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Figure P 12.37 shows a group pile in clay. Determine the consolidation settlement of the group. Use the 2:1 method to estimate the average effective stress in the clay layers. Figure P 12.37 1335 kN... Determine the force in members CD, CJ, and KJ and state if these members are in tension or compression. 6 kN 6 kN 6 kN 6 kN 6 kN K 3 m B C DE F 12 m, 6 @ 2 m Determine the maximum force P the connection can support so that no slipping occurs between the plates. There are four bolts used for the connection and each is tightened so that it is subjected to a... The relay regulates voltage and current. Determine the force in the spring CD, which has a stiffness of k 120 N m, so that it will allow the armature to make contact atA in figure (a) with a vertical... The breaking strength of a fiber is required to be at least 150 psi. Past experience has indicated that the standard deviation of breaking strength is = 3 psi. A random sample of four specimens is... For Fig. A151 , let = 2 in, d = 0.3 in, and estimate Kt. Use 1/4 symmetry and 1/8-inthick 2-D elements. 3.0 d 2.8 F 2.6 K, 2.4 2.2 2.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 dhw For Fig. A153 , let = 1.5 in, d = 1.0 in, r = 0.10 in, and estimate Kt. Use 1/4 symmetry and 1/8-in-thick 2-D elements. 3.0 wld = 3 F 2.6 1.5 2.2 1.2 K, 1.1 1.8 1.05 1.4 1.0 0.05 0.10 0.15 0.20 0.25... The yield of a chemical process was measured using five batches of raw material, five acid concentrations, five standing times (A, B, C, D, E), and five catalyst concentrations (, , , , ). The... A construction crane lifts a prestressed concrete beam weighing 3 short tons from the ground to the top of piers that are 24 ft above the ground. Determine the amount of work done considering (a) The... In a process development study on yield, four factors were studied, each at two levels: time (A), concentration (B), pressure (C), and temperature (D). A single replicate of a 2 4 design was run, and... A chemical plant produces oxygen by liquifying air and separating it into its component gases by fractional distillation. The purity of the oxygen is a function of the main con-denser temperature and... The air in a house is at 25C and 65 percent relative humidity. Now the air is cooled at constant pressure. The temperature at which the moisture in the air will start condensing is (a) 7.4C (b) 16.3C... An AISI 1018 steel has a yield strength, S y = 295 MPa. Using the distortion-energy theory for the given state of plane stress, (a) Determine the factor of safety, (b) Plot the failure locus, the... For the motor, load, and torque-speed curve shown in Figure P2.30, find the transfer function, G(s) = L (s)/E a (s). Ra N = 50 ea(t) J = 4 kg-m2 D = 8 N-m-s/rad N2 = 150 = 36 kg-m D2 = 36 N-m-s/rad... For an ASTM 30 cast iron, (a) Find the factors of safety using the BCM and MM theories, (b) Plot the failure diagrams in the A , B plane to scale and locate the coordinates of the stress state, (c)... For the rotational system shown in Figure P2.25, write the equations of motion from which the transfer function, G(s) = 1 (s)/T(s), can be found. Figure P2.25 T(t) 0,(1) N J. K D N2 N3 J2 N4 JL. J4... Repeat Probs. 527 using the modified-Mohr theory. A cast aluminum 195-T6 exhibits S ut = 36 kpsi, S uc 5 35 kpsi, and f = 0.045. For the given state of plane stress, (a) Using the Coulomb-Mohr... Find the transfer function, G(s) = X 2 (s)/F(s), for the translational mechanical network shown in Figure P2.10. X(1) X(1) 1 N/m ft) 1 kg 1 N-s/m 1 kg Frictionless" FIGURE P2.10 Air enters an adiabatic nozzle steadily at 300 kPa, 200C, and 45 m/s and leaves at 100 kPa and 180 m/s. The inlet area of the nozzle is 110 cm 2 . Determine (a) The mass flow rate through the nozzle... A hot-water stream at 80C enters a mixing chamber with a mass flow rate of 0.5 kg/s where it is mixed with a stream of cold water at 20C. If it is desired that the mixture leave the chamber at 42C,... The adiabatic compressor of a refrigeration system compresses R-134a from a saturated vapor at 160 kPa to 800 kPa and 50C. What is the minimum power required by this compressor when its mass flow... What is required to represent a system in state space? For each system shown in Figure P3.9, write the state equations and the output equation for the phase-variable representation. R(s) 8s + 10 C(s) s4 + 5s + s2 + 5s + 13 (a) R(s) C(s) s4+ 2s3+ 12s2+ 7s... Find the capacitor voltage in the network shown in Figure P4.2 if the switch closes at t = 0. Assume zero initial conditions. Also