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The Hamiltonian of this model may be written as \[ H=-\frac{1}{2} c \sum_{i eq j} \sigma_{i} \sigma_{j}-\mu B \sum_{i} \sigma_{i} \] The double sum here is equal to \(\sum_{i} \sigma_{i} \sum_{j}... Ozone (O 3 ) has an absorptivity at 300. nm of 0.000500 torr 1 cm 1 . In atmospheric chemistry the amount of ozone in the atmosphere is quantified using the Dobson unit (DU), where 1 DU is equivalent... Determine the force in each member of the truss. State if the members are in tension or compression. 3k 2k 3 NG 12 ft D |C 10 ft- 10 ft - 10 ft- 10 ft- B. Determine the force in each member of the roof truss. State if the members are in tension or compression.Assume B is a pin and C is a roller support. H60. 60 60 30 60 B 2 m - 2 m- 2 kN 2 kN Determine the shear and moment throughout the beam as functions of x. 8 k 10 k 2 k/ft 40 k-ft - 6 ft 4 ft - A venturi meter is a device that uses a constriction in a flow system to measure the velocity of flow. Figure 6.17 illustrates one type of design. If the main pipe section is a standard hydraulic... A pipeline transporting crude oil (sg = 0.93) at 1200 L/min is made of DN 150 Schedule 80 steel pipe. Pumping stations are spaced 3.2 km apart. If the oil is at 10C, calculate (a) The pressure drop... Water at 10°C is being delivered to a tank on the roof of a building, as shown in Fig. 11.29. The elbow is standard. What pressure must exist at point A for 200 L/min to be delivered? 2.5 m... A circular culvert under a highway is 6 ft in diameter and is made of corrugated metal. It drops 1 ft over a length of 500 ft. Calculate the normal discharge when the culvert runs half full. Use the phasor method, described in conjunction with Fig. 7.17, to explain how two equal-amplitude waves of sightly different frequencies generate the beat pattern shown in Fig. 7.19 or Fig. P.7.19a.... A cart of mass m 1 = 10 kg slides down a friction less ramp and is made to collide with a second cart of mass m 2 = 20 kg, which then heads into a vertical loop of radius 0.25 m as shown in Figure... A beam of natural light is incident on an airglass interface (n ti = 1.5) at 40. Compute the degree of polarization of the reflected light. Figure P12.40 shows an experiment in which sound waves generated by a singer and having a single frequency are emitted by two speakers. These sound waves interfere at a listener located at point P.... An ion with the formula C 7 H 10 NO 2 + appears at m/z 140. (a) Write the formulas of the isotopologues contributing to m/z 141 and predict the intensity at m/z 141 relative to the intensity at m/z... a. Draw a dot-and-cross diagram for a molecule of selenium hexafluoride, SeF6. A single selenium atom has six electrons in its outer shell. b. Predict the shape of selenium hexafluoride. An object moving with s.h.m. goes through two complete cycles in 1.0 s. Calculate: a. The period T b. The frequency f c. The angular frequency . The diagram below shows a uniform metre rule, weight W, pivoted at the 75 cm mark and balanced by a force of 2 N acting at the 95 cm mark. a. Calculate the moment of the 2 N force about the pivot. b.... A boy stands on a cliff edge and throws a stone vertically upwards at time t = 0. The stone leaves his hand at 20 m s 1 . Take the acceleration of the ball as 9.81 m s 2 . a. Show that the equation... A 0.7812-g sample of impure Al 2 (CO 3 ) 3 decomposed with HCl; the liberated CO 2 was collected on calcium oxide and found to weigh 0.04380 g. Calculate the percentage of aluminum in the sample. Write down the expression for the radial distribution function of a 2p electron in a hydrogenic atom and determine the radius at which the electron is most likely to be found. (a) Can an intermediate appear as a reactant in the first step of a reaction mechanism? (b) On a reaction energy profile diagram, is an intermediate represented as a peak or a valley? (c) If a... The axial skeleton consists of the _______, while the appendicular skeleton consists of the _______. In the above question, calculate the thickness of the steady state overland flow at the base of the slope if the slope is uniform at 8 and the Darcy-Weisbach friction coefficient