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Select the lightest-weight wide-flange beam from Appendix B that will safely support the loading. The allowable bending stress is \(\sigma_{\text {allow }}=22 \mathrm{ksi}\) and the allowable shear... The truss shown is used to support the floor deck. The uniform load on the deck is \(3 \mathrm{k} / \mathrm{ft}\). This load is transferred from the deck to the floor beams, which rest on the top... The equilibrium adsorption of methane on a given activated carbon was studied by Grant et al. (1962). They proposed a Langmuir-type adsorption isotherm with parameters \(q_{m}=48 \mathrm{~g}... For the original concrete composite post design of Problem 1.13, assume that the steel rods are made of 4340 steel, and that the rods are to be replacedby IM9 carbon fiber bundles of the same length... In the mechanism shown in Fig.2.14(a), the crank \(O_{1} A\) rotates at a uniform speed of \(650 \mathrm{rpm}\). Determine the linear velocity of the slider \(C\) and the angular speed of the link... An unknown sample of Ni 2+ gave a current of 2.36 A in an electrochemical analysis. When 0.500 mL of solution containing 0.028 7 M Ni 2+ was added to 25.0 mL of unknown, the current increased to 3.79... Calculate the pH when 25.0 mL of 0.020 0 M 2-aminophenol have been titrated with 10.9 mL of 0.015 0 M HClO 4 . A large piece of dry rock has a mass of 2450 kg and volume of 0.925 m 3 . The specific gravity of the rock mineral is 2.80. Determine the porosity of the rock. The bulk density of a compacted soil specimen (Gs = 2.70) and its water content are 2060 kg/m 3 and 15.3%, respectively. If the specimen is soaked in a bucket of water for several days until it is... Determine the magnitude of the resultant force and its direction, measured counterclockwise from the positive x axis. F = 8 kN F2 = 5 kN 60 45 F = 4 kN If the roller at A and the pin at B can support a load up to 4 kN and 8 kN, respectively, determine the maximum intensity of the distributed load w, measured in kN/m, so that failure of the supports... A free-headed drilled shaft is shown in Figure P13.10. Let Q g = 260 kN, M g = 0, = 17.5 kN/m 3 , ' = 35, c' = 0, and E p = 22 10 6 kN/m 2 . Determine a. The ground line deflection, xo b. The... Determine the location of the centroid C for the loop of the lemniscate, r 2 = 2a cos2, (-45 45). 12 = 2a? cos 20 Three different washing solutions are being compared to study their effectiveness in retarding bacteria growth in 5-gallon milk containers. The analysis is done in a laboratory, and only three trials... An aluminum master alloy manufacturer produces grain refiners in ingot form. The company produces the product in four furnaces. Each furnace is known to have its own unique operating characteristics,... Two missing values in a randomized block. Suppose that in Problem 4-1 the observations for chemical type 2 and bolt 3 and chemical type 4 and bolt 4 are missing. (a) Analyze the design by iteratively... Air is expanded from 1000 kPa and 600C at the inlet of a steady-flow turbine to 100 kPa and 200C at the outlet. The inlet area and velocity are 0.1 m 2 and 30 m/s, respectively, and the outlet... Determine the total heat transfer for the reversible process 1-3 shown in Fig. P758. 3 360 55 1 2 S, kJ/K T, C Consider the reaction 2H 2 O 2H 2 + O 2 at 4000 K and 10 kPa. Will the amount of hydrogen gas produced be increased when the reaction occurs at 100 kPa rather than 10 kPa? A mixture of 2 mol of CO 2 and 1 mol of O 2 is heated to 2800 K at a pressure of 4 atm. Determine the equilibrium composition of the mixture, assuming that only CO 2 , CO, O 2 , and O are present. A 0.40-m 3 insulated pistoncylinder device initially contains 1.3 kg of air at 30C. At this state, the piston is free to move. Now air at 500 kPa and 70C is allowed to enter the cylinder from a... Find the transfer function, G(s) = V o (s)/V i (s), for each network shown in Figure P2.5. Solve the problem using mesh analysis. + V(1)- 1 H 1 H 10 2 H 3 H vi(1) 12 vi(1) 1F Volt) (a) (b) FIGURE... A two-stage compression refrigeration system with an adiabatic liquid-vapor separation unit like that in Fig. P11 60 uses refrigerant-134a as the working fluid. The system operates the evaporator at... Represent the following transfer function in state space. Give your answer in vector-matrix form. s(s + 2) T(s) (s+ 1Xs + 2s + 5) Given the dc servomotor and load shown in Figure P3.11, represent the system in state space, where the state variables are the armature current, i a , load displacement, L , and load angular... The velocity of a