find the time constant, rise time, and settling time for the... Solve for x(t) in the system shown in Figure P4.5 if f (t) is a unit step. x(t) M = 2 kg Ks K, = 6 N/m fy = 2 N-s/m f(1) = u(1)N 000 M f(t) FIGURE P4.5 In the past, Type-1 diabetes patients had to inject themselves with insulin three to four times a day. New delayed-action insulin analogues such as insulin Glargine require a single daily dose. A... The stories of a tall building are uniformly 10 feet in height. A ball A is dropped from the rooftop position shown. Determine the times required for it to pass the 10 feet of the first, tenth, and... With what minimum horizontal velocity u can a boy throw a rock at A and have it just clear the obstruction at B? 40 m A B 26 m 16 m Problem 2/64 Determine the maximum speed for each car if the normal acceleration is limited to 0.88g. The roadway is unbanked and level. 21 m 16 m Problem 2/100 Derive the unit step response for each transfer function in Example 4.8. Data From Example 4.8: Find the step response of each of the transfer functions shown in Eqs. (4.62) through (4.64) and... In typical conventional aircraft, longitudinal flight model linearization results in transfer functions with two pairs of complex conjugate poles. Consequently, the natural response for these... In a basketball game, the point guard A intends to throw a pass to the shooting guard B, who is breaking toward the basket at a constant speed of 12 ft /sec. If the shooting guard is to catch the... A 60-kg woman holds a 9-kg package as she stands within an elevator which briefly accelerates upward at a rate of g /4. Determine the force R which the elevator floor exerts on her feet and the... A bicyclist finds that she descends the slope 1 = 3 at a certain constant speed with no braking or pedaling required. The slope changes fairly abruptly to 2 at point A. If the bicyclist takes no... The 4-lb collar is released from rest against the light elastic spring, which has a stiffness of 10 lb /in. and has been compressed a distance of 6 in. Determine the acceleration a of the collar as a... The system is released from rest with no slack in the cable and with the spring unstretched. Determine the distance s traveled by the 4-kg cart before it comes to rest (a) If m approaches zero (b) If... The two particles of mass m and 2m, respectively, are connected by a rigid rod of negligible mass and slide with negligible friction in a circular path of radius r on the inside of the vertical... A railroad car of mass m and initial speed v collides with and becomes coupled with the two identical cars. Compute the final speed v of the group of three cars and the fractional loss n of energy if... The small particle of mass m and its restraining cord are spinning with an angular velocity on the horizontal surface of a smooth disk, shown in section. As the force F is slightly relaxed, r... The ball A of mass 10 kg is attached to the light rod of length l = 0.8 m. The mass of the carriage alone is 250 kg, and it moves with an acceleration a O as shown. If = 3 rad/s when = 90, fi nd... Given the block diagram of a system shown in Figure P5.8, find the transfer function G(s) = 22 (s)/ 11 (s). O1 (s) +7 021 (s) G|(s) G2(s) G3(8) G-(s) O12 (s) + O22 (s) G4(s) G5(3) G6(s) FIGURE P5.8 Find the closed-loop transfer function, T(s) = C(s)/R(s) for the system shown in Figure P5.2, using block diagram reduction. H1 R(s) GI G2 C3 C(s) FIGURE P5.2 In the Journal of Agricultural, Biological and Environmental Sciences (Sept., 2000), researchers evaluated the risk posed by hazardous pollutants using an ecotoxicological survival model. For one... Using Masons rule, find the transfer function, T(s) = C(s)/R(s), for the system represented in Figure P5.22. G|(s) G(s) G3(s) G,(s) Rs) C(s) -1 -1 -1 FIGURE P5.22 Given the system represented in state space as follows: convert the system to one where the new state vector, z, is -1 -7 6 -5 -8 4 8 x+ -7r 4 7 -8 y = [-9 -9 -8] x For the system shown in Figure P7.3, what steady-state error can be expected for the following test inputs: 10u(t); 10tu(t); 10t 2 u(t). R(s) + 3 C(s) s+4 2 6s FIGURE P7.3 A drive system with an elastically coupled load was presented in Problem 71, Chapter 4. The mechanical part of this drive (Thomsen, 2011) was reduced to a two-inertia model. Using slightly different... Statistical software packages, such as SAS and MINITAB, are capable of generating random numbers from a uniform distribution. For example, the SAS function RANUNI uses a prime modulus 2 31 1... The rod OB slides through the collar pivoted