f = 0.3. From Figure 2.2, how much did the Earth warm between (a) 1880 and 2020 and (b) 1970 and 2020? Provide answers in both degrees Celsius and degrees Fahrenheit. Figure 2.2 anomaly (C) temperature 1.0... Consider the circumferential and translational vectors of a potential carbon nanotube shown below. (a) What are the n and m values of the circumferential vector C? (b) Is the T vector shown below a... Write a computer program to determine the height and base width (feet or meters) of the triangular spoil bank that will result from a rectangular trench excavation. Input should include the ditch... Predict the product and draw the mechanism for each of the following reactions: a. b. c. 1) LAH 2) H20 1) LAH 2) H20 Tetrahydrofuran (THF) can be formed by treating 1, 4-butanediol with sulfuric acid. Propose a mechanism for this transformation. H,SO, H;SO. 1,4-Butanediol Tetrahydrofuran (THF) Determine the maximum average shear stress in pin A of the truss. A horizontal force of P = 40 kN is applied to joint C. Each pin has a diameter of 25 mm and is subjected to double shear. 1.5 m A 2 m The shear stressstrain diagram for an alloy is shown in the figure. If a bolt having a diameter of 0.25 in. is made of this material and used in the lap joint, determine the modulus of elasticity E... The device is used to measure a change in temperature. Bars AB and CD are made of A-36 steel and 2014-T6 aluminum alloy, respectively. When the temperature is at 75°F, ACE is in the horizontal... The beam is constructed from three boards. If it is subjected to a shear of V = 5 kip, determine the maximum allowable spacing s of the nails used to hold the top and bottom flanges to the web. Each... The bell crank is pinned at A and supported by a short link BC. If it is subjected to the force of 80 N, determine the principal stresses at (a) point D and (b) point E. The crank is constructed from... The wide-flange beam is subjected to the 50-kN force. Determine the principal stresses in the beam at point A located on the web at the bottom of the upper flange. Although it is not very accurate,... The Howe truss is subjected to the loading shown. Determine the forces in members GF, CD, and GC. State if the members are in tension or compression. Assume all members are pin connected. 5 kN G- 5... Determine the force developed in each member of the space truss and state if the members are in tension or compression.The crate has a weight of 150 lb. 6 ft. RC 6 ft 6 ft, B. 6 ft Use the portal method of analysis and draw the moment diagram for column AFE. 5 k 12 ft 4 k 12 ft 15 ft- Convert 1250 millimeters to meters. If air has a constant specific weight of 0.075 lb/ft 3 , what pressure difference would result when driving from the base to the top of Pikes Peak, if the climb for the trip is 8400 ft? For the system shown in Fig. 6.24, calculate (a) the volume flow rate of oil from the nozzle and (b) the pressures at A and B. Oil 3,0 m (sg = 0.85) 35-mm diameter 120-mm OD x 3.5-mm wall Flow B+ FA+... What pressure is required above the water in Fig. 6.12 to cause the jet to rise to 28.0 ft? The water depth is 4.50 ft. h To what height will the jet of fluid rise for the conditions shown in Fig. 6.39? Jet 2.60 m 75 mm 0.85 m Determine the maximum power delivered to the variable resistor R shown in the circuit of Fig. 4.136. 2 Vx 10 (4 20 20 : 10 . www Use the superposition principle to obtain v x in the circuit of Fig. 10.89 . Let v s = 50 sin 2t V and i s = 12 cos(6t + 10°) A. 20 50 mF is Vx 20 X. Vs (+1 Two ideal HN-50 linear polarizers are positioned one behind the other. What angle should their transmission axes make if an incident unpolarized 100 W/m 2 beam is to be reduced to 30.0 W/m 2 on... Figure P.10.30 is a computer-generated Fraunhofer irradiance distribution. Describe the aperture that would give rise to such a pattern and give your reasoning in detail. Figure P.10.30 What alcohol would be obtained from treatment of each alkene in Problem 37 with aqueous sulfuric acid? Would any of these alkenes give a different product upon oxymercuration demercuration? Upon... Give the expected products of the following reactions or reaction sequences. (a) (b) (c) H,O, A