What is the prime purpose of selecting a composite material over material from the other family groups? MODULE 3 – STRUCTURE OF SOLID MATERIALS The ability of a material to exist in different space lattices is called a. Allotropic b. Crystalline c. Solvent d. Amorphous Amorphous metals develop their microstructure as a result of ___________. a. Dendrites b. Directional solidification c. Slip d. Extremely rapid cooling In an alloy, the material that dissolves the alloying element is the ___________. a. Solute b. Solvent c. Matrix d. Allotrope What is the coordination number (CN) for the fcc structure formed by ions of sodium and chlorine that is in the chemical compound NaCl (salt) ? a. 6 b. 8 c. 14 d. 16 What pressure is normally used in constructing a phase diagram? a. 100 psi b. Depends on material c. Ambient d. Normal atmospheric pressure What line on a binary diagram indicates the upper limit of the solid solution phase? a. Liquidus b. Eutectic c. Eutectoid d. Solidus What holds the atoms (ions) together in a compound such as NaCl are electrostatic forces between ___________. a. Atom and ion b. Covalent bonds c. Electrons and nuclei d. Neutrons Diffusion of atoms through a solid takes place by two main mechanisms. One is diffusion through vacancies in the atomic structure. Another method of diffusion is ___________. a. Cold b. APF c. Substitutional d. Interstitial Give a brief explanation of the Lever rule (P117) Grain boundaries ___________ movement of dislocations through a solid. a. Improve b. Inhibit c. Do not affect Iron can be alloyed with carbon because it is ___________. a. Crystalline b. Amorphous c. A mixture d. Allotropic Metals can be cooled only to crystalline solids. a. T (true) b. F (false) Sketch an fcc unit cell. Metals are classified as crystalline materials. Name one metal that is an amorphous solid and name at least one recent application in which its use is saving energy or providing greater strength and/or corrosion resistance. MODULE 4 – MECHANICAL PROPERTIES Give two examples of a mechanical property. a. Thermal resistance b. Wear resistance c. Hardness d. Strength Scissors used in the home cut material by concentrating forces that ultimately produce a certain type of stress within the material. Identify this stress. a. Bearing stress b. Shearing stress c. Compressive stress An aluminum rod 1 in. in diameter (E =10.4 x 106psi) experiences an elastic tensile strain of 0.0048 in./in. Calculate the stress in the rod. a. 49,920 ksi b. 49,920 psi c. 49,920 msi A 1-in.-diameter steel circular rod is subject to a tensile load that reduces its cross-sectional area to 0.64 in2. Express the rod’s ductility using a standard unit of measure. a. 18.5% b. 1.85% c. 18.5 d. (a) and (c) What term is used to describe the low-temperature creep of polymerics? a. Springback b. Creep rupture c. Cold flow d. Creep forming MODULE 7 – TESTING, FAILURE ANALYSIS, STANDARDS, & INSPECTION Factors of safety are defined either in terms of the ultimate strength of a material or its yield strength. In other words, by the use of a suitable factor, the ultimate or yield strength is reduced in size to what is known as the design stress or safe working stress. Which factor of safety would be more appropriate for a material that will be subjected to repetitious, suddenly applied loads? Product liability court cases have risen sharply in recent years because of poor procedures in selecting materials for particular applications. Assuming that a knowledge of a material’s properties is a valid step in the selection process, cite two examples where such lack of knowledge could or did lead to failure or unsatisfactory performance. Make a sketch and fully dimension an Izod impact test specimen. Which agency publishes the Annual Book of standard test methods used worldwide for evaluation of materials? a. NASA b. NIST c. ASTM d. SPE

