  2 H2O (g) E) all of the above 12) Given the data in the table below, H rxn D ° for the reaction 3 2 3 PCl (g) + 3HCl(g)®3Cl (g) + PH (g) is __________ kJ. A) -570.37 B) -385.77 C) 570.37 D) 385.77 E) The f DH° of 2 Cl (g) is needed for the calculation. 13) Given the following reactions (1) 2 2 2NO® N +O H = -180 kJ (2) 2 2 2NO+O ®2NO H = -112 kJ the enthalpy of the reaction of nitrogen with oxygen to produce nitrogen dioxide 2 2 2 N + 2O ®2NO is __________ kJ. A) 68 B) -68 C) -292 D) 292 E) -146 14) Of the following transitions in the Bohr hydrogen atom, the __________ transition results in the absorption of the lowest-energy photon. A) n = 1  n = 6 B) n = 6  n = 1 C) n = 6  n = 5 D) n = 3  n = 6 E) n = 1  n = 4 -5- CHM 114: Exam #2 15) Which equation correctly represents the electron affinity of calcium? A) Ca (g)  Ca+ (g) + e- B) Ca (g)  Ca- (g) + e- C) Ca (g) + e-  Ca- (g) D) Ca- (g)  Ca (g) + e- E) Ca+ (g) + e-  Ca (g) 16) Which of the following does not have eight valence electrons? A) Ca+ B) Rb+ C) Xe D) Br− E) All of the above have eight valence electrons. 17) The specific heat of liquid bromine is 0.226 J/g · K. The molar heat capacity (in J/mol-K) of liquid bromine is __________. A) 707 B) 36.1 C) 18.1 D) 9.05 E) 0.226 18) Given the electronegativities below, which covalent single bond is least polar? Element: H C N O F Electronegativity: 2.1 2.5 3.0 3.5 4.0 A) C-H B) C-F C) O-H D) O-C E) F-H 19) The bond length in an HCl molecule is 1.27 Å and the measured dipole moment is 1.08 D. What is the magnitude (in units of e) of the negative charge on Cl in HCl? (1 debye = 3.34 10 30 coulomb-meters − × ; e=1.6 10 19 coulombs − × ) A) 1.6 10 19 − × B) 0.057 C) 0.18 D) 1 E) 0.22 -6- CHM 114: Exam #2 20) The F-B-F bond angle in the BF3 molecule is approximately __________. A) 90° B) 109.5° C) 120° D) 180° E) 60° 21) Which isoelectronic series is correctly arranged in order of increasing radius? A) K+ < Ca2+ < Ar < Cl- B) Cl- < Ar < K+ < Ca2+ C) Ca2+ < Ar < K+ < Cl- D) Ca2+ < K+ < Ar < Cl- E) Ca2+ < K+ < Cl- < Ar 22) What is the electron configuration for the Fe2+ ion? A) [Ar]4s03d6 B) [Ar]4s23d4 C) [Ar]4s03d8 D) [Ar]4s23d8 E) [Ar]4s63d2 23) The formal charge on carbon in the Lewis structure of the NCS - ion is __________: A) -1 B) +1 C) +2 D) 0 E) +3 -7- CHM 114: Exam #2 24) Using the table of bond dissociation energies, the H for the following gas-phase reaction is __________ kJ. A) 291 B) 2017 C) -57 D) -356 E) -291 25) According to VSEPR theory, if there are six electron domains in the valence shell of an atom, they will be arranged in a(n) __________ geometry. A) octahedral B) linear C) tetrahedral D) trigonal planar E) trigonal bipyramidal -8- CHM 114: Exam #2

CHM114: Exam #2 CHM 114, S2015 Exam #2, Version C 16 March 2015 Instructor: O. Graudejus Points: 100 Print Name Sign Name Student I.D. # 1. You are responsible for the information on this page. Please read it carefully. 2. Code your name and 10 digit affiliate identification number on the separate scantron answer sheet. Use only a #2 pencil 3. If you enter your ASU ID incorrectly on the scantron, a 3 point penalty will be assessed. 4. Do all calculations on the exam pages. Do not make any unnecessary marks on the answer sheet. 5. This exam consists of 25 multiple choice questions worth 4 points each and a periodic table. Make sure you have them all. 6. Choose the best answer to each of the questions and answer it on the computer-graded answer sheet. Read all responses before making a selection. 7. Read the directions carefully for each problem. 8. Avoid even casual glances at other students’ exams. 9. Stop writing and hand in your scantron answer sheet and your test promptly when instructed. LATE EXAMS MAY HAVE POINTS DEDUCTED. 10. You will have 50 minutes to complete the exam. 11. If you leave early, please do so quietly. 12. Work the easiest problems first. 13. A periodic table is attached as the last page to this exam. 14. Answers will be posted online this afternoon. Potentially useful information: K = ºC + 273.15 RH=2.18·10-18 J R=8.314 J·K-1·mol-1 1Å=10-10 m c=3·108 m/s Ephoton=h·n=h·c/l h=6.626·10-34 Js Avogadro’s Number = 6.022 × 1023 particles/mole DH°rxn =  n DHf° (products) –  n DHf° (reactants) ) 1 1 ( 2 2 f i H n n DE = R − \ -2- CHM114: Exam #2 1) Which one of the following is an incorrect orbital notation? A) 2s B) 2p C) 3f D) 3d E) 4s 2) The energy of a photon that has a frequency of 8.21 1015s 1 − × is __________ J. A) 8.08 10 50 − × B) 1.99 10 25 − × C) 5.44 10 18 − × D) 1.24×1049 E) 1.26 10 19 − × 3) The ground state electron configuration of