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Write, but do not solve, the equations of motion for the translational mechanical system shown in Figure P2.15. x3(1) K = 5 N/m M3 = 5 kg: fvz = 3 N-s/m fv, = 2 N-s/m- K2 = 4 N/m ML=4 kg: 0000M2 = 5... A rigid tank contains 7.5 kg of saturated water mixture at 400 kPa. A valve at the bottom of the tank is now opened, and liquid is withdrawn from the tank. Heat is transferred to the steam such that... Find the transfer function, G(s) = V o (s)/Vi(s), for each operational amplifier circuit shown in Figure P2.8. 110 k2 4 F (1ya 400 k2 4 F (a) 110 k2 HE 600 k2 4 F 400 k2 4 F 600 k2 (b) FIGURE P2.8... On a summer day in New Orleans, Louisiana, the pressure is 1 atm: the temperature is 32C; and the relative humidity is 95 percent. This air is to be conditioned to 24C and 60 percent relative... Using the Laplace transform pairs of Table 2.1 and the Laplace transform theorems of Table 2.2, derive the Laplace transforms for the following time functions: a. e -at sin t u(t) b. e -at cos t u(t)... For the unity feedback system of Figure P8.3, where sketch the root locus and find the following: a. The breakaway and break-in points b. The j-axis crossing c. The range of gain to keep the system... Determine your mass in slugs. Convert your weight to newtons and calculate the corresponding mass in kilograms. Refer to the Centers for Disease Control study of sanitation levels for 186 international cruise ships, Exercise 2.19. (Recall that sanitation scores ranged from 0 to 100.) Find and interpret... A golf ball is launched with the initial conditions shown in the figure. Determine the radius of curvature of the trajectory and the time rate of change of the speed of the ball (a) just after launch... At the instant illustrated, car B has a speed of 30 km/h and car A has a speed of 40 km/h. Determine the values of r and for this instant where r and are measured relative to a longitudinal axis... A man pulls himself up the 15 incline by the method shown. If the combined mass of the man and cart is 100 kg, determine the acceleration of the cart if the man exerts a pull of 175 N on the rope.... The speed of a car increases uniformly with time from 50 km/h at A to 100 km/h at B during 10 seconds. The radius of curvature of the hump at A is 40 m. If the magnitude of the total acceleration of... At a certain instant, the 80-lb crate has a velocity of 30 ft /sec up the 20 incline. Calculate the time t required for the crate to come to rest and the corresponding distance d traveled. Also,... The position s of a particle along a straight line is given by s = 8e 0.4t 6t + t 2 , where s is in meters and t is the time in seconds. Determine the velocity v when the acceleration is 3 m/s 2 . The small cart has a speed v A = 4 m /s as it passes point A. It moves without appreciable friction and passes over the top hump of the track. Determine the cart speed as it passes point B. Is... When the 10-lb plunger is released from rest in its vertical guide at = 0, each spring of stiffness k = 20 lb /in. is uncompressed. The links are free to slide through their pivoted collars and... The particle of mass m is launched from point O with a horizontal velocity u at time t = 0. Determine its angular momentum HO relative to point O as a function of time. m y L--x The circular sector rotates about a fixed axis through point O with angular velocity = 2 rad/s and angular acceleration = 4 rad/s 2 with directions as indicated in the figure. Determine the... A coil of heavy flexible cable with a total length of 100 m and a mass of 1.2 kg/m is to be laid along a straight horizontal line. The end is secured to a post at A, and the cable peels off the coil... Refer to the Canadian Journal of Civil Engineering (Jan. 2013) investigation of the use of variable speed limits to control freeway traffic congestion, Exercise 4.9. Recall that the study site was an... The 9-m steel beam is being hoisted from its horizontal position by the two cables attached at A and B. If the initial angular accelerations of the hoisting drums are a 1 = 0.5 rad/s 2 and a 2 = 0.2... The disk rotates about a fixed axis through O with angular velocity w = 5 rad/s and angular acceleration a = 3 rad/s 2 at the instant represented, in the directions shown. The slider A moves in the... The 20-kg wheel has an eccentric mass which places the center of mass G a distance r = 70 mm away from the geometric center O. A constant couple M = 6 N m is applied to the initially stationary... The