to the rotating link at A. If CA has an angular velocity = 3 rad/s for an interval of motion, calculate the angular velocity of OB when = 45. CA = 200... An inverted pendulum, mounted on a motor-driven cart was presented in Chapter 3, Problem 30. The systems state-space model was linearized around a stationary point, x 0 = 0, corresponding to the... Motion of the roller A against its restraining spring is controlled by the downward motion of the plunger E. For an interval of motion the velocity of E is v = 0.2 m/s. Determine the velocity of A... The uniform steel I-beam has a mass of 300 kg and is supported in the vertical plane as shown. Calculate the force R supported by the pin at O for the condition immediately after the support at B is... The 1800-kg rear-wheel-drive car accelerates forward at a rate of g/2. If the modulus of each of the rear and front springs is 35 kN/m, estimate the resulting momentary nose-up pitch angle . (This... A linear harmonic oscillator having a mass of 1.10 kg is set into motion with viscous damping. If the frequency is 10 Hz and if two successive amplitudes a full cycle apart are measured to be 4.65 mm... For each of the root loci shown in Figure P8.1, tell whether or not the sketch can be a root locus. If the sketch cannot be a root locus, explain why. Give all reasons. jo ja ja ja s-plane s-plane... Find C(z) in general terms for the digital system shown in Figure P13.3. R(s) +, C(s) G,(s) O- G,(s) G3(3) G(s) T T H (s) H,(s) T H,(s) FIGURE P13.3 In order to determine controllability mathematically, the controllability matrix is formed, and its rank evaluated. What is the final step in determining controllability if the controllability matrix... A 6-in. steel cube is cut along its diagonal plane. Calculate the moment of inertia of the resulting prism about the edge x-x. 6" 6" 6" The uniform rod of mass m is freely pivoted about point O. Assume small oscillations and determine an expression for the damping ratio . For what value c cr of the damping coefficient c will the... Calculate the bending moment M in the shaft at O for the rotating assembly of Prob. 7/144 as it starts from rest with an initial angular acceleration of 200 rad/s 2 . N - 150 mm 75 mm 150 mm 75 mm... Refer to the Behavioral Neuroscience (Feb. 2004) study of the drug scopolamines effects on memory for word-pair associates, Exercise 14.13. Recall that a completely randomized design with three... Refer to the Evolutionary Ecology Research (July 2003) study of the New Zealand bird population prior to European contact, Exercise 1.12. Two quantitative variables measured for each of The 116 bird... The body composed of slender rods of mass p per unit length is lying motionless on the smooth horizontal surface when a linear impluse P dt is applied as shown. Determine the velocity v B of corner B... Glycolysis is a feedback process through which living cells use glucose to generate adenosine triphosphate (ATP), necessary for cell operations. A linearized glycolysis model (Chandra, 2011) is given... The one-dimensional monatomic harmonic crystal (Sect. 6.1.3) is in fact a particular case of the diatomic model described in Sect. 6.1.4, for which the two atoms are identical. To prove this, show... A marine biologist was hired by the EPA to determine whether the hot-water runoff from a particular power plant located near a large gulf is having an adverse effect on the marine life in the area.... Corporate sustainability refers to business practices designed around social and environmental considerations (e.g., going green and energy conservation). Business and Society (March 2011) published... Refer to the Behavioral Neuroscience (Feb. 2004) study of the drug scopolamines effects on memory for word-pair associates, Exercise 14.13. Recall that the researchers theorized that the mean number... Refer to the Journal of Food Engineering (Sep., 2013) study of the characteristics of sweet potato chips fried at different temperatures, Exercise 7.75. Recall that a sample of 6 sweet potato slices... A jet of water (60F) is discharging at a constant rate of 2.0 cfs from the upper tank. If the jet diameter at section 1 is 4 in., what forces will be measured by scales A and B? Assume the empty tank... The discharge in the siphon is 2.5 cfs, D = 7 in., L 1 = 4 ft , and L 2 = 5 ft. Determine the head loss between the reservoir surface and point C. Determine the pressure at point B if three quarters... Consider a single jet of water striking the buckets of the impulse wheel as shown. Assume ideal conditions for power generation [V bucket = (1/2)V j and the jet is turned through 180 of arc]. With... Liquid benzene at 25C and 1.2 bar is converted to vapor at 200C and 5 bar in a twostep steady-flow process: compression by a pump to 5 bar, followed by vaporization in a counterflow heat exchanger.... The following empirical two-parameter expression has been proposed for correlation of excess properties of symmetrical liquid mixtures: Here, quantities A and B are parameters that depend at most on... If V BR2 is 6.4 V, determine the range for V BR1 using Eq. (17.1). Eq. (17.1) VBR, = VBR, + 0.1VBR, For the network of Fig. 7.81 , determine: a. V GSQ and I DQ . b. V DS , V D , V G , and V S . 