Ga is __________. A) 1s22s23s23p64s23d104p1 B) 1s22s22p63s23p64s24d104p1 C) 1s22s22p63s23p64s23d104p1 D) 1s22s22p63s23p64s23d104d1 E) [Ar]4s23d11 4) Of the bonds N–N, N=N, and NN, the N-N bond is __________. A) strongest/shortest B) weakest/longest C) strongest/longest D) weakest/shortest E) intermediate in both strength and length 5) Of the atoms below, __________ is the most electronegative. A) Br B) O C) Cl D) N E) F 6) Of the following, __________ cannot accommodate more than an octet of electrons. A) P B) O C) S D) Cl E) I -3- CHM 114: Exam #2 7) Which electron configuration represents a violation of Hund’s Rule? A) B) C) D) E) 8) A tin atom has 50 electrons. Electrons in the _____ subshell experience the highest effective nuclear charge. A) 1s B) 3p C) 3d D) 5s E) 5p 9) In ionic compounds, the lattice energy_____ as the magnitude of the ion charges _____ and the radii _____. A) increases, decrease, increase B) increases, increase, increase C) decreases, increase, increase D) increases, increase, decrease E) increases, decrease, decrease 10) Which of the following ionic compounds has the highest lattice energy? A) LiF B) MgO C) CsF D) CsI E) LiI -4- CHM 114: Exam #2 11) For which one of the following reactions is the value of H°rxn equal to Hf° for the product? A) 2 C (s, graphite) + 2 H2 (g)  C2H4 (g) B) N2 (g) + O2 (g)  2 NO (g) C) 2 H2 (g) + O2 (g)  2 H2O (l) D) 2 H2 (g) + O2 (g)  2 H2O (g) E) all of the above 12) Given the data in the table below, H rxn D ° for the reaction 3 2 3 PCl (g) + 3HCl(g)®3Cl (g) + PH (g) is __________ kJ. A) -570.37 B) -385.77 C) 570.37 D) 385.77 E) The f DH° of 2 Cl (g) is needed for the calculation. 13) Given the following reactions (1) 2 2 2NO® N +O H = -180 kJ (2) 2 2 2NO+O ®2NO H = -112 kJ the enthalpy of the reaction of nitrogen with oxygen to produce nitrogen dioxide 2 2 2 N + 2O ®2NO is __________ kJ. A) 68 B) -68 C) -292 D) 292 E) -146 14) Of the following transitions in the Bohr hydrogen atom, the __________ transition results in the absorption of the lowest-energy photon. A) n = 1  n = 6 B) n = 6  n = 1 C) n = 6  n = 5 D) n = 3  n = 6 E) n = 1  n = 4 -5- CHM 114: Exam #2 15) Which equation correctly represents the electron affinity of calcium? A) Ca (g)  Ca+ (g) + e- B) Ca (g)  Ca- (g) + e- C) Ca (g) + e-  Ca- (g) D) Ca- (g)  Ca (g) + e- E) Ca+ (g) + e-  Ca (g) 16) Which of the following does not have eight valence electrons? A) Ca+ B) Rb+ C) Xe D) Br− E) All of the above have eight valence electrons. 17) The specific heat of liquid bromine is 0.226 J/g · K. The molar heat capacity (in J/mol-K) of liquid bromine is __________. A) 707 B) 36.1 C) 18.1 D) 9.05 E) 0.226 18) Given the electronegativities below, which covalent single bond is least polar? Element: H C N O F Electronegativity: 2.1 2.5 3.0 3.5 4.0 A) C-H B) C-F C) O-H D) O-C E) F-H 19) The bond length in an HCl molecule is 1.27 Å and the measured dipole moment is 1.08 D. What is the magnitude (in units of e) of the negative charge on Cl in HCl? (1 debye = 3.34 10 30 coulomb-meters − × ; e=1.6 10 19 coulombs − × ) A) 1.6 10 19 − × B) 0.057 C) 0.18 D) 1 E) 0.22 -6- CHM 114: Exam #2 20) The F-B-F bond angle in the BF3 molecule is approximately __________. A) 90° B) 109.5° C) 120° D) 180° E) 60° 21) Which isoelectronic series is correctly arranged in order of increasing radius? A) K+ < Ca2+ < Ar < Cl- B) Cl- < Ar < K+ < Ca2+ C) Ca2+ < Ar < K+ < Cl- D) Ca2+ < K+ < Ar < Cl- E) Ca2+ < K+ < Cl- < Ar 22) What is the electron configuration for the Fe2+ ion? A) [Ar]4s03d6 B) [Ar]4s23d4 C) [Ar]4s03d8 D) [Ar]4s23d8 E) [Ar]4s63d2 23) The formal charge on carbon in the Lewis structure of the NCS - ion is __________: A) -1 B) +1 C) +2 D) 0 E) +3 -7- CHM 114: Exam #2 24) Using the table of bond dissociation energies, the H for the following gas-phase reaction is __________ kJ. A) 291 B) 2017 C) -57 D) -356 E) -291 25) According to VSEPR theory, if there are six electron domains in the valence shell of an atom, they will be arranged in a(n) __________ geometry. A) octahedral B) linear C) tetrahedral D) trigonal planar E) trigonal bipyramidal -8- CHM 114: Exam #2

A warning sign for cancerous cells may be Question 48 options: a mole changing color a mole decreasing in size a twin mole a mole becoming symmetrical

A warning sign for cancerous cells may be Question 48 options: a mole changing color a mole decreasing in size a twin mole a mole becoming symmetrical

A warning sign for cancerous cells may be Question 48 … Read More...
