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A car driver is travelling at speed v on a straight road. He comes over the top of a hill to find a fallen tree on the road ahead. He immediately brakes hard but travels a distance of 60 m at speed v... A 120 kg crate is dragged along the horizontal ground by a 200 N force acting at an angle of 30 to the horizontal, as shown. The crate moves along the surface with a constant velocity of 0.5 m s 1 .... Does It Make Sense? For Exercises, determine whether the statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain clearly. Not all of these statements have... This diagram shows an electron tube. Electrons emitted from the cathode accelerate towards the anode and then pass into a uniform electric field created by two oppositely charged horizontal metal... Let X~N(35, 42). Find: a. P(X < 30.5) b. P(30.5 X < 40.5) c. P(40.5 X 46.5) d. P(X 46.5) For each following question, clearly state: Your hypotheses The value of the test statistic The number... Listed below are measurements of the head injury criterion (hic) for seven small cars tested in crashes by the National Highway Traffic Safety Administration: Chevrolet Aveo, Honda Civic, Volvo S40,... Suggest reasons why different techniques produce different molar mass averages. Suppose you have a list of blood platelet counts from 500 patients in a hospital. Which of the following is most helpful in understanding the distribution of those values: frequency table, pie chart,... Show that the dipole moment of a collection of charges is independent of origin, provided that the net charge is zero. Also, show that the quadrupole moment is independent of origin if the dipole... Adult males have sitting knee heights that are normally distributed with a mean of 21.4 inches and a standard deviation of 1.2 inches. Use the 6 895 99.7 rule to find the indicated quantity. a. Find... Find all the possible angles with respect to the z-axis for an angular momentum vector of magnitude 6h. A 4.0 L sample of O 2 gas has a pressure of 1.0 bar. A 2.0 L sample of N 2 gas has a pressure of 2.0 bar. If these two samples are mixed and then compressed in a 2.0 L vessel, what is the final... ``Geometric Programming, by Robert E. D. Woolsey, UMAP 737. This unit provides some alternative optimization formulations, including geometric programming. Familiarity with basic differential... Calculate the surface area of (a) A 1 g single crystal of cristobalite (density = 2.3 g/cm 3 , assume the crystal takes a spherical shape), (b) A uniform powder of spherical crystals each with a... The generalized coordinates of a simple pendulum are the angular displacement \(\theta\) and the angular momentum \(m l^{2} \dot{\theta}\). Study, both mathematically and graphically, the nature of... A sample of gravel from a stockpile weighs 15 lb (6.80 kg). After oven drying, the sample weighs 14.2 lb (6.44 kg). Calculate the moisture content of the sample. Using Table 21, how many working minutes per hour would you expect to achieve on a project whose job conditions and management conditions are both rated poor? Table 2 -1: Below are two potential methods for preparing the same ether, but only one of them is successful. Identify the successful aproach and explain your choice. NaOMe ONa CH3I Using any compounds that contain two carbon atoms or fewer, show a way to prepare a racemic mixture of (2R, 3R)- 2,3-dihydroxypentane and (2S,3S)-2,3-dihydroxypentane. Each of the following compounds contains two carbonyl groups. Identify which carbonyl group will exhibit a signal at lower wave number. a. b. c. O: Draw a mechanism and predict the major product of the following reaction. 