uniform slender bar of mass p per unit length is freely pivoted about the y-axis at the clevis, which rotates about the fixed vertical z-axis with a constant angular velocity w. Determine the... Determine if the unity feedback system of Figure P6.3 with K(s? + 1) G(s) = %3D (s + 1)(s +2) Plot of the Fermi distribution function at two different temperatures. Calculate the Fermi function at 6.5 eV if E F = 6.25 eV and T = 300 K. Repeat for T =950 K assuming that the Fermi energy does... Determine the Debye temperature D, Debye wavelength, and the Debye frequency D for diamond given that the lattice constant for this material is 3.56 , the density of diamond is 3.52 10 3 kg.m -3 ,... Find the equilibrium concentration of defects for T = 0, 200, 400, 600, 800, 1000, and 1200 K if the energy to form a defect is 1 eV/atom. Assume A is unity. Graph your results. For T = 1200 K, how... Give some examples of physical properties that defects can change. Refer to the Engineering Project Organizational Journal (Vol. 3., 2013) study of how the emotional intelligence of individual team members relates directly to the performance of their team, Exercise... Refer to the Landscape Ecology Engineering (Jan. 2013) study of an ecological network, Exercise 10.37. Recall that the researchers used the data collected for 21 bird habitats to fit the model, E(y)... A U-tube is rotated about one leg, as shown. Before being rotated the liquid in the tube fills 0.25 m of each leg. The length of the base of the U-tube is 0.5 m, and each leg is 0.5 m long. What... The discharge of water in a 27-cm-diameter pipe is 0.057 m 3 /s. What is the mean velocity? A shell and tube heat exchanger consists of a one pipe inside another pipe as shown. The liquid flows in opposite directions in each pipe. If the speed and discharge of the liquid is the same in each... A bicyclist is coasting down a hill with a slope of 4 into a headwind (measured with respect to the ground) of 7 m/s. The mass of the cyclist and bicycle is 80 kg, and the coefficient of rolling... Water (10C) is flowing at a rate of 0.35 m 3 /s, and it is assumed that h L = 2V 2 /2g from the reservoir to the gage, where V is the velocity in the 30 cm pipe. What power must the pump supply?... Air enters this square duct at section 1 with the velocity distribution as shown. Note that the velocity varies in the y direction only (for a given value of y, the velocity is the same for all... Consider a closed vessel of fixed volume containing equal masses of water, ethanol, and toluene at 70C. Three phases (two liquid and one vapor) are present. (a) How many variables, in addition to the... What is the composition of the liquid phase in equilibrium with a vapor phase chloroform(1)/tetrahydrofuran(2) mixture of the following compositions at P = 1 bar? (a) y 1 = 0.1 (b) y 1 = 0.2 (c) y 1... For the voltage-divider configuration of Fig. 7.95, determine: a. IDQ and V GSQ . b. V D and V S Fig. 7.95 22 V 1.2 k2 Vas m) =4 V Vas (on) = 7 V Ip (on) = 5 mA I MO Vpse 0.51 k2 FIG. 7.94 Given V DS = 4 V for the network of Fig. 7.89 , determine: a. I D . b. V D and V S . c. V GS . 20 V 3 k2 4 V Vas 1.2 k2 6+2 V FIG. 7.89 The clutch system shown in Fig. P1024 is used to transmit torque through a 2-mm-thick oil film with = 0.38 Ns/m 2 between two identical 30-cm-diameter disks. When the driving shaft rotates at a... The moisture content of a soil sample is 18.4%, and its dry unit weight is 100 lb/ft 3 . Assuming that the specific gravity of solids is 2.65, a. Calculate the degree of saturation. b. What is the... Consider the closed-loop transfer function Develop an m-file to, obtain the Bode plot and verify that the resonant frequency is 5.44 rad/s and that the peak magnitude M p is 14.8 dB. T(s) || 30 s + s... Represent each of the following combinations of units in the correct SI form using an appropriate prefix: (a) Mg/mm (b) mN/s (c) m Mg The 9500-lb pipe is supported by three cables. Determine the force in each cable for equilibrium of the hook at A B C 9500 lb A 135 -1 ft 135 2.4 ft D If V = 2x 2 + 6y 2 V in free space, find the energy stored in a volume defined by 1 x 1, 1 y 1, and 1 z 1. The bent rod is supported at A, B, and C by smooth journal bearings. Determine the components of reaction at the bearings if the rod is subjected to the force F = 800 N. The bearings are in proper... The crane supports the load of 800 kg. Determine the reactions at the supports A and B as a function of position d of the trolley. Plot the reactions vs. d for 0.5 