What is the prime purpose of selecting a composite material over material from the other family groups? MODULE 3 – STRUCTURE OF SOLID MATERIALS The ability of a material to exist in different space lattices is called a. Allotropic b. Crystalline c. Solvent d. Amorphous Amorphous metals develop their microstructure as a result of ___________. a. Dendrites b. Directional solidification c. Slip d. Extremely rapid cooling In an alloy, the material that dissolves the alloying element is the ___________. a. Solute b. Solvent c. Matrix d. Allotrope What is the coordination number (CN) for the fcc structure formed by ions of sodium and chlorine that is in the chemical compound NaCl (salt) ? a. 6 b. 8 c. 14 d. 16 What pressure is normally used in constructing a phase diagram? a. 100 psi b. Depends on material c. Ambient d. Normal atmospheric pressure What line on a binary diagram indicates the upper limit of the solid solution phase? a. Liquidus b. Eutectic c. Eutectoid d. Solidus What holds the atoms (ions) together in a compound such as NaCl are electrostatic forces between ___________. a. Atom and ion b. Covalent bonds c. Electrons and nuclei d. Neutrons Diffusion of atoms through a solid takes place by two main mechanisms. One is diffusion through vacancies in the atomic structure. Another method of diffusion is ___________. a. Cold b. APF c. Substitutional d. Interstitial Give a brief explanation of the Lever rule (P117) Grain boundaries ___________ movement of dislocations through a solid. a. Improve b. Inhibit c. Do not affect Iron can be alloyed with carbon because it is ___________. a. Crystalline b. Amorphous c. A mixture d. Allotropic Metals can be cooled only to crystalline solids. a. T (true) b. F (false) Sketch an fcc unit cell. Metals are classified as crystalline materials. Name one metal that is an amorphous solid and name at least one recent application in which its use is saving energy or providing greater strength and/or corrosion resistance. MODULE 4 – MECHANICAL PROPERTIES Give two examples of a mechanical property. a. Thermal resistance b. Wear resistance c. Hardness d. Strength Scissors used in the home cut material by concentrating forces that ultimately produce a certain type of stress within the material. Identify this stress. a. Bearing stress b. Shearing stress c. Compressive stress An aluminum rod 1 in. in diameter (E =10.4 x 106psi) experiences an elastic tensile strain of 0.0048 in./in. Calculate the stress in the rod. a. 49,920 ksi b. 49,920 psi c. 49,920 msi A 1-in.-diameter steel circular rod is subject to a tensile load that reduces its cross-sectional area to 0.64 in2. Express the rod’s ductility using a standard unit of measure. a. 18.5% b. 1.85% c. 18.5 d. (a) and (c) What term is used to describe the low-temperature creep of polymerics? a. Springback b. Creep rupture c. Cold flow d. Creep forming MODULE 7 – TESTING, FAILURE ANALYSIS, STANDARDS, & INSPECTION Factors of safety are defined either in terms of the ultimate strength of a material or its yield strength. In other words, by the use of a suitable factor, the ultimate or yield strength is reduced in size to what is known as the design stress or safe working stress. Which factor of safety would be more appropriate for a material that will be subjected to repetitious, suddenly applied loads? Product liability court cases have risen sharply in recent years because of poor procedures in selecting materials for particular applications. Assuming that a knowledge of a material’s properties is a valid step in the selection process, cite two examples where such lack of knowledge could or did lead to failure or unsatisfactory performance. Make a sketch and fully dimension an Izod impact test specimen. Which agency publishes the Annual Book of standard test methods used worldwide for evaluation of materials? a. NASA b. NIST c. ASTM d. SPE

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Two loads in the circuit shown in Figure 2 can be described as follows: Load 1 absorbs an average of 8kW at a leading power factor of 0.80. Load 2 absorbs 20kVA at a lagging power factor of 0.60. a. Determine the power factor of the combined two loads in parallel. b. Determine the source current. c. If the frequency is 60Hz, find the value of the capacitor which, if placed in parallel with the two loads, would correct the power factor to 1.00.

Two loads in the circuit shown in Figure 2 can be described as follows: Load 1 absorbs an average of 8kW at a leading power factor of 0.80. Load 2 absorbs 20kVA at a lagging power factor of 0.60. a. Determine the power factor of the combined two loads in parallel. b. Determine the source current. c. If the frequency is 60Hz, find the value of the capacitor which, if placed in parallel with the two loads, would correct the power factor to 1.00.

A three phase four pole winding of the double layer type is to be installed on a 48 slot stator. The pitch of the stator windings is 5 / 6 and there are 10 turns per coil in the windings. All coils in each phase are connected in series and the three phases are connected in Δ. The flux per pole in the machine is 0.054 Wb and the speed of rotation of the magnetic field is 1800 RPMWhat is the pitch factor of this winding?

A three phase four pole winding of the double layer type is to be installed on a 48 slot stator. The pitch of the stator windings is 5 / 6 and there are 10 turns per coil in the windings. All coils in each phase are connected in series and the three phases are connected in Δ. The flux per pole in the machine is 0.054 Wb and the speed of rotation of the magnetic field is 1800 RPMWhat is the pitch factor of this winding?