1) Excess LAH 2) H30* Predict the major organic product for each of the following reactions. a. b. c. d. e. f. ? PCC C-Clz - - NazCrz07 H2SO4. H20 In some circumstances, dehydrogenation is observed. Dehydrogenation involves the loss of two hydrogen atoms (the reverse of hydrogenation). Analyze each of the following dehydrogenation reactions and... (S)-1-Bromo-1,2-diphenylethane reacts with a strong base to produce cis-stilbene and trans-stilbene: a) This reaction is stereo-selective, and the major product is trans-stilbene. Explain why the... Draw the major product for each of the following reactions: (a) (b) (c) 1) 9-BBN 2) H2O2, NaOH 1) Disiamylborane 2) H20, NaOH Draw the mechanism for each of the following reaction. a. b. c. socl, Py Br PBr3 For each of the following reactions, predict the product and draw the mechanism of its formation. a. b. c. d. e. f. 1) PhMgBr 2) H20 Me 1) NaCN 2) H20 *Me For each reaction, predict the product and draw the mechanism of its formation. a. b. Provide a systematic (IUPAC) name for each of the following compounds: (a) (b) (c) (d) H. Predict the major product of the following reaction. HOS Dilute H2SO. ,5S. O,H We set the potential energy in the particle in the box equal to zero and justified it by saying that there is no absolute scale for potential energy. Is this also true for kinetic energy? Calculate the expectation value for the potential energy of the H atom with the electron in the 1s orbital. Compare your result with the total energy. Propose an efficient synthesis for each of the following compounds using the malonic ester synthesis. (a) (b) (c) (d) (e) Which of the following functions are acceptable wave functions over the indicated interval? a. e x 0 < x < b. e 2ix 100 < x < 100 c. e x < x < d. 1/x 1 < < Which of the following functions are acceptable wave functions over the indicated interval? a. e x2/2 < x < b. e ix 0 < x < 2 c. x 2 e 2ix 0 < x < d. xe x 0 < x < Some symmetry operations can be carried out physically using a ball-and-stick model of a molecule without disassembly and reassembly and others can only be imagined. Give two examples of each... The Doppler broadening in a gas can be expressed as where M is the molar mass. For the sodium transition, ν 0 5.0933 à 10 14 s -1 . Calculate Îν and... A certain reaction is first order, and 540. s after initiation of the reaction, 32.5% of the reactant remains. a. What is the rate constant for this reaction? b. At what time after initiation of the... Classify the following functions as symmetric, antisymmetric, or neither in the exchange of electrons 1 and 2: a. [1s (1) 2s (2) + 2s (1) 1s (2)] [ (1) (2) (1) (2)] b. [1s (1) 2s (2) + 2s (1) 1s... Prednisolone acetate is an anti-inflammatory agent in clinical use. It is similar in structure to cortisol, with the following two differences: (1) Prednisolone acetate exhibits a double bond between... Draw the mechanism of formation of PET in acidic conditions. It might be helpful to first review the mechanism for the Fischer esterification process. Identify which of the following monomers would be most reactive toward anionic polymerization: CH3 OAc CN A technique for radioactively labeling proteins is electrophilic radioiodination, in which an aromatic substitution of 131 I onto a tyrosine residue is performed as follows: Using the activity of 131... Hydrogen abstraction from hydrocarbons by atomic chlorine is a mechanism for Cl · loss in the stratosphere. Consider the reaction of Cl· with ethane: C 2 H 6 (g) + Cl· (g) C 2 H... Determine the maximum normal stress developed in the bar when it is subjected to a tension of P = 8 kN. 5 mm 40 mm 20 mm r = 10 mm 20 mm The bars of the truss each have a cross-sectional area of 1.25 in 2 . Determine the average normal stress in members AB, BD, and CE due to the loading P = 6 kip. State whether the stress is tensile... Determine the largest intensity w of the uniform loading that can be applied to the frame without causing either the average normal stress or the average shear stress at section bb to exceed s = 15... Part of a control linkage for an airplane consists of a rigid member CB and a flexible cable AB. If a force is applied to the end B of the member and causes it to rotate by θ = 0.5°,... The load is supported by the four 304 stainless steel wires that are connected to the rigid members AB and DC. Determine the angle of tilt of each member after the 500-lb load is applied. The members... The 60-mm-diameter shaft is made of 6061-T6 aluminum having an allowable shear stress of Ï allow = 80 MPa. Determine the maximum allowable torque T. Also, find the corresponding angle of twist... The composite shaft consists of a mid-section that includes the 1-in.