m < d < 3 m. 5 m A The block has a mass of 80 kg and a center of mass at G. Determine the smooth reactions on the supporting platform at A, B, and C. 60 G. B 60 0.3 m -0.8 m The bar of negligible weight is supported by two springs, each having a stiffness k = 100 N > m. If the springs are originally upstretched, determine the angle the bar makes with the horizontal when... The cantilevered jib crane is used to support the load of 780 lb. If x = 5, determine the reactions at the supports. Note that the supports are collars that allow the crane to rotate freely about the... If the beam is horizontal and the springs are upstretched when the load is removed, determine the angle of tilt of the beam when the load is applied. k= 1 kN/m 3 m 600 N/m 3m B kB = 1.5 kN/m D If the crane has a mass of 800 kg and a center of mass at G, and the maximum rated force at its end is F = 15 kN, determine the reactions at its bearings. The bearing at A is a journal bearing and... Three parallel bolting forces act on the circular plate. Determine the resultant force, and specify its location (x, z) on the plate. F A = 200 lb, F B = 100 lb, and F C = 400 lb. 1.5 ft 30 If F = 80N, determine the magnitude and coordinate direction angles of the couple moment. The pipe assembly lies in the xy plane. x Z -F 200 mm 300 mm 200 mm 300 mm AF 300 mm -y The spring has an unstretched length of 0.3 m. Determine the mass m of each uniform bar if = 30 for equilibrium. wwwwwww A C k = 150 N/m 2 m 0 OB Determine the components of reaction at A and B. 800 N-m 2 m B -2 m 1.5 m 45% 600 N 1.5 m When the tide water A subsides, the tide gate automatically swings open to drain the marsh B. For the condition of high tide shown, determine the horizontal reactions developed at the hinge C and... Determine the horizontal and vertical components of force that the pins exert on member ABCD. The pin at C is attached to member ABCD and passes through the smooth slot in member ECF. 1 ft 80 lb F 4... If the 300-kg drum has a center of mass at point G, determine the horizontal and vertical components of force acting at pin A and the reactions on the smooth pads C and D. The grip at B on member DAB... A man having a weight of 175 lb attempts to hold himself using one of the two methods shown. Determine the total force he must exert on bar AB in each case and the normal reaction he exerts on the... The nail cutter consists of the handle and the two cutting blades. Assuming the blades are pin connected at B and the surface at D is smooth, determine the normal force on the fingernail when a force... Identify the zero-force members in the truss. 1.5 m E A -2 m. 3 kN D B -2m- 'C Determine the moment of inertia for the area about the x axis. y T 4 in. y = x 16 in. X A 3-lb weight is attached to the end of rod ABC. If the rod is supported by a smooth slider block at C and rod BD, determine the angle for equilibrium. Neglect the weight of the rods and the slider.... Determine the moment of inertia of the area about the the x axis. 80 mm y E 20 mm = (400-x) X Determine the centroid (x, ) of the area. 1m -y=x -1m- Prob. F9-1 X Major floor loadings in a shop are caused by the weights of the objects shown. Each force acts through its respective center of gravity G. Locate the center of gravity (x, ) of all these objects. Z... Determine the location of the centroid of the solid made from a hemisphere, cylinder, and cone. y 80 mm- - -60 mm T 30 mm -30 mm- -X Locate the centroid of the cross-sectional area of the beam. 1 6 in. 10 in. 8 in.- -8 in.- -1 in. 4+ 1 in. IA 1 in. -X Determine the friction developed between the 50-kg crate and the ground if (a) P = 200 N, and (b) P = 400 N. The coefficients of static and kinetic friction between the crate and the ground are s =... Sij and Tij (a) What property must S ij have if ijk S ij = 0? (b) Let b and y be vectors. The components of the latter are defined by y i = b k T ki where T ij = T ji is an anti-symmetric object.... Without using vector identities, prove that: (a) f (r r) = (r r). (b) [A(r) r] = 0. (c) dQ = (ds )Q where dQ is a differential change in Q and ds is an element of arc length. An airplane lands on the straight runway, originally traveling at 110 ft/s when s = 0. If it is subjected to the decelerations shown, determine the time t' needed to stop the plane and construct the... The 4-Mg helicopter maneuvers a horizontal turn having a radius of curvature = 400 m. Determine the lift force F L required and the angle of the bank when it is flying horizontally with a constant... A ride in an amusement park consists of a rotating platform P, having a constant angular velocity P = 1.5 rad/s and four cars, C, mounted on the platform, which have constant angular velocities C/P... A bowling ball is cast on the "alley" with a backspin of = 10 rad/s while its center O has a forward velocity of V 0 = 8 m/s. Determine the velocity of the contact point A in contact with the alley.... Determine the moment of inertia I z of the frustum of the cone, which has a conical depression. The material has a density of 200 kg/m 3 . 