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The wheel rolls without slipping. For the instant portrayed, when O is directly under point C, link OA has a velocity v = 1.5 m/s to the right and = 30. Determine the angular velocity w of the... The four-bar mechanism lies in a vertical plane and is controlled by crank OA which rotates counterclockwise at a steady rate of 60 rev /min. Determine the torque M which must be applied to the crank... The results of a standard Proctor test are given in the following table. Determine the maximum dry density (kg/m 3 ) of compaction and the optimum moisture content. Volume of Proctor mold (cm) 943.3... An element of material in plain strain has the following strains: x = 20.001 and y = 0.0015. (a) Determine the strains for an element oriented at an angle = 258. (b) Find the principal strains of... The 100-lb door has its center of gravity at G. Determine the components of reaction at hinges A and B if hinge B resists only forces in the x and y directions and A resists forces in the x, y, z... Determine the magnitude of the moment of the force F = {50i - 20j - 80k} N about the base line AB of the tripod. X 1.5 m 2 m 2m 0.5 m B D N 1 m 4 m A. 2.5 m y The bent rod is supported at A, B, and C by journal bearings. Determine the components of reaction at bearings if the rod is subjected to the 200-lb vertical force and the 30 lb-ft couple moment. The... Determine the location (x, ) of the centroid of the sheet metal cross section. Neglect the thickness of the material and slight bends at the corners. y 2 in. 8 in. -3 in.3 in. X The two segments of the girder are pin connected at B. Draw the shear and moment diagrams for the girder. 15 kip 3 ft-4 ft- 2 ft B C 8 kip. ft 500 lb/ft 12 ft D A 50-g pencil (uniform slender rod) falls down onto the table with a velocity of 0.2 m/s just before impact. If it is at an angle of 60 with the horizontal, and it does not slip during the impact,... A wire loop with radius b in the x-y plane carries a time-harmonic current I 0 cos t. (a) Find the value of I0 needed to levitate a small sphere with mass m, radius a, and conductivity at a height z... Reconsider Prob. 253. Assuming a linear pressure increase during the compression, estimate the energy needed to compress the water isothermally. Data from Problem 53. A frictionless piston-cylinder... Laboratory tests of a membrane for \(\mathrm{H}_{2} / \mathrm{CH}_{4}\) separation gave a permeate composition of \(80 \% \mathrm{H}_{2}\) and a \(20 \%\) cut when the feed was \(50 \%... Large central power stations (about 1000 MW electrical) using fluidized bed combustors may be built some day (see Fig. P1.2). These giants would be fed 240 tons of coal/hr (90% C, 10% H,), 50% of... In a continuous manufacturing process, chlorodifluoromethane (CHClF 2 ) initially at 10 bar and 420 K, passes through an adiabatic pressure reducing valve so that its pressure is 0.1 bar (this last... The composite post in Figure 1.49 has the same properties and dimensions as in Problem 1.13, except that there is a gap = 0.1 mm between the top of thecover plate on the post and the upper support.... For a simplified analysis of the vibration of an airplane in the vertical direction, a threedegree-of-freedom model, as shown in Fig. 6.26, can be used. The three masses indicate the masses of the... In the toggle mechanism, shown in Fig.2.59, crank \(O_{1} A\) rotates at \(30 \mathrm{rpm}\) clockwise. \(O_{1} A=40 \mathrm{~mm}\), \(A B=140 \mathrm{~mm}, B C=100 \mathrm{~mm}, B D=80... Find a real physical example of a mechanical structure or machine that has tensile stress present. (a) Make a clear, labeled drawing of the situation. (b) Estimate the dimensions of the structure or... The currents i 1 , i 2 , and i 3 in the circuit shown in Figure P12 are described by the following equation set if all the resistances are equal to R. Here 1 and 2 are applied voltages; the other... For the soil A, B, and C in Problem 2.7, find the suitability numbers using Eq. (5.17) and the suitability of these soil for densification using vibroflotation method. What are these soil? Eq. (5.17)... A horizontal force of F = {-50i} N is applied perpendicular to the handle of the pipe wrench. Determine the moment that this force exerts along the axis OA (z axis) of the pipe assembly. Both the... Figure P.8.12 shows an embankment load on a silty clay soil layer. Determine the stress increase at points A, B, and C, which are located at a depth of 5 m below the ground surface. Figure P.8.12 K 6... The pliers are used to grip the tube at B. If a force of 20 lb is applied to the handles,determine the internal shear force and moment at point C. Assume the jaws of the pliers exert only normal... Select a mechanical