Lab #03 Studying Beam Flexion Summary: Beams are fundamental structural elements used in a variety of engineering applications and have been studied for centuries. Beams can be assembled to create large structures that carry heavy loads, such as motor vehicle traffic. Beams are also used in micro- or nano-scale accelerometers to delicately measure and detect motions that trigger the deployment of an airbag. From a technical standpoint, a beam is a structure that supports transverse load. Transverse load is load that is perpendicular to the long axis of the beam. As a result, of transverse load, beams undergo bending, in which the beam develops a curvature. As the beam bends, material fibers along the beam’s long axis are forced to stretch or contract, which in turn causes a resistance to the bending. The fibers that are the farthest away from the center of the beam are forced to stretch or contract the most and thus, material at these extremities is the most important to resist bending and deflection. This topic is studied quantitatively in Strength of Materials (CE-303). Purpose: The purpose of this assignment is to accomplish the following goals: • Develop a simple experiment to achieve a goal. • Statistically and observationally analyze your data and interpret the results. • Summarize and present your data, results and interpretations. Procedure: 1. Working as a team, develop a procedure to carefully document the amount of bending a beam under-goes as loads are placed on it (this is your experimental protocol). You must select at least two different beam styles. 2. Collect the data points your experimental protocol calls for. You should conduct at least three trials and the order of data collection within those trials should be randomized. 3. Using the provided Excel deflection calculator, calculate the “predicted” deflection for each of the trials in your protocol. 4. Please observe the following MAXIMUM test torques to avoid damaging the beams. • Width Effect Beams: Small beam: 48 in-lbs, Medium beam: 80 in-lbs, Large beam: 120 in-lbs • Depth Effect Beams: Small beam: 8 in-lbs, Medium beam: 48 in-lbs, Large beam: 160 in-lbs Report and Presentation Requirements: 1. Title Page: Should include the title of the lab experiment, groups individual names (in alphabetical order by last name), data collection date, report due date, and course name and section. 2. Introduction: Briefly explain what you are trying to accomplish with this experiment. 3. Hypothesis Development: Should clearly state the three hypotheses, with respect to distance, beam size, and calculated versus actual deflection. Be sure to include logic to support your educated guess. 4. Method: Explain each activity performed during the data collection and analysis process. Provide a list of the equipment used and its purpose. 5. Analysis and Results: (1) Using the raw data, provide a table of descriptive statistics (mean, variance, and range) for each beam at each distance. (2) Provide a data table (average across 3 trials) showing the deflection for each beam at each distance. (3) Create one or more charts demonstrating the difference, if any, between the calculated and observed deflection for each beam. (4) Use the t-Test: Paired Two Sample for Means in Excel to determine if there is a statistically significant difference between predicted (calculated) deflection and actual (observed) deflection, assuming α = 0.05. Show the results for each beam. Note: To add in the Data Analysis package (under the data tab), go to Office Button -> Excel Options -> Add-Ins -> Manage Excel Add-Ins -> GO… -> check Analysis TookPak and click OK. For each table or chart, provide a description and explanation of what is being displayed. 6. Conclusions: Restate the hypotheses and explain whether or not the educated guess was correct. Include limitations of the experiment (in other words, describe other factors that would make the experiment better or possible errors associated with the experiment). Provide suggestions for future research. 7. Last Page: Include, at the end of the document, a summary of all the tasks required to complete the assignment, and which member or members of the group were principally responsible for completing those tasks. This should be in the form of a simple list. 8. Presentation: Summarize the report, excluding the last page. Due Date: This assignment is to be completed and turned in at the beginning of your laboratory meeting during the week of 11th March. Microsoft office package: Excel: Data tab functions, round, drag-drop, $-sign functions, Beginning of analysis toolpak-t-tests