The Classic Five-Part Structure 1. Introduce the topic to be argued. Establish its importance. 2. Provide background information so readers will be able to follow your discussion. 3. State your claim (your argumentative thesis) and develop your argument by making a logical appeal. Support your claims with facts, opinions, and examples. If appropriate, mix an emotional appeal or an appeal to authority with your logical appeals. 4. Acknowledge counterarguments and treat them with respect. Rebut these arguments. Reject their evidence or their logic or concede some validity and modify your claim accordingly. Be flexible; you might split the counterarguments and rebut them one at a time at different locations in the paper, or you might begin the paper with a counterargument, rebut it, and then move on to your own claim. 5. Conclude by summarizing the main points of your argument. Then remind readers of what you want them to believe or do. Give them something to remember. The Problem-Solution Structure I. There is a serious problem. A. The problem exists and is growing. (Provide support for argument.) B. The problem is serious. (Provide support.) C. Current methods cannot cope with the problem. (Provide support.) II. There is a solution to the problem. (Your claim goes here.) A. The solution is practical. (Provide support.) B. The solution is desirable. (Provide support.) C. We can implement the solution. (Provide support.) D. Alternate solutions are not as strong as the proposed solution. (Review – and reject – competing solutions.) In both cases, you know before you begin writing whether you will use an inductive (analytic) or deductive (synthetic) arrangement for your argument. The decision to move inductively or deductively is about strategy. Induction moves from support to a claim. Deduction moves from a claim to support – to particular facts, opinions, and examples. This is the preferred form for most writing in the humanities. You can position your claim at the beginning, middle, or end of your presentation. In the problem/solution structure, the claim is made only after the writer introduces a problem. With the five-part structure, you have more flexibility in positioning your claim. One factor that can help determine placement is the likelihood of your audience agreeing with you. When your audience is likely to be neutral or supportive, making your claim early on will not alienate readers (synthetic presentation). When your audience is likely to disagree, placing your thesis at the end of your presentation allows you time to build a consensus, step by step, until you reach your conclusion (analytical presentation).

The Classic Five-Part Structure 1. Introduce the topic to be argued. Establish its importance. 2. Provide background information so readers will be able to follow your discussion. 3. State your claim (your argumentative thesis) and develop your argument by making a logical appeal. Support your claims with facts, opinions, and examples. If appropriate, mix an emotional appeal or an appeal to authority with your logical appeals. 4. Acknowledge counterarguments and treat them with respect. Rebut these arguments. Reject their evidence or their logic or concede some validity and modify your claim accordingly. Be flexible; you might split the counterarguments and rebut them one at a time at different locations in the paper, or you might begin the paper with a counterargument, rebut it, and then move on to your own claim. 5. Conclude by summarizing the main points of your argument. Then remind readers of what you want them to believe or do. Give them something to remember. The Problem-Solution Structure I. There is a serious problem. A. The problem exists and is growing. (Provide support for argument.) B. The problem is serious. (Provide support.) C. Current methods cannot cope with the problem. (Provide support.) II. There is a solution to the problem. (Your claim goes here.) A. The solution is practical. (Provide support.) B. The solution is desirable. (Provide support.) C. We can implement the solution. (Provide support.) D. Alternate solutions are not as strong as the proposed solution. (Review – and reject – competing solutions.) In both cases, you know before you begin writing whether you will use an inductive (analytic) or deductive (synthetic) arrangement for your argument. The decision to move inductively or deductively is about strategy. Induction moves from support to a claim. Deduction moves from a claim to support – to particular facts, opinions, and examples. This is the preferred form for most writing in the humanities. You can position your claim at the beginning, middle, or end of your presentation. In the problem/solution structure, the claim is made only after the writer introduces a problem. With the five-part structure, you have more flexibility in positioning your claim. One factor that can help determine placement is the likelihood of your audience agreeing with you. When your audience is likely to be neutral or supportive, making your claim early on will not alienate readers (synthetic presentation). When your audience is likely to disagree, placing your thesis at the end of your presentation allows you time to build a consensus, step by step, until you reach your conclusion (analytical presentation).

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A random sample of size n = 100 is taken from a population of size N = 3,000 with a population proportion of p = 0.34. a. Is it necessary to apply the finite population correction factor? Explain. Calculate the expected value and the standard deviation of the sample proportion. b. What is the probability that the sample proportion is greater than 0.37?

A random sample of size n = 100 is taken from a population of size N = 3,000 with a population proportion of p = 0.34. a. Is it necessary to apply the finite population correction factor? Explain. Calculate the expected value and the standard deviation of the sample proportion. b. What is the probability that the sample proportion is greater than 0.37?