component from Part 3 of this book (roller bearings, springs, etc.), go to your universitys library or the appropriate internet website, and, using the Thomas Register of American... An article in Industrial Quality Control (1956, pp. 5-8) describes an experiment to investigate the effect of the type of glass and the type of phosphor on the brightness of a television tube. The... The percentage of hardwood concentration in raw pulp, the vat pressure, and the cooking time of the pulp are being investigated for their effects on the strength of paper. Three levels of hardwood... An Otto cycle with a compression ratio of 8 begins its compression at 94 kPa and 10C. The maximum cycle temperature is 900C. Utilizing air-standard assumptions, determine the thermal efficiency of... A balloon initially contains 40 m 3 of helium gas at atmospheric conditions of 100 kPa and 17C. The balloon is connected by a valve to a large reservoir that supplies helium gas at 125 kPa and 25C.... Find the transfer function, G(s) = V o (s)/V i (s), for each operational amplifier circuit shown in Figure P2.7. 100 kQ 2 F 500 k2 2 F 100 k2 100 k2 2 F (1)'a 100 k2 2 uF (b) Image-based homing for robots can be implemented by generating heading command inputs to a steering system based on the following guidance algorithm. Suppose the robot shown in Figure P3.13(a) is to... A minivan starts from rest on the road whose constant radius of curvature is 40 m and whose bank angle is 10. The motion occurs in a horizontal plane. If the constant forward acceleration of the... A golf ball is driven with the initial conditions shown in the figure. If the wind imparts a constant horizontal deceleration of 4 ft/sec 2 , determine the values of r, r, r, , , and when t = 1.05... The 50-kg crate is stationary when the force P is applied. Determine the resulting acceleration of the crate if (a) P = 0, (b) P = 150 N, and (c) P = 300 N. s = 0.20 %3D Hk = 0.15 50 kg P 15 The two spheres, each of mass m, are connected by the spring and hinged bars of negligible mass. The spheres are free to slide in the smooth guide up the incline . Determine the acceleration a C of... U.S. airlines average about 1.6 fatalities per month. (Statistical Abstract of the United States: 2010.) Assume the probability distribution for Y, the number of fatalities per month, can be... Given the system shown in Figure P9.10, find the values of K and K f so that the closed-loop dominant poles will have a damping ratio of 0.5 and the underdamped poles of the minor loop will have a... Design the values of K 1 and K 2 in the system of Figure P7.15 to meet the following specifications: Steady-state error component due to a unit step disturbance is -0.00001; steady-state error... Air with a density of 0.07 lbm/ft 3 is flowing upward in the vertical duct, as shown. The velocity at the inlet (station 1) is 90 ft/s, and the area ratio between stations 1 and 2 is 0.3 (A 2 /A 1 =... Determine V D and V GS for the fixed-bias configuration of Fig. 7.79. 20 V 18 V 2 k2 2,2 k2 VD OVD Ipss = 5 mA Vp = -5 V Ipss Vp = -4 V = 8 mA 1 M2 2 4 V FIG. 7.78 FIG. 7.79 Determine the stretch of each spring for equilibrium of the 20-kg cylinder. D A KAD=400 N/m B KAB = 300 N/m KAC = 200 N/m -3 m- 4 m 3 m The mechanism shown was thought by its inventor to be the perpetual-motion machine. It consists of stand A, two smooth idler wheels B and C, and in between a uniform hollow cylindrical ring D... The disk has a mass of 10 kg. If it is suspended from a spring having an unstretched length of 400 mm, determine the angle for equilibrium. k = 600 N/m 200 mm Determine the force in the cable as a function of , needed to support the 100-kg hatch door. P 2 m C 2 m B The cantilevered jib crane is used to support the load of 780 lb. If the trolley T can be placed anywhere between 1.5 ft < x < 7.5 ft determine the maximum magnitude of reaction at the supports A and... Determine the force in each member of the truss and state if the members are in tension or compression. Assume all member are pin connected. 