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

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...

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

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 P5.13, find the poles of the closed-loop transfer function, T(s) = C(s)/R(s). 3 C(s) 5s R(s) 4 FIGURE P5.13

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

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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....

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

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

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

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

Determine the moment of each of the three forces about point A. F=250 N 30% A -2 m- -3 m B F = 300 N 60 4'm 5 F3 = 500 N

An antenna located at the origin has a far-zone electric field as (a) Obtain the corresponding H s field. (b) Determine the power radiated. (c) What fraction of the total power is radiated in the...

Determine the radius of gyration k y of the parabolic area. 160 mm y -y=0.1(1600-x) 40 mm X

Determine the moment of inertia I y of the shaded area about the y axis. 150 mm 150 mm O -100 mm-+-1 |- 100 mm-|-150 mm - 75 mm X

Determine the weight of the wedge which is formed by rotating a right triangle of base 6 in. and height 3 in. through an angle of 30. The specific weight of the material is = 0.22 lb/in 3 . 6 in. 30...

The load can be supported by two boys when the cord is suspended over the pipe (a half-turn). If each boy can pull with a force of 125 lb, determine the maximum weight of the load. Can one boy...

The 50-lb cylinder is attached to a cord which passes over the fixed drum. If the coefficient of static friction at the drum is s = 0.3, determine the maximum force P that can be applied to the...

Determine the minimum tension in the rope at points A and B which is necessary to maintain equilibrium. The coefficient of static friction between the rope and the fixed post D is s = 0.3. The rope...

Determine the force P that must be applied to the handle of the lever so that the wheel is on the verge of turning if M = 300 N m. The coefficient of static friction between the belt and the wheel...

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 ofThe hand clamp is constructed using a...

A cone is attached to the hemisphere. If both pieces have the same density, determine the height h of the cone if the configuration is to be in neutral equilibrium. 3 ft h

Express the following in terms of r, , and : ar ar a 20

When the motorcyclist is at A, he increases his speed along the vertical circular path at the rate of v = (0.3t) ft/s, where t is in seconds and t = 0 at A. If he starts from rest at A, determine the...

When t = 0, the train has a speed of 8 m/s, which is increasing at 0.5 m/s 2 . Determine the magnitude of the acceleration of the engine when it reaches point A, at t = 20 s. Here the radius of...

a. Let (e1, e2, e2) be unit vectors of a right-handed, orthogonal coordinate system. Showthat the Levi-Civit`a symbol satisfies b. Prove that c. Prove that: d. In quantum mechanics, the Cartesian...

The uniform slender rod has a mass of 5 kg. If the cord at A is cut, determine the reaction at the pin O, (a) When the rod is still in the horizontal position, and (b) When the rod swings to the...

A uniform plate has a weight of 50 lb. Link AB is subjected to a couple moment of M = 10 lb ft and has a clockwise angular velocity of 2 rad/s at the instant = 30. Determine the force developed in...

The door has a weight of 200 lb and a center of gravity at G. Determine the constant force F that must be applied to the door to push it open 12 ft to the right in 5 s, starting from rest. Also, find...

The slender rods have a weight of 3 lb/ft Determine the moment of inertia of the assembly about an axis perpendicular to the page and passing through point A. A -1.5 ft 1.5 ft 2 ft 1 ft

The uniform bar AB has a mass of 12 kg and is pin connected at A. If the support at B is remove ( = 90), determine the velocity of the 5-kg block C at the instant the bar rotates downward to = 150....

The 25-lb slender rod AB is attached to spring BC which has an unstretched length of 4 ft. If the rod is released from rest when = 30, determine its angular velocity at the instant = 90. C 4 ft k =...

A uniform ladder having a weight of 30 lb is released from rest when it is in the vertical position. If it is allowed to fall freely, determine the angle at which the bottom end A starts to lift off...

The 2-kg disk is thrown down onto the rough surface with the velocity and angular velocity shown. If there is no slipping, and the coefficient of restitution is e = 0.5, determine the velocity of the...

The global robot industry is growing rapidly A typical industrial robot has multiple degrees of freedom. A unity feedback position control system for a force-sensing joint has a loop transfer...

In the figure for Problem 13-35, pinion 2 is to be a right-hand helical gear having a helix angle of 30, a normal pressure angle of 20, 16 teeth, and a normal diametral pitch of 6 teeth/in. A motor...

Consider a pistoncylinder assembly containing 0.12 kg of superheated steam at 700 kPa and 800 K (state 1). Energy is removed from the steam by heat transfer until a temperature of 400 K is reached...

Knowing that at the instant shown bar DE has an angular velocity of 20 rad/s clockwise and an angular acceleration of 5 rad/s 2 counterclockwise, determine in the position shown (a) The angular...

Estimate the capital cost of a plant that produces 80,000 metric tons per year of caprolactam.

Given that what is the relation between the rates of formation and disappearance of the three reaction components? 1/1/0 = NO5, 2 2NO +

On typical summer days, field crickets nibble, jump, and chirp now and then. But at a night when great numbers congregate, chirping seems to become a serious business and tends to be in unison. In...