-diameter solid shaft and a tube that is welded to the rigid flanges at A and B. Neglect the thickness of the flanges and... The beam is made from three boards nailed together as shown. If the moment acting on the cross section is M = 600 N m, determine the maximum bending stress in the beam. Sketch a three-dimensional... The shaft is supported by smooth journal bearings at A and B that only exert vertical reactions on the shaft. Determine its smallest diameter d if the allowable bending stress is Ï allow = 180... Determine the smallest allowable diameter of the shaft. The shaft is supported by a thrust bearing at A and a journal bearing at B. The allowable bending stress is Ï allow = 22 ksi. 400 lb 300... The H-beam is subjected to a shear of V = 80 kN. Determine the shear flow at point A. 250'mm 30 mm 300 mm -25 mm 50 mm -25 mm The assembly is subjected to a vertical shear of V = 7 kip. Determine the shear flow at points A and B and the maximum shear flow in the cross section A- 0.5 in. B- 6 in. 2 in 6 in.. 0.5 in. 0.5 in.... The solid rod is subjected to the loading shown. Determine the state of stress at point C, and show the results on a differential volume element located at this point. 200 mm 200 mm 20 kN 'B 100 kN... Determine the principal stresses in the cantilevered beam at points A and B 30 mm- 40 mm- Bz 800 mm 120 mfm 1200 mm 150 mm 15 kN Determine (a) the principal stresses and (b) the maximum in-plane shear stress and average normal stress. Specify the orientation of the element in each case. 80 MPa 60 MPa Draw Mohrs circle that describes each of the following states of stress. 2 ksi | 600 psi 20 MPa 800 psi (a) (b) (c) Determine (a) the principal stresses and (b) the maximum in-plane shear stress and average normal stress. Specify the orientation of the element in each case. 30 ksi 9 ksi The thin-walled pipe has an inner diameter of 0.5 in. and a thickness of 0.025 in. If it is subjected to an internal pressure of 500 psi and the axial tension and torsional loadings shown, determine... The T-beam is made from concrete having a specific weight of 150 lb/ft 3 . Determine the dead load per foot length of beam. Neglect the weight of the steel reinforcement. 40 in.- 8 in. 26 in. F10 in. Classify each of the frames as statically determinate or indeterminate. If indeterminate, specify the degree of indeterminacy. All internal joints are fixed connected. a. b. c. d. Determine the force in each member of the truss. State if the members are in tension or compression.Assume all members are pin connected.AG = GF = FE = ED. 8 kN 8 kN 8 kN 4 kN 4 kN 2 m 4 m - 4 m Determine the forces in all the members of the complex truss. State if the members are in tension or compression. 600 lb 130 30 FO 12 ft 45 45 -6 ft 6 ft Determine the force in each member and state if the members are in tension or compression. 4 kN 4 kN m- 2 m Draw the shear and moment diagrams for each member of the frame. 10 kN 5 kN 5 kN IB 2 kN/m 4 m F3m -3 m--2 m--2 m-3 m- The beam supports a uniform dead load of 500 N/m and a single live concentrated force of 3000 N. Determine (a) The maximum positive moment at C, and (b) The maximum positive shear at C. Assume the... Determine the absolute maximum moment in the girder bridge due to the truck loading shown. The load is applied directly to the girder. 15 k 10 k 3k 20 ft 8 ft 4 ft B. 80 ft Glycerin has a specific gravity of 1.258. How much would 0.50 m 3 of glycerin weigh? What would be its mass? A storage vessel for gasoline (sg = 0.68) is a vertical cylinder 30 ft in diameter. If it is filled to a depth of 22 ft, calculate the number of gallons in the tank and the weight of the gasoline. The viscosity of an oil is given as 80 SUS at 100F. Determine the viscosity in m 2 /s. Calculate the mass of 1 gal of oil if it weighs 7.8 lb. A boater travels from some initial point P 1? to a final point P 2 along the dashed line shown in Figure P1.58. Find and the total distance traveled. Figure P1.58 ? y P -77 m- 195 m P2 Require that you convert the given pressure from gage to absolute pressure or from absolute to gage pressure as indicated. The value of the atmospheric pressure is given. Given Pressure P atm Express... For the manometer shown in Fig. 3.30, calculate (p A - p B ). Water IB 150 mm - Mercury (sg = 13.54) 900 mm Oil (sg = 0.86) 600 mm A vat has a sloped side, as shown in Fig. 4.27. Compute the resultant force on this side if the vat contains 15.5 ft of glycerin. Also compute the location of the center of pressure and show it on a... Refer to Fig. 4.31. 