3 m 1 m E -2 m D B -2 m C 20 KN Determine the shear force and moment acting at point C of the beam. For the calculation use Simpsons rule to evaluate the integrals. W 2 kip/ft ' W = 1/2 (2x +x + 4) 2 ft C 2 ft 11.58 kip/ft B X Determine the moment of inertia of the thin plate about an axis perpendicular to the page and passing through the pin at O. The plate has a hole in its center. Its thickness is 50 mm, and the... If F = {16i + 10j - 14k) N, determine the magnitude of the of F along the axis of the pole and perpendicular projection to it. X N 4 m 60 F 2 m Determine the shear and moment as a function of x, where 0 x < 3m and 3m < x 6m, and then draw the shear and moment diagrams. A -3 m- 30 kN-m C -3 m- B Determine the couple moment M needed to create a force of F = 200 N on the slider block at C. F= 200 N 300 mm B -200 mm 80 mm A woman having a weight of 175 lb attempts to hold herself using one of the two methods shown. Determine the total force she must exert on bar AB in each case and the normal reaction she exerts on... A small solar engine is used for water pumping in a desert area. Water is the working fluid. Water enters the pump as saturated liquid at 50C and is pumped up to 2 bar by a small centrifugal pump.... The cooling system for a small private jet airplane consists of the hardware shown here. High-pressure air from the aircraft engine compressor is fed to a small turbine at state 1 (temperature T 1 ).... Before the trunk of a large tree is felled, cables AB and BC are attached as shown. Knowing that the tensions in cables AB and BC are 555 N and 660 N, respectively, determine the moment about O of... The average amount of solar energy received at the earths surface in a certain location is approximately 1350 W/m 2 . This energy can be used in a solar power plant, because of the reradiation of... Use the moment-area theorems and determine the slope at A and displacement at C. EI is constant. A 3 m- C 8 kN Probs. F7-13/14 3 m B Solar radiation incident on a large body of clean water (k = 0.61 W/m K and = 0.15 10 -6 m 2 /s) such as a lake, a river, or a pond is mostly absorbed by water, and the amount of absorption varies... Two common examples of activities needed to develop a performance economy are car sharing and electronics take-back (see Box 19.3). Sketch an approximate life cycle system boundary of these... A slipper-pad bearing (Fig. P1023) is often encountered in lubrication problems. Oil flows between two blocks; the upper one is stationary, and the lower one is moving in this case. The drawing is... The double-web girder is constructed from two plywood sheets that are secured to wood members at its top and bottom. If each fastener can support \(600 \mathrm{lb}\) in single shear, determine the... In a continuous manusfacturing process chlorodifluoromethane (CHClF 2 ) initially at 10 bar and 420C passes through and adiabatic pressure reducing valve so that its pressure is reduced to 0.1 bar... Consider the pistoncylinder assembly containing a pure gas shown below. The initial volume of the gas is 0.05 m3, the initial pressure is 1 bar, and the cross-sectional area of the piston is 0.1 m2.... Solve Prob. 8-33 using Castigliano's theorem. Data From Problem 8.33 A 2 k/ft 12 ft B 6 ft C A four-bar mechanism with ternary link is shown in Fig.3.9(a). The lengths of various links is given as below: \[ \begin{aligned} O_{1} O_{2} & =600 \mathrm{~mm}, O_{1} A=300 \mathrm{~mm}, A B=400... For each of the following systems, give two examples of how a mechanical engineer would be involved in its analysis. (a) Jet engine for a commercial airliner (b) Rover robot for planetary exploration... The mobile boom lift is used in construction and maintenance applications (Figure P4.16). The hydraulic cylinder AB exerts a 10-kN force on joint B that is directed along the cylinder. By using the... Channel-lock pliers hold a round metal bar as a machinist grips the handles with P = 50 N (Figure P4.21). Using the free body diagram shown for the combined lower jaw and upper handle, calculate the... A spur gear transmits 35 N m of torque to the 20-mm-diameter driveshaft. The 5-mm-diameter setscrew threads onto the gears hub, and it is received in a small hole that is machined in the shaft.... For the compound geartrain, obtain an equation for the velocity and torque ratios in terms of the numbers of teeth labeled in Figure P8.20. Figure P8.20 Output Input Ns N6 N, II Ns N2 N; U N4 Figure P2.7 shows the grain-size distribution of four soil A, B, C, and D. The plastic limit and liquid limit of the fines are as follows. Describe the four soil and give their USCS symbols. Figure... For the soil profile described in Problem 3.5, estimate an average peak soil friction angle. Use Eq. (3.31b). Problem 3.5 Following is the variation of the field standard penetration number (N 60 )... A 500 mm diameter and 20 m long concrete pile is driven into a sand where = 18.5 kN/m 3 and ' = 32. Assuming ' = 0.7' and K = 1.5 K o , determine the loadcarrying capacity of the pile, with a factor... An engineer has performed an experiment to study the effect of four factors on the surface roughness of a machined part. The factors (and their levels) are A = tool angle (12, 15). B = cutting fluid... For the rotational mechanical system shown in Figure P2.18, find the transfer function G(s) = 2 (s)/T(s) 1 N-m/rad T(1t) O2(1) 1 kg-m2 1 N-m-s/rad 1 N-m-s/rad 1 N-m-s/rad FIGURE P2.18 For the rotational mechanical system with gears shown in FigureP2.20,findthe transfer function, G(s) = 3 (s)/T(s). The gears have inertia and bearing friction as shown. T(t) to J1. D N2 N3 Jz, D2... One kilogram of water vapor at 200 kPa fills the 1.1989-m 3 left chamber of a partitioned system shown in Fig. P337. The right chamber has twice the volume of the left and is initially evacuated.... Find the transfer function, G(s) = X 2 (s)/F(s), for the translational mechanical system shown in Figure P2.11. 