particle is given by v = 25t 2 80t 200, where v is in feet per second and t is in seconds. Plot the velocity v and acceleration a versus time for the first 6 seconds of motion and... Refer to the Journal of Engineering, Computing and Architecture (Vol. 3., 2009) study of cell phone handoff behavior, Exercise 3.15. Recall that the different color codes accessed by two different... Refer to the IEICE Transactions on Information & Systems (Jan. 2005) study of impedance to leg movement, Exercise 2.46. Recall that Korean engineers attached electrodes to the ankles and knees of... The sprinter begins from rest at position A and accelerates along the track. If the stationary tracking camera at O is rotating counterclockwise at the rate of 12.5 deg/s when the sprinter passes the... Motion of the sliding block P in the rotating radial slot is controlled by the power screw as shown. For the instant represented, = 0.1 rad/s, = 0.04 rad /s2, and r = 300 mm. Also, the screw turns... A skier starts from rest on the 40 slope at time t = 0 and is clocked at t = 2.58 s as he passes a speed checkpoint 20 m down the slope. Determine the coefficient of kinetic friction between the snow... The collar of mass m is released from rest while in position A and subsequently travels with negligible friction along the vertical-plane circular guide. Determine the normal force (magnitude and... The system is released from rest with no slack in the cable and with the spring stretched 200 mm. Determine the distance s traveled by the 4-kg cart before it comes to rest (a) If m approaches zero... Reduce the block diagram shown in Figure P5.9 to a single transfer function, T(s) = C(s)/R(s). Figure P5.9 G1 C(s) R(s) G2 G5 G6 G3 G4 G7 Find the equivalent transfer function, T(s) = C(s)/R(s), for the system shown in Figure P5.3. G1 R(s) + G5 G6 C(s) G2 G3 G4 G7 FIGURE P5.3 Refer to the Journal of Waterway, Port, Coastal, and Ocean Engineering (March/April, 2013) study of coastal sea level rise, Exercise 5.6. Recall that the acceleration Y in sea level rise... The HIV infection linearized model developed in Problem 84, Chapter 4, can be shown to have the transfer function It is desired to develop a policy for drug delivery to maintain the virus count at... End A of the slender pole is given a velocity v A to the right along the horizontal surface. Show that the magnitude of the velocity of end B equals v A when the midpoint M of the pole comes in... The 30,000-lb concrete pipe section is being transported on a flatbed truck. Five inextensible cables are passed across the top of the pipe and tightened securely to the flatbed with an initial... The system of Prob. 5/101 is repeated here. Crank OA is rotating at a counterclockwise angular rate of 9 rad /s, and this rate is decreasing at 5 rad/s 2 . Determine the angular acceleration a AB of... An external force F = F 0 sin wt is applied to the cylinder as shown. What value w c of the driving frequency would cause excessively large oscillations of the system? k 2m m YF The system of Figure P7.12 is to have the following specifications: K v = 20; = 0.7. Find the values of K 1 and K f required for the specifications of the system to be met. O(s) + A(s) K1 s(s + 2)... What is the approximate mass in units of slugs for a. A 2-liter bottle of water? b. A typical adult male? c. A typical automobile? Apply the grid method to calculate the cost in U.S. dollars to operate a pump for one year. Th e pump power is 20 hp. The pump operates for 20 hr/day, and electricity costs $0.10 per kWh. This problem involves a cylinder falling inside a pipe that is filled with oil, as depicted in the figure. The small space between the cylinder and the pipe is lubricated with an oil film that has... If for a binary solution one starts with an expression for M (or M R or M E ) as a function of x 1 and applies Eqs. (10.15) and (10.16) to find M 1 and M 2 (or M R 1 and M R 2 or M E 1 and M E 2 )... Consider a binary mixture for which the excess Gibbs energy is given by G E /RT = 2.1x 1 x 2 (x 1 + 2x 2 ). For each of the following overall compositions, determine whether one or two liquid phases... A room in the lower level of a cruise ship has a 40-cm-diameter circular window. If the midpoint of the window is 2 m below the water surface, determine the hydrostatic force acting on the window,... Determine the magnitude and coordinate direction angles of the resultant force acting on the bracket. X N 45 60 F = 450 N 45. 30 F = 600 N -y Determine the resultant of the two forces and express the result as a Cartesian vector. x F= 180 lb 60 60 24. 