200 mm- 800 mm Z 600 mm 400 mm A large roll of paper having a mass of 20 kg and a radius r = 150 mm is resting over the edge of a corner, such that the end of the paper on the roll is attached to the horizontal surface. If the... Determine the differential equation of motion for the damped vibratory system shown. What type of motion occurs? Take k = 100 N/m, c = 200 N s/m,m = 25 kg. C et C www.c In a coal-fired power station, steam (H 2 O) enters the nozzle in a turbine at T 1 = 800 K, P 1 = 2 MPa at negligible velocity, and emerges at high velocity as a liquidvapor mixture having quality x... Estimate the temperature to which water at a the bottom of a 150 m deep lake would have to be raised before it would begin to boil. In an adiabatic constant-volume container, a fluid is to be stirred mechanically with a motor providing 40 W of shaft power. How long can this go on if the internal energy of the fluid is not allowed... Two links AB and DE are connected by a bell crank as shown. Knowing that the tension in link AB is 150 lb, determine (a) The tension in link DE, (b) The reaction at C. 3 in. A B -4 in.. 90 C -6 in..... A crane column supports a 16-kip load as shown. Replace the load with an equivalent system consisting of an axial force along AB and a couple. A, 5 in. 7 in. B dibo ilbo dip dib bo 16 kips Knowing that at the instant shown bar AB has a constant angular velocity of 10 rad/s clockwise, determine the angular acceleration of (a) Bar BD, (b) Bar DE. 200 mm B 75 mm D 175 mm 100 mm A Fig.... Roll up an ohmic sheet to form an infinitely long, origin-centered cylinder of radius a. Cut a narrow slot along the length of the cylinder and insert a line source of EMF so the electrostatic... The motion actuator for a robotic manipulator consists of a simple pistoncylinder system where the pressure of the gas contained in the cylinder can be controlled by heating or cooling. The moving... On doubling the concentration of reactant, the rate of reaction triples. Find the reaction order. A frictionless piston-cylinder device contains 10 kg of water at 20C at atmospheric pressure. An external force F is then applied on the piston until the pressure inside the cylinder increases to 100... Consider the following three liquid mixtures. A. Water + n-propane B. n-hexane + benzene C. Ortho-xylene + para-xylene Which mixtures, if any, do you expect to behave as an ideal solution and why?... What is the difference between potable and nonpotable water? For what purposes may each be used? An incompressible Newtonian liquid is confined between two concentric circular cylinders of infinite length a solid inner cylinder of radius R i and a hollow, stationary outer cylinder of radius R o... A reaction with stoichiometric equation has the following rate expression What is the rate expression for this reaction if the stoichiometric equation is written as A + 2B = 2R + S? A+B A + B = R + S... The aqueous decomposition of A produces R as follows: The following results are obtained in a series of steady state runs, all having no R in the feed stream. From this kinetic information, find the... Substance A in a liquid reacts to produce R and S as follows: A feed (C A0 = 1, C R0 = 0, C S0 = 0) enters two mixed flow reactors in series, ( 1 = 2.5 min, 2 = 5 min). Knowing the composition in... A shell-and-tube exchanger with two tube passes is used to heat ethanol from 60F to 140F with steam condensing at 230F in the shell. The BWG 14 steel tubes are in. OD. The design overall coefficient... Determine the shear stress at point C in the T-beam where the internal shear is maximum. Show the result on a volume element at this point. A 20 kN/m 30 kN/m 3 m- 200 mm B -1.5 m- 200 mm 20 mm -20 mm Select the lightest-weight steel wide-flange beam from Appendix B that will safely support the machine loading shown. The allowable bending stress is \(\sigma_{\text {allow }}=24 \mathrm{ksi}\) and...
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