Lab #03 Studying Beam Flexion Summary: Beams are fundamental structural elements used in a variety of engineering applications and have been studied for centuries. Beams can be assembled to create large structures that carry heavy loads, such as motor vehicle traffic. Beams are also used in micro- or nano-scale accelerometers to delicately measure and detect motions that trigger the deployment of an airbag. From a technical standpoint, a beam is a structure that supports transverse load. Transverse load is load that is perpendicular to the long axis of the beam. As a result, of transverse load, beams undergo bending, in which the beam develops a curvature. As the beam bends, material fibers along the beam’s long axis are forced to stretch or contract, which in turn causes a resistance to the bending. The fibers that are the farthest away from the center of the beam are forced to stretch or contract the most and thus, material at these extremities is the most important to resist bending and deflection. This topic is studied quantitatively in Strength of Materials (CE-303). Purpose: The purpose of this assignment is to accomplish the following goals: • Develop a simple experiment to achieve a goal. • Statistically and observationally analyze your data and interpret the results. • Summarize and present your data, results and interpretations. Procedure: 1. Working as a team, develop a procedure to carefully document the amount of bending a beam under-goes as loads are placed on it (this is your experimental protocol). You must select at least two different beam styles. 2. Collect the data points your experimental protocol calls for. You should conduct at least three trials and the order of data collection within those trials should be randomized. 3. Using the provided Excel deflection calculator, calculate the “predicted” deflection for each of the trials in your protocol. 4. Please observe the following MAXIMUM test torques to avoid damaging the beams. • Width Effect Beams: Small beam: 48 in-lbs, Medium beam: 80 in-lbs, Large beam: 120 in-lbs • Depth Effect Beams: Small beam: 8 in-lbs, Medium beam: 48 in-lbs, Large beam: 160 in-lbs Report and Presentation Requirements: 1. Title Page: Should include the title of the lab experiment, groups individual names (in alphabetical order by last name), data collection date, report due date, and course name and section. 2. Introduction: Briefly explain what you are trying to accomplish with this experiment. 3. Hypothesis Development: Should clearly state the three hypotheses, with respect to distance, beam size, and calculated versus actual deflection. Be sure to include logic to support your educated guess. 4. Method: Explain each activity performed during the data collection and analysis process. Provide a list of the equipment used and its purpose. 5. Analysis and Results: (1) Using the raw data, provide a table of descriptive statistics (mean, variance, and range) for each beam at each distance. (2) Provide a data table (average across 3 trials) showing the deflection for each beam at each distance. (3) Create one or more charts demonstrating the difference, if any, between the calculated and observed deflection for each beam. (4) Use the t-Test: Paired Two Sample for Means in Excel to determine if there is a statistically significant difference between predicted (calculated) deflection and actual (observed) deflection, assuming α = 0.05. Show the results for each beam. Note: To add in the Data Analysis package (under the data tab), go to Office Button -> Excel Options -> Add-Ins -> Manage Excel Add-Ins -> GO… -> check Analysis TookPak and click OK. For each table or chart, provide a description and explanation of what is being displayed. 6. Conclusions: Restate the hypotheses and explain whether or not the educated guess was correct. Include limitations of the experiment (in other words, describe other factors that would make the experiment better or possible errors associated with the experiment). Provide suggestions for future research. 7. Last Page: Include, at the end of the document, a summary of all the tasks required to complete the assignment, and which member or members of the group were principally responsible for completing those tasks. This should be in the form of a simple list. 8. Presentation: Summarize the report, excluding the last page. Due Date: This assignment is to be completed and turned in at the beginning of your laboratory meeting during the week of 11th March. Microsoft office package: Excel: Data tab functions, round, drag-drop, $-sign functions, Beginning of analysis toolpak-t-tests

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