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1) If a superalloy jet engine is heated so that its length in each direction expands by 1%, what is its percentage change in volume (assume it is roughly cubic)? Hint: Calculate its volume before and after heating, assuming that its length, height, and width are the same, i.e., a cubic engine. 2) Calculate the density of Al in g/cm3, given that it forms an FCC crystal structure with an atomic radius of 0.143 nm (10-7 cm) and a mass of 27 g/mole. Avogadro’s number is 6.02 x 1023 atoms/mole. Hint: calculate the number of atoms in each cell carefully. 3) Calculate the vacancy concentration in aluminum at 50%, 70%, and 90% of TMP=923 K. Gvf = 0.66 eV, and k = 8.62 x 10-5 eV/K. Calculate ln (nv/N) and 1/T, and plot on a linear scale (hint: should be a straight line). 4) a) If the vacancy concentration in Cu is measured to be 10-5 at 1300K (near its melting point), what is Evf? (assume the pre-exponential factor is 1; ie, nv/N = exp (-Evf/kT) b) What would be the concentration at 650 K? 5) Determine the largest size of an interstitial hole in FCC Fe. RFe = 0.124 nm. Would a C atom sit in an interstitial or substitutional site (rC = 0.077 nm)?

1) If a superalloy jet engine is heated so that its length in each direction expands by 1%, what is its percentage change in volume (assume it is roughly cubic)? Hint: Calculate its volume before and after heating, assuming that its length, height, and width are the same, i.e., a cubic engine. 2) Calculate the density of Al in g/cm3, given that it forms an FCC crystal structure with an atomic radius of 0.143 nm (10-7 cm) and a mass of 27 g/mole. Avogadro’s number is 6.02 x 1023 atoms/mole. Hint: calculate the number of atoms in each cell carefully. 3) Calculate the vacancy concentration in aluminum at 50%, 70%, and 90% of TMP=923 K. Gvf = 0.66 eV, and k = 8.62 x 10-5 eV/K. Calculate ln (nv/N) and 1/T, and plot on a linear scale (hint: should be a straight line). 4) a) If the vacancy concentration in Cu is measured to be 10-5 at 1300K (near its melting point), what is Evf? (assume the pre-exponential factor is 1; ie, nv/N = exp (-Evf/kT) b) What would be the concentration at 650 K? 5) Determine the largest size of an interstitial hole in FCC Fe. RFe = 0.124 nm. Would a C atom sit in an interstitial or substitutional site (rC = 0.077 nm)?

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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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Normal time for a stopwatch study is equal to which of the following? Answer Average observed time × Performance rating factor Average observed time + Performance rating factor Average observed time / Performance rating factor Average observed time – Performance rating factor

Normal time for a stopwatch study is equal to which of the following? Answer Average observed time × Performance rating factor Average observed time + Performance rating factor Average observed time / Performance rating factor Average observed time – Performance rating factor

Normal time for a stopwatch study is equal to which … Read More...
NAME: _____________________________________________ (print) INTRODUCTORY SURVEYING – MINING ENGINEERING 2400 Second Midterm Exam October 24, 2014 Work all four problems in the space provided. Solutions must be neat and logically presented for full credit. 1. (25 pts) Put an “X” over the letter corresponding to correct answers for the following multiple choice questions. A theodolite is used to estimate a distance using stadia. The stadia factor is 100, the stadia constant is zero, the zenith angle is 90°, the upper reading is 10.20, the rod reading is 7.75 and the lower reading is 5.30. The best estimate for horizontal distance is: (a) 1020 ft; (b) 490 ft; (c) 245 ft; (d) if none of the preceding – provide your answer . From B the azimuth to A is 233° 15′ 30″. The angle right to C is 215° 05′ 15″. The azimuth of C to B is: (a)88°20’45”; (b) 268°20’45”; (c) 250°10’30”; (d) if none of the preceding – provide your answer. A five-level station is described as C3.5/34.1 C4.8/25.0 C6.7/0.0 C9.2/25.0 C10.8/33.6. How wide is the road? (a) 50.0 ft, (b) 67.7 ft, (c) 25.0 ft, (e) if none of the preceding – provide your answer . An engineer used a total station to complete a closed traverse at a construction site. The sum of LAT and sum of DEP were determined to be 0.04 and 0.07 respectively. The total horizontal distance measured 2510.00 ft. What is the corresponding precision? (a) 1/63000; (b) 1/36000; (c) 1/31000; (d) if none of the preceding-provide your answer. The interior angles of a closed six sided traverse measure: 34° 28′ 20″ 185° 37′ 00″ 110° 59′ 20″ 195° 10′ 40″ 81° 40′ 20″ 112° 05′ 20″ In adjusting this traverse, the adjusted value for the first angle is: (a) 34° 28′ 20″; (b) 34° 28′ 10″; ( c) 34° 28′ 30″; (d) if none of the preceding – provide your answer . 2. (15 pts) Given the position of points A and B, determine the azimuth of A to B to the nearest second. Point A 5470.00N 4710.00E Point B 5130.00N 5350.00E 3. (25 pts) The volume of a fill between station 24+00 and 26+00 on a 50-foot wide road is to be determined by the prismoidal method. The three level sections are given by: Stn. 24+00 F10.0 F12.0 F8.0 52.0 0.0 65.0 Stn. 25+00 F8.0 F10.0 F10.0 55.0 0.0 52.0 Stn. 26+00 F12.0 F8.0 F15.0 61.0 0.0 55.0 Determine the volume to the nearest 100 cubic feet. (All fill dimensions are in feet.) (Hint: The area at Stn. 25 is 760 sq ft and the area at Stn. 26 is 801.5 sq ft.) 4. (35 points) The following information was obtained from an angle-right traverse conducted on the surface with a total station (conventional practice for HI and HS, i.e. HS is above the target of interest and, therefore, indicated as negative in the notes): BS IS FS Angle Rt. Zenith Angle SD HI HS A B C 261°12’20” 97° 25’20” 355.33 4.99 -0.33 261°11’40” 262° 34’20” The position of B is N5000.00, E5000.00, El 5000.00. The azimuth of A to B is 49°18’30”. Determine the coordinates and elevation of C. Show and identify all intermediate calculations.