BCH-CH,CH> CH,Br a. Predict the shapes of the following molecules i. Tetrachloromethane, CCl 4 ii. Beryllium chloride, BeCl 2 iii. Phosphorus(III) chloride. b. Draw dot-and-cross diagrams for the following molecules... A metal ball is dropped into a tall cylinder of oil. The ball initially accelerates but soon reaches a terminal velocity. a. By considering the forces on the metal ball bearing, explain why it first... A ball is fixed to the end of a string, which is attached to the ceiling at point P. As the drawing shows, the ball is projected downward at A with the launch speed 0 . Traveling on a circular path,... Two small spheres each of mass 20 g hang side by side with their centres 5.00 mm apart. Calculate the gravitational attraction between the two spheres. Prove that tanh -1 A + tanh -1 B = tanh -1 (A + B/1 + AB). a. The wave in the shallow tank of water shown in the figure moves at 0.08 m/s towards the left. How long does it take for the wave to return to the position 3CY, but moving to the right? b. A man is... A girl wearing a parachute jumps from a helicopter. She does not open the parachute straight away. The table shows her speed during the 9 seconds after she jumps. a. Copy and complete the table by... Copy and complete the following table. Place a tick or a cross in each box as appropriate. monomer polymer macromolecule polysaccharide contains subunits that form branched chains contains amino... A ship is pulled at a constant speed by two small boats, A and B, as shown. The engine of the ship does not produce any force. The tension in each cable between A and B and the ship is 4000 N. a.... This is a velocitytime graph for a vertically bouncing ball. The ball is released at A and strikes the ground at B. The ball leaves the ground at D and reaches its maximum height at E. The effects of... In a KRC Research poll, 1002 adults were asked if they felt vulnerable to identity theft, and 53% of them said yes. Test the claim that the majority of adults feel vulnerable to identity theft. A company makes climbing rope, which is cut to lengths of 50m with a standard deviation of 1.5m. A sample of 150 pieces of rope is measured and the results are recorded. Test, at the 5% significance... The chart shows average CO2 CO 2 emissions for fossil fuel vehicles (gasoline, diesel, and hybrid gas-electric), as well as electric vehicles. The abscissa is mg CO2 CO 2 per mile driven per pound... The backbone of organic compounds forms when ________atoms are covalently bonded. The diagram below depicts the concept of ________. a. Evolution b. Reproduction c. Levels of organization d. Energy transfers in the living world What are the structural and functional differences between slow and fast muscle? Match the terms and definitions. bone collagen synovial fluid osteocyte marrow metacarpals mandible sinuses a. spaces in certain skull bones b. all in the hands c. blood cell production d. a fibrous... Design a piece of art based on a magic square. Consider the unit of a carbon nanotube projected onto a graphene sheet shown below. (a) What are the n and m values of this carbon nanotube? (b) Is this a metallic or semiconducting nanotube? (c)... Identify the most electronegative element in each of the following compounds: a) CH 3 OCH 2 CH 2 NH 2 b) CH 2 ClCH 2 F c) CH 3 Li Propose a plausible mechanism for the following tautomerization process: . CH CH3 , Draw the mechanism and predict the product of the following reaction. In this case, H 3 O + must be used as a proton source instead of water. Explain why. 1) xs MeMgBr 2) H* Predict the major product of the following reaction. CI- AICI, CI Draw the structure of the major product obtained when aniline is treated with each of the following reagents: (a) Excess Br 2 (b) PhCH 2 COCl, py (c) Excess methyl iodide (d) NaNO 2 and HCl followed... The long bolt passes through the 30-mm-thick plate. If the force in the bolt shank is 8 kN, determine the average normal stress in the shank, the average shear stress along the cylindrical area of... The linkage is made of three pin-connected A992 steel members, each having a diameter of 1¼ in. Determine the magnitude of the force P needed to displace point B 0.25 in. to the right. t - 3... If the allowable bending stress is Ï allow = 150 MPa, determine the maximum intensity w of the uniform distributed load. -6 m 300 mm 150 mm The floor of the office building is made of 4-in.