8 kg 2 N/m 4 N-s/m 2 N-s/m FIGURE P2.11 In this chapter, we described the state-space representation of single input, single-output systems. In general, systems can have multiple inputs and multiple outputs. An autopilot is to be designed... A boy tosses a ball onto the roof of a house. For the launch conditions shown, determine the slant distance s to the point of impact. Also, determine the angle which the velocity of the ball makes... The game of roulette. Refer to the game of roulette and the events described in Exercise 3.20. Find a. P(A| B) b. P(B | C) c. P(C | A) Data from Exercise 3.20 One game that is popular in many... The winch takes in cable at the rate of 200 mm /s, and this rate is momentarily increasing at 500 mm /s each second. Determine the tensions in the three cables. Neglect the weights of the pulleys. 2... Refer to Exercise 6.16. a. Find E(X). b. Find E(Y). c. Find E (X + Y). d. Find E(XY). Data from Exercise 6.16 Let X and Y have the joint density Scxy if 0 s x < 1; 0 s ys 1 lo f(x, y) elsewhere Steam-driven power generators rotate at a constant speed via a governor that maintains constant steam pressure in the turbine. In addition, automatic generation control (AGC) or load frequency... Determine the standard heat for one of the reactions of Prob. 4.23: part (a) at 600C, part (b) at 50C, part (f) at 650C, part (i) at 700C, part (j) at 590(F), part (l) at 770(F), part (m) at 850 K,... The excess Gibbs energy for binary systems consisting of liquids not too dissimilar in chemical nature is represented to a reasonable approximation by the equation: where A is a function of... You have liquid in each graduated cylinder shown: You then add both samples to a beaker. How would you write the number describing the total volume? What limits the precision of this number? mL 5 4 3... Consider the state variable model with parameter K given by Plot the characteristic values of the system as a function of K in the range 0 K 100. Determine that range of K for which all the... Determine the tension developed in cables AB and AC and the force developed along strut AD for equilibrium of the 400-lb crate. 3 5.5 ft 2 ft Z D 2 ft B 6 ft. 4 ft A 2.5 ft y A vector field is given by H = 10yz 2 a x 8xyza y + 12y 2 a z (a) Evaluate H at P(1, 2, 4) (b) Find the component of H along a x a y at P. The 25-kg bar has a center of mass at G. If it is supported by a smooth peg at C, a roller at A, and cord AB, determine the reactions at these supports. A DOD 0.5 m 0.2 m G 30 15 0.3 m C D B Replace the force system acting on the frame by an equivalent resultant force, and specify where the resultants line of action intersects member BC, measured from point B. 40 lb B 2 ft 20 lb 5 ft A 5... Determine the magnitude and orientation of of force F and its placement d on the beam so the loading system is equivalent to a resultant force of 15 kN acting vertically downward at point O and a... Determine the components of reaction at C. 250 N B C D -1.5 m-1.5 m- -1.5 m-1.5 m- 2 m 2 m E The sign has a mass of 100 kg with center of mass at G. Determine the x, y, z components of reaction at the ball-andsocket joint A and the tension in wires BC and BD. 1m GC 2 m A 2 m 1 m QD 1'm G 1 m The 50-lb cylinder is attached to a cord which passes over the fixed drum. If the coefficient of static friction between the cord and the drum is s = 0.3, determine the angle of of the cord if the... A two-dimensional diverging duct is being designed to diffuse the high-speed air exiting a wind tunnel. The x-axis is the centerline of the duct (it is symmetric about the x-axis), and the top and... Consider a municipal water treatment plant for a small community (Fig. P1.1). Waste water, 32,000 m 3 /day, flows through the treatment plant with a mean residence time of 8 hr, air is bubbled... For a cylindrical particle, derive the relationship between the ratio of surface area to volume, A/V, and the particle aspect ratio, l/d, and verify the shape of the curve shown in Figure 1.3. FIGURE... For the case of methanol synthesis discussed in Example 22.2, determine the appropriate expression for the equilibrium constant K(T) for the case when inerts are present in the feed along with the...
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