135 25 F = 50 lb Express the following vectors in rectangular coordinates: (a) A = sin a + cos a 2za z (b) B = 4r cos a r + r a Replace the loading by an equivalent resultant force and specify its location on the beam, measured from A. W 2 kN/m -4 m- B -2m- 5 kN/m X The weights of the various components of the truck are shown. Replace this system of forces by an equivalent resultant force and specify its location measured from B. B 3 ft 3500 lb 8 5500 lb A -14... Members AB and BC can each support a maximum compressive force of 800 lb, and members AD, DC, and BD can support a maximum tensile force of 1500 lb. If a = 10, determine the greatest load P the truss... Determine the force in each member of the truss. State if the members are in tension or compression. D 300 lb -2 ft + -2 ft- Prob. F6-2 B A 3 ft The pipe assembly is subjected to the 80-N force. Determine the moment of this force about point A. x 200 mm 30 N F = 80 N 400 mm 40 250 mm 300 mm 200 mm y Locate the centroid, y, and determine the orientation of the principal centroidal axes for the composite area. What are the moments of inertia with respect to these axes? -8 in.. 2 in. 2 in. + 8 in..... Evaluate (204 mm)(0.00457 kg) (34.6 N) to three significant figures and express the answer in SI units using an appropriate prefix. Round off the following numbers to three significant figures: (a) 3.45555 m, (b) 45.556 s, (c) 5555 N, (d) 4525 kg. The piston C moves vertically between the two smooth walls. If the spring has a stiffness of k = 15 lb/in., and is unstretched when = 0, determine the couple M that must be applied to AB to hold the... If couple forces of F = 10 lb are applied perpendicular to the lever of the clamp at A and B, determine the clamping force on the boards. The single square-threaded screw of the clamp has a mean... The hand clamp is constructed using a square-threaded screw having a mean diameter of 36 mm, a lead of 4 mm, and a coefficient of static friction at the screw of s = 0.3. If the clamping force in... A vector function Z(r) satisfies Z = 0 and Z = 0 everywhere in a simply-connected volume V bounded by a surface S. Modify the proof of the Helmholtz theorem in the text and show that Z(r) can be... Evaluate the following expressions which exploit the Einstein summation convention. (a). ii. (b). ij ijk. (c). ijk jk. (d). ijk ijk. (a) Place two charges +q at two diagonal corners of a square (a,a, 0) and two minus charges q at the two other diagonals of the square (a,a, 0). Evaluate the primitive quadrupole moment components Q... Find the electric dipole moment of: (a) A ring with charge per unit length = 0 cos where is the angular variable in cylindrical coordinates. (b) A sphere with charge per unit areas = 0 cos ... By modern standards, the shaft design of Problem 5-76 is poor because it is so long. Suppose it is redesigned by halving the length dimensions. Using the same material and design factor as in Problem... (a) Show that the magnetic dipole moment of a magnetized body can be written where (r) = M(r) is the density of fictitious magnetic charge.(b) Let B 1 and B 2 be the magnetic fields produced by... Show that the following scheme proposed by R. Ogg, J. Chem. Phys., 15,337 (1947) is consistent with, and can explain, the observed first-order decomposition of N 2 0 5 . k NO5NO + NO** k NO NO* + NO... How much would you need to save annually to be willing to invest $1.75 million in a process improvement? The internal hurdle rate for process improvements is 18% before taxes over eight years. (a) LEP Table 12-2: Exothermic Reaction with Heat Exchange Download the Polymath, MATLAB, Python, or Wolfram codes for the algorithm and data given in Table T12-2 for the exothermic gas phase... Compute the reactions and draw the shear and moment curves for the beam in Figure P9.19. Given: EI is constant. Use the reactions at \(B\) as the redundants. A W L B Assuming that no load acts, compute the reactions and draw the shear and moment curves for the beam in Figure P9.1 if support \(A\) settles 0.5 in. and support \(C\) settles 0.75 in. Given:... Draw the influence lines for \(R_{A}\) and the bar forces in members \(A D, E F, E M\), and \(N M\). Loads are transmitted into the truss through the lower chord panel points. Vertical members \(E... A mixture that contains 40% by mole n-heptane in n-decane is to be separated in a series of flush separators until a stream is obtained that contains at least 95% n-heptane. Determine the number of... The following portfolio of investment projects has been proposed for a company for next year: i. Develop a spreadsheet