Experience has shown that a manufacturer of rewritable CDs produces, on the average, only 1 defective CD in 100. Suppose that of the next 4 CDs manufactured, at least 1 is defective. What would you...

Solve the following state equation and output equation for y(t), where u(t) is the unit step. Use the Laplace transform method. -3 x+ u(t) -1 y = [1 0]x; x(0) =

Figure P4.16 shows the step response of an electric vehicles mechanical brakes when the input is the drive torque (N-m) and the output is the hydraulic brake pressure (bar) (Ringdorfer, 2011). a....

Given the following system represented in state space, solve for Y(s) using the Laplace transform method for solution of the state equation: -2 -4 1 x+ |0 0 e- 0 -6 y = [0 0 1]x; x(0) =

Given the following state-space representation of a system, find Y(s): 1 x + sin 3t -3 3. y = [1 2]x; x(0) = %3D

Two uniform spheres are positioned as shown. Determine the gravitational force which the titanium sphere exerts on the copper sphere. The value of R is 40 mm. y opper 2R 6R 35 R Titanium Problem 1/6

A train which is traveling at 80 mi/hr applies its brakes as it reaches point A and slows down with a constant deceleration. Its decreased velocity is observed to be 60 mi/hr as it passes a point 1/2...

Two configurations for raising an elevator are shown. Elevator A with attached hoisting motor and drum has a total mass of 900 kg. Elevator B without motor and drum also has a mass of 900 kg. If the...

The standard test to determine the maximum lateral acceleration of a car is to drive it around a 200-ft-diameter circle painted on a level asphalt surface. The driver slowly increases the vehicle...

The car of Prob. 3/61 is traveling at 25 mi/hr when the driver applies the brakes, and the car continues to move along the circular path. What is the maximum deceleration possible if the tires are...

The particle of mass m = 0.2 kg travels with constant speed v in a circular path around the conical body. Determine the tension T in the cord. Neglect all friction, and use the values h = 0.8 m and v...

The hollow tube assembly rotates about a vertical axis with angular velocity = = 4 rad /s and = = 2 rad /s 2 . A small 0.2-kg slider P moves inside the horizontal tube portion under the control...

Once under way at a steady speed, the 1000-kg elevator A rises at the rate of 1 story (3 m) per second. Determine the power input P in into the motor unit M if the combined mechanical and electrical...

The cars of an amusement-park ride have a speed v 1 = 90 km/h at the lowest part of the track. Determine their speed v 2 at the highest part of the track. Neglect energy loss due to friction....

A 60-g bullet is fired horizontally with a velocity v 1 = 600 m/s into the 3-kg block of soft wood initially at rest on the horizontal surface. The bullet emerges from the block with the velocity v 2...

The 90-kg man dives from the 40-kg canoe. The velocity indicated in the figure is that of the man relative to the canoe just after loss of contact. If the man, woman, and canoe are initially at rest,...

The rigid assembly which consists of light rods and two 1.2-kg spheres rotates freely about a vertical axis. The assembly is initially at rest and then a constant couple M = 2 N m is applied for 5 s....

The 2-kg sphere is projected horizontally with a velocity of 10 m /s against the 10-kg carriage which is backed up by the spring with stiffness of 1600 N/m. The carriage is initially at rest with the...

Compute the final velocities v 1 and v 2 after collision of the two cylinders which slide on the smooth horizontal shaft. The coefficient of restitution is e = 0.8. v1 = 7 m/s U2 = 1 m/s %3D m1 = 2...

The assembly of two 5-kg spheres is rotating freely about the vertical axis at 40 rev/min with = 90. If the force F which maintains the given position is increased to raise the base collar and...

A system is represented by the state and output equations that follow. Without solving the state equation, find a. The characteristic equation; b. The poles of the system 0 2 3 i = 0 6 5x+ 1 u(t) 4 2...

A system is represented by the state and output equations that follow. Without solving the state equation, find the poles of the system. X = -4 3. x+ -2 u(t) y = [5 1]x

If v i (t) is a step voltage in the network shown in Figure P4.25, find the value of the resistor such that a 20% overshoot in voltage will be seen across the capacitor if C = 10 -6 F and L = 1 H. R...