NAME: _____________________________________________ (print) INTRODUCTORY SURVEYING – MINING ENGINEERING 2400 Second Midterm Exam October 24, 2014 Work all four problems in the space provided. Solutions must be neat and logically presented for full credit. 1. (25 pts) Put an “X” over the letter corresponding to correct answers for the following multiple choice questions. A theodolite is used to estimate a distance using stadia. The stadia factor is 100, the stadia constant is zero, the zenith angle is 90°, the upper reading is 10.20, the rod reading is 7.75 and the lower reading is 5.30. The best estimate for horizontal distance is: (a) 1020 ft; (b) 490 ft; (c) 245 ft; (d) if none of the preceding – provide your answer . From B the azimuth to A is 233° 15′ 30″. The angle right to C is 215° 05′ 15″. The azimuth of C to B is: (a)88°20’45”; (b) 268°20’45”; (c) 250°10’30”; (d) if none of the preceding – provide your answer. A five-level station is described as C3.5/34.1 C4.8/25.0 C6.7/0.0 C9.2/25.0 C10.8/33.6. How wide is the road? (a) 50.0 ft, (b) 67.7 ft, (c) 25.0 ft, (e) if none of the preceding – provide your answer . An engineer used a total station to complete a closed traverse at a construction site. The sum of LAT and sum of DEP were determined to be 0.04 and 0.07 respectively. The total horizontal distance measured 2510.00 ft. What is the corresponding precision? (a) 1/63000; (b) 1/36000; (c) 1/31000; (d) if none of the preceding-provide your answer. The interior angles of a closed six sided traverse measure: 34° 28′ 20″ 185° 37′ 00″ 110° 59′ 20″ 195° 10′ 40″ 81° 40′ 20″ 112° 05′ 20″ In adjusting this traverse, the adjusted value for the first angle is: (a) 34° 28′ 20″; (b) 34° 28′ 10″; ( c) 34° 28′ 30″; (d) if none of the preceding – provide your answer . 2. (15 pts) Given the position of points A and B, determine the azimuth of A to B to the nearest second. Point A 5470.00N 4710.00E Point B 5130.00N 5350.00E 3. (25 pts) The volume of a fill between station 24+00 and 26+00 on a 50-foot wide road is to be determined by the prismoidal method. The three level sections are given by: Stn. 24+00 F10.0 F12.0 F8.0 52.0 0.0 65.0 Stn. 25+00 F8.0 F10.0 F10.0 55.0 0.0 52.0 Stn. 26+00 F12.0 F8.0 F15.0 61.0 0.0 55.0 Determine the volume to the nearest 100 cubic feet. (All fill dimensions are in feet.) (Hint: The area at Stn. 25 is 760 sq ft and the area at Stn. 26 is 801.5 sq ft.) 4. (35 points) The following information was obtained from an angle-right traverse conducted on the surface with a total station (conventional practice for HI and HS, i.e. HS is above the target of interest and, therefore, indicated as negative in the notes): BS IS FS Angle Rt. Zenith Angle SD HI HS A B C 261°12’20” 97° 25’20” 355.33 4.99 -0.33 261°11’40” 262° 34’20” The position of B is N5000.00, E5000.00, El 5000.00. The azimuth of A to B is 49°18’30”. Determine the coordinates and elevation of C. Show and identify all intermediate calculations.

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