12 V 2.2 ka oss = 6 mA. Vp =-6 V Vase 1 MO. 1.6 kn 3 V FIG. 7.81 Determine V D and V GS for the fixed-bias configuration of Fig. 7.78 . 20 V 2,2 k2 VD Ipss = 5 mA Vp = -5 V 1 MN FIG. 7.78 For the network of Fig. 4.136 , determine: a. I B . b. I C . c. V CE . d. V C . Fig. 4.136 9.1 9+16 V '12 le + = 80 15 6-12V FIG. 4.136 A specimen of an AISI-SAE type 416 stainless steel with a 0.505-in. diameter was machined to a 2.00-in.-gage length and the following data were collected: After fracture, the gage length was 2.20 in.... The specific weight (wt./vol.) of brass is 520 lb/ft3. Determine its density (mass/vol.) in SI units. Use an appropriate prefix. Determine the coordinate angle for F 2 and express each force acting on the bracket as a Cartesian vector. X N 45 60 F = 450 N 45. 30 F = 600 N -y Determine the force in each cable needed to support the 500-lb cylinder. 3 ft 6 ft B -6 ft- D N 3 ft 5 ft C 6 ft 2 ft y Determine the magnitude and coordinate direction angles of the resultant of the two forces acting at point A. X Fc= 400 N, 2m FE=350 N FB = 400 N 3 m E 2 m E 2 m B 3m Three forces act on the ring. Determine the magnitude and coordinate direction angles of the resultant force. F = 500 N 30 X 60 F3 = 100 N 60 120 F = 400 N 45 y The hold-down clamp exerts a compressive force of 400 N on the wood block at C. If the clamp is loosely bolted to the bench using two symmetrically placed bolts B, one of which is shown, determine... Replace the loading acting on the beam by a single resultant force. Specify where the force acts, measured from B. 60 450 N |--2m--- -4 m- 300 N B -3m- 700 N 30 1500 Nm Replace the loading acting on the frame by an equivalent resultant force and couple moment acting at point B. 80 lb + -3 ft- B -3 ft- 75 lb 60 lb + -3 ft- -3 ft- 2 ft + 40 lb A 4 ft The clamp has a rated load capacity of 1500 lb. Determine the compressive force this creates along segment AB of the screw and the magnitude of force exerted at pin C. The screw is pin connected at... Determine the reactions at pins A and B of the frame needed to support the 200-lb load. The pulley at C has a radius of 0.5 ft. The pulley at D has a radius of 0.25 ft. 4 ft 60% 30 30 3 ft B Determine the horizontal and vertical components of force which pin C exerts on member ABC. The 600-N force is applied to the pin. 3 m 1.5 m -2m- E A F D B -2 m 300 N C 600 N Determine the horizontal and vertical components of force acting at the pins A, B, and C of the frame. 4 ft 45 4 ft 100 lb 4 ft 100 lb 8 ft 30% Determine the horizontal and vertical components of force that pins A and B exert on the frame. 4 m A -3 m- B C 2 kN/m Determine the force required to hold the 50-kg mass in equilibrium. B C A B P 191 Determine the force in each member of the space truss and state if the members are in tension or compression. The The truss is supported by ball-and-socket joints at A, B, and E. Set F = {800j} N. 5... Determine the components of reaction E. A E -1.5 m- 4 kN/m D -1.5 m- Prob. F6-23 B 2m C 5 kN Determine the normal force that the 100-lb plate A exerts on the 30-lb plate B. -1 ft- A B -4 ft- Prob. F6-17 +1 ft- If a 100-N force is applied to the handles of the pliers, determine the clamping force exerted on the smooth pipe B and the magnitude of the resultant force that one of the members exerts on pin A.... Determine the force in members DC, HI, and JI of the truss and state if the members are in tension or compression. Suggestion: Use the sections shown. G T 6 ft 6 ft 12 ft ----|-6 ft-|-6 ft-|-- F -9... Determine the force in members GF, GD, and CD of the truss and state if the members are in tension or compression. 1 m 2m A H B -2m-2m- 10 kN G C -2 m- D -2 m- 25 kN 15 kN Determine the force in members EF, CF, and BC of the truss and state if the members are in tension or compression. G 30 6 ft B 300 lb F -6 ft- 300 lb E 30 6 ft
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