optimization program to select the optimal portfolio of projects to maximize... Material R is to be produced from the following microbial fermentation, using a feed stream C A0 = 10 6 , C Ro = 0, C co = 0. All quantities are given in consistent SI units. In each of the following... Material R is to be produced from the following microbial fermentation, using a feed stream C A0 = 10 6 , C Ro = 0, C co = 0. All quantities are given in consistent SI units. In each of the following... Figure 7.3-4 is the phase diagram for a van der Waals fluid. Within the vapor-liquid coexistence envelope one can draw another envelope representing the limits of supercooling of the vapor and... By observing that the circuit of 7-51 (a) is an inverting Schmitt trigger (introduced in Problem 5.58), argue that the capacitor voltage and the op amps output are correctly shown in Fig. 7-51(c).... To examine this issue, imagine that banks can charge any borrower 150 basis points above the interest rate at which the bank would break even (in an expected value sense) on that borrower. This is a... In Problem 9.D23, fractions were collected from ethanol mole fractions \(\mathrm{x}_{\mathrm{F}}=0.10\) to \(\mathrm{x}_{\mathrm{W} 1}=0.07\), from \(\mathrm{x}_{\mathrm{W} 1}\) to... Fill in the blanks. (a) If you double the frequency of electromagnetic radiation, you __________ the energy. (b) If you double the wavelength, you _________ the energy. (c) If you double the... The absorbance of a 2.31 10 -5 M solution of a compound is 0.822 at a wavelength of 266 nm in a 1.00-cm cell. Calculate the molar absorptivity at 266 nm. For each of the following systems, give two examples of how a mechanical engineer would be involved in its manufacture. (a) Graphite-epoxy skis, tennis racket, or golf club (b) Elevator (c) Blu-ray... One U.S. gallon is equivalent to 0.1337 ft 3 , 1 ft is equivalent to 0.3048 m, and 1000 L are equivalent to 1 m 3 . By using those definitions, determine the conversion factor between gallons and... A robotic-wheeled vehicle that contains science instruments is used to study the geology of Mars. The rover weighs 408 lb on Earth. (a) In the USCS dimensions of slugs and lbm, what is the rovers... A 1-Mg container hangs from a 15-mm-diameter steel cable. What is the stress in the cable? A two-tier system to repair bridge infrastructures is supported by two steel cables for each platform (Figure P5.15). All the support cables have a diameter of 0.50 in. Assume the applied loads are... Adhesive tape is capable of supporting relatively large shear stress, but it is not able to support significant tensile stress. In this problem, you will measure the shear strength of a piece of... A plastic pipe carries deionized water in a microelectronics clean room, and one end of it is capped (Figure P5.25). The water pressure is p 0 = 50 psi, and the cap is attached to the end of the pipe... The Boeing 787 Dreamliner is billed to be 20% more fuel efficient than the comparable Boeing 767 and will fly at Mach 0.85. The midsize Boeing 767 has a range of 12,000 km, a fuel capacity of 90,000... A 500 m long levee made of compacted clay impounds water in a reservoir as shown in Figure P2.8. There is a 1 m thick (measured in the direction perpendicular to the seam) sand seam continuing along... Express the force F in Cartesian vector form if it acts at the midpoint B of the rod. A 4 m B 4 m F = 600 N 3 m 6 m D For the following cases, determine the allowable gross vertical load bearing capacity of the foundation. Use Terzaghis equation and assume general shear failure in soil. Use F S = 4. Part D; c'... A square foundation is shown in Figure P6.19. Use FS = 6, and determine the size of the foundation. Use Prakash and Saran's method [Eq. (6.59)]. Figure P6.19. 450 kN 70 kN-m y = 16 kN/m3 c' = 0 o'=... In Problem 7.3, if no bedrock was present for at least 4 m below the foundation, determine the ultimate bearing capacity. Problem 7.3 A 1.5 m 2.0 m rectangular foundation is placed at 1.0 m depth in... If the soil exerts a trapezoidal distribution of load on the bottom of the footing, determine the intensities w 1 and w2 of this distribution needed to support the column loadings. 80 kN 60 kN 50 kN... Replace the loading by a single resultant force, and specify its location on the beam measured from point A. 400 N/m B 3 m 3 m Redo Problem 12.30 assuming that the water table coincides with the top of the fill and that satsfilld = 19.8 kN/m 3 . If the other quantities remain the same, what would be the downward drag force...
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