-thick lightweight concrete. If the office floor is a slab having a length of 20 ft and width of 15 ft, determine the resultant force caused by the... Determine the force in each member of the truss. State if the members are in tension or compression. 4 k 4 k 9 ft 2 k |C B 30 12 ft - 12 ft 12 ft Determine the force in each member of the roof russ. State if the members are in tension or compression. 8 kN 4 kN 4 kN 4 kN 4 kN - 4 kN - | 3.5 m 4 kN 6 @ 4 m = 24 m Determine the force in members GF, FB, and BC of the Fink truss and state if the members are in tension or compression. 600 lb 800 lb 800 lb E 60 30 60 30 D -10 ft -10 ft- -10 ft- Solve the equations x 1 + 2x 2 - 2x 3 = 5, x 1 - x 2 + x 3 = -1, x 1 - x 2 - x 3 = 1 Using the matrix equation x = A -1 C. Compute the pressure change required to cause a decrease in the volume of machine oil by 1.00 percent. Express the result in both psi and MPa. Water at 40C. Appendix D gives dynamic viscosity for a variety of fluids as a function of temperature. Using this appendix, give the value of the viscosity for the following fluids Describe the difference between an SAE 20 oil and an SAE 20W oil. Carbon dioxide has a density of 1.964 kg/m 3 at 0C. Calculate its specific weight. Figure P2.15 shows several hypothetical positiontime graphs. For each graph, sketch qualitatively the corresponding velocity time graph. Figure P2.15 Case 1 Case 2 Case 3 For the manometer shown in Fig. 3.28, calculate (p A - p B ). Oil (sg = 0.85) 8 in Water 33 in 12 in An isotropic quasimonochromatic point source radiates at a rate of 100 W. What is the flux density at a distance of 1 m? What are the amplitudes of the vector E- and vector B-fields at that point? When 2000 L/min of water flows through a circular section with an inside diameter of 300 mm that later reduces to a 150-mm diameter, calculate the average velocity of flow in each section. Fuel oil is flowing in a 4-in Schedule 40 steel pipe at the maximum rate for which the flow is laminar. If the oil has a specific gravity of 0.895 and a dynamic viscosity of 8.3 10 -4 lb - s/ft 2 ,... Design a problem to help other students better understand wye-delta transformations using Fig. 2.114. What value of R in the circuit of Fig. 2.114 would cause the current source to deliver 800 mW to... Assuming that the capacitors are initially uncharged, find v o (t) in the circuit of Fig. 6.62 . (mA) A 6 F 90 is 3 F vo(t) 2 t(s) Determine the energy loss due to a gradual enlargement from a 25 mm OD 2.0 mm wall copper hydraulic tube to a 80 mm OD 2.8 mm wall tube when the velocity of flow is 3 m/s in the smaller tube and... Determine the energy loss that will occur if water flows from a reservoir into a pipe with a velocity of 3 m/s if the configuration of the entrance is (a) An inward-projecting pipe, (b) A... A proposed alternate form for the heat exchanger described in Problem 10.37 is shown in Fig. 10.33. The entire flow conduit is a 3/4-in steel tube with a wall thickness of 0.065 in. the ID for this... Find all of the 1-hazards in the given circuit. Indicate which changes are necessary to eliminate the hazards. c' Air with a specific weight of 12.7 N/m 3 and a kinematic viscosity of 1.3 Ã 10 5 m 2 /s is flowing through a flow nozzle similar to that shown in Fig. 15.4. A manometer using water as the gage... Compute the specific weight of propane at 12.6 psig and 85F. Show that for a double-slit Fraunhofer pattern, if = mb, the number of bright fringes (or parts thereof) within the central diffraction maximum will be equal to 2m. A ball rolls without slipping down the track shown in Figure P9.24, starting from rest at a height h 1 = 20 m as shown. The ball is traveling horizontally when it leaves the bottom of the track,... Consider a simple harmonic oscillator whose position as a function of time is given by Figure P11.38. At what times in this plot is the kinetic energy a maximum? At what time(s) is the potential...
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