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...

You just borrowed $250,000 to purchase a new house. The nominal interest rate is 6% p.a., compounded monthly, and the monthly payment is $1612 for the loan. What is the duration of the loan?

A 60-Hz, three-phase, four-pole induction motor delivers full load torque at 3% slip. If the load torque rises by 20% (overload condition), determine the new speed.

a. Example 8-1: Trambouze Reactions Wolfram 1. Fix k 2 at 0.015 and then describe how the selectivity varies with k 1 and k 3 . 2. Write a conclusion about your experiments. Polymath 3. What would...

(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...

What is the pH of a solution prepared by dissolving 1.23 g of 2-nitrophenol (FM 139.11) in 0.250 L?

(a) If a diffraction grating has a resolution of 10 4 , is it possible to distinguish two spectral lines with wavelengths of 10.00 and 10.01 m? (b) With a resolution of 10 4 , how close in...

Imagine you are tasked with designing a single dishwasher for both the European and American markets. Determine a set of global, social, environmental, and economic issues you would have to consider...

An 8-mm-diameter aluminum rod has lines scribed on it that are exactly 10 cm apart (Figure P5.9, see on page 228). After a 2.11-kN force has been applied, the separation between the lines has...

A circular rod of length 25 cm and diameter 8 mm is made of 1045 grade steel. (a) Calculate the stress and strain in the rod, and its extension, when it is subjected to 5 kN of tension. (b) At what...

The tires of the 4555-lb sedan are 6.5 in. wide (Figure P5.10). Each tire contacts the ground over a distance of 4.25 in. as measured along the vehicles length. Calculate the compressive stress...

Compound lever shears cut through a piece of wire at A (Figure P5.32). (a) By using the free body diagram of handle CD, determine the magnitude of the force at rivet D. (b) Referring to the magnifi...

(a) A 1.5-mm-diameter steel sphere (7830 kg/m 3 ) is dropped into a tank of SAE 30 oil. What is its terminal velocity? (b) If the sphere is instead dropped into a different oil of the same density...

A fenced enclosure consists of a rectangle of length L and width 2R, and a semicircle of radius R, as shown in Figure P20. The enclosure is to be built to have an area A of 1600 ft 2 . The cost of...

A fence around a field is shaped as shown in Figure P12. It consists of a rectangle of length L and width W, and a right triangle that is symmetrical about the central horizontal axis of the...

A granular soil with G s = 2.65, e max = 0.870, and e min = 0.515 is compacted to a moist unit weight of 17.36 kN/m 3 at moisture content of 10.5%. What is the relative density of this compacted sand?

The equation of motion for a pendulum whose base is accelerating horizontally with an acceleration a(t) is Suppose that g = 9.81 m/s 2 , L " 1 m, and (0) = 0. Plot ,(t) for 0 t 10 s for the...

Force F acts on the frame such that its component acting along member AB is 650 lb, directed from B towards A, and the component acting along member BC is 500 lb, directed from B towards C. Determine...

If FB = 3kN and = 45, determine the magnitude of the resultant force of the two tugboats and its direction measured clockwise from the positive x axis. F= 2 kN 30 FB B.

Determine the x and y components of each force acting on the gusset plate of a bridge truss. Show that the resultant force is zero. F = 6 kN F = 8 kN 888 F = 4 kN F, = 6 kN 888 888

Determine the magnitude of the resultant force and its direction measured counterclockwise from the positive x axis. F2 = 26 kN 1213 5 30 F, = 30 kN

Following is the variation of the field standard penetration number (N 60 ) in a sand deposit: Depth (m) .............. N 60 1.5 ............................. 6 3 ................................ 8...

Refer to Problem 3.5. Using Eq. (3.22), determine the average relative density of the sand. Problem 3.5 Following is the variation of the field standard penetration number (N 60 ) in a sand deposit:...

The tower crane is used to hoist the 2-Mg load upward at constant velocity. The 1.5-Mg jib BD, 0.5-Mg jib BC, and 6-Mg counterweight C have centers of mass at G1 , G2 , and G3 , respectively....

If the 1500-lb boom AB, the 200-lb cage BCD, and the 175-lb man have centers of gravity located at points G 1 , G 2 and G 3 , respectively, determine the resultant moment produced by each weight...

If the resultant couple of the three couples acting on the triangular block is to be zero, determine the magnitude of forces F and P. -F F 150 N B 300 mm 500 mm 600 mm 150 N -P -400 mm

Determine the magnitude of F so that the resultant couple moment is 12 kNm, counterclockwise. Where on the beam does the resultant couple moment act? -F F 30 30 8 kN 0.3 m 1.2 m 0.4 m- 8 kN

Two couples act on the beam as shown.If F = 150 lb, determine the resultant couple moment. 200 Ib 1.5 ft 200 lb F 4 ft

Replace the loading by an equivalent resultant force and couple moment acting at point O. 50 Ib/ft -9 ft 9 ft 50 Ib/ft

Replace the loading by an equivalent resultant force and specify its location on the beam, measured from point A. 5 kN/m 2 kN/m 4 m- 2 m