450-mm diameter 0.45 m 1.5 m Circular view port is centered in inclined side of Oil tank. (sg = 0.85) 0.30 m 300 Use Fig. 4.52. The surface is 1.50 m long. Water 2,80 m 1.20-m radius What is the critical angle for total internal reflection for diamond in air? What, if anything, does the critical angle have to do with the luster of a well-cut diamond? The instrument package shown in Fig. 5.18 weighs 258 N. Calculate the tension in the cable if the package is completely submerged in seawater having a specific weight of 10.05 kN/m 3 . Water surface... Repeat Problem 6.47, but use Schedule 80 DN pipe. Repeat Problem Table 6.2 shows the typical volume flow rate for centrifugal fire-fighting pumps is in the range of 1800 L/min to 9500 L/min. Specify... What pressure is required above the water in Fig. 6.13 to cause the jet to rise to 9.50 m? The water depth is 1.50 m. 40.0 ft Air pressure h = 6.0 ft Figure 6.30 shows a manometer being used to indicate the pressure difference between two points in a fabricated system. Calculate the volume flow rate of water in the system if the manometer... For the siphon in Fig. 6.26, calculate the distance X required to obtain a volume flow rate of 7.1 à 10 -3 m 3 /s. +B Water 50-mm OD x 1.5-mm wall 25-mm diameter A+ A flow nozzle, shown in Fig. 6.18, is used to measure the velocity of flow. If the nozzle is installed inside a 14-in Schedule 40 pipe and the nozzle diameter is 4.60 in, compute the velocity of flow... Hot water at 80C is flowing to a dishwasher at a rate of 15.0 L/min through a standard hydraulic copper tube, 15 mm OD 1.2 mm wall. Is the flow laminar or turbulent? Benzene at 60C is flowing in a DN 25 Schedule 80 steel pipe at the rate of 20 L/min. The specific weight of the benzene is 8.62 kN/m 3 . Calculate the pressure difference between two points 100 m... Water at 60°F is being pumped from a stream to a reservoir whose surface is 210 ft above the pump. See Fig. 8.19. The pipe from the pump to the reservoir is an 8-in Schedule 40 steel pipe, 2500... Calculate the mesh currents i 1 and i 2 in Fig. 3.92 . 10 ww 10 www + 10 2 40 V Find v o in the op amp circuit of Fig. 5.92 . 100 k2 www 100 k2 10 k2 100 k2 30 2 30 k2 +. ww- 70 mv 70 kQ Vo Q+ Determine the voltage input to the inverting terminal of an op amp when 40 V is applied to the noninverting terminal and the output through an openloop gain of 150,000 is 15 V. Using Fig. 4.102 , design a problem that will help other students better understand Thevenin equivalent circuits. Find the Thevenin equivalent at terminals a-b of the circuit in Fig. 4.102. R3 R, R2... Use source transformation to find v o in the circuit of Fig. 4.97 . 4 k2 3vo 2 k2 Vo 1 k2 3 mA Compute points on the velocity profile from the pipe wall to the centerline of a 2-in Schedule 40 steel pipe if the volume flow rate of castor oil at 77F is 0.25 ft 3 /s. Figure 9.20 shows a liquid-to-air heat exchanger in which air flows at 50 m 3 /h inside a rectangular passage and around a set of five vertical tubes. Each tube is a standard hydraulic steel tube, 15... Calculate the pressure difference across a fully open angle valve placed in a 5-in Schedule 40 steel pipe carrying 650 gal/min of oil (sg = 0.90). Compute the energy loss that would occur as 50 gal/min of water flows from a tank into a steel tube with an OD of 2.0 in and a wall thickness of 0.065 in. The tube is installed flush with the inside... Determine the energy loss due to a sudden enlargement from a 50 mm OD 2.4 mm wall plastic pipe to a 90 mm OD 2.8 mm wall plastic pipe when the velocity of flow is 3 m/s in the smaller pipe.
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