For the unity feedback system shown in Figure P7.1, where find the steady-state errors for the following test inputs: 25u(t); 37tu(t); 47t 2 u(t). 450(s + 8)(s + 12)(s+ 15) G(s) = s(s + 38)(s + 2s+...

The two attached pulleys are driven by the belt with increasing speed. When the belt reaches a speed v = 2 ft/sec, the total acceleration of point P is 26 ft/sec 2 . For this instant determine the...

The thin hoop of negligible mass and radius r contains a homogeneous semicylinder of mass m which is rigidly attached to the hoop and positioned such that its diametral face is vertical. The assembly...

Briefly describe the difference between an edge dislocation and a screw dislocation.

Some instruments having angular motion are damped by means of a disk connected to the shaft . The disk, in turn, is immersed in a container of oil, as shown. Derive a formula for the damping torque...

Is the block in this figure stable floating in the position shown? Show your calculations. L= 3H - W= 2H- H H Water

A pipe 15 cm in diameter bends through 135. The velocity of flow of gasoline (SG = 0.8) is 8 m/s, and the pressure is 100 kPa gage throughout the bend. Neglecting gravitational force, determine the...

State Newtons second law of motion. What are the limitations on the use of Newtons second law? Explain.

How long will it take the water surface in the tank shown to drop from h = 3 m to h = 50 cm? 60 cm diameter h 3 cm diameter V= V2gh

A bicyclist is capable of delivering 275 W of power to the wheels. How fast can the bicyclist travel in a 3 m/s headwind if his or her projected area is 0.5 m 2 , the drag coefficient is 0.3, and the...

Flow over a rectangular plate produces an average wall shear stress of 1.2 pascals. Calculate the friction drag in units of N. The plate dimensions are 1.5 m by 2.0 m. The plate is inclined at 20...

Air at 60F and atmospheric pressure flows in a horizontal duct with a cross section corresponding to an equilateral triangle (all sides equal). The duct is 100 ft long, and the dimension of a side is...

What is the head loss in terms of V 0 2 /2g for the flow nozzle shown? Vo D 3

An electric hand mixer draws 1.5 amperes at 110 volts. It is used to mix 1 kg of cookie dough for 5 minutes. After mixing, the temperature of the cookie dough is found to have increased by 5C. If the...

Justify the following equations: ( - VR aln T P.x RT RT2 T.x GR Ex, In Exd In = 0 (const T, P) RT

If the molar density of a binary mixture is given by the empirical expression: find the corresponding expressions for V 1 and V 2 p= ag + ajx1 +a2xf

Given below are values of G E /Jmol 1 , H E /Jmol 1 , and C E P / J mol 1 K 1 for some equimolar binary liquid mixtures at 298.15 K. Estimate values of G E , H E , and S E at 328.15 K for one of...

Consider a binary liquid mixture for which the excess Gibbs energy is given by G E /RT = Ax 1 x 2 (x 1 + 2x 2 ). What is the minimum value of A for which liquid/liquid equilibrium is possible?

Determine the output voltage of an op-amp for input voltages of V i1 = 200 mV and V i2 = 140 mV. The amplifier has a differential gain of Ad = 6000 and the value of CMRR is: a. 200. b. 10 5 .

The pressure above a mixture of ethanol and ethyl acetate at 70C is measured to be 78 kPa. What are the possible compositions of the liquid and vapor phases? Problems 12.3 through 12.8 refer to the...

Assuming an ideal diode, sketch v i , v d , and i d for the half-wave rectifier of Fig. 2.168. The input is a sinusoidal waveform with a frequency of 60 Hz. Determine the profit value of v i from the...

Given the information provided in Fig. 4.123 , determine: a. R C . b. R E . c. R B . d. V CE . e. V B . 12 V 2 mA RC RB o 7.6 V Va Vce B = 80 02.4 V RE FIG. 4.123

a. For the common-emitter characteristics of Fig. 3.13, find the dc beta at an operating point of V CE = 6 V and I C = 2 mA. b. Find the value of a corresponding to this operating point. c. At V CE =...

a. In Fig. 17.22, if V Z = 50 V, determine the maximum possible value the capacitor C 1 can charge to (VGK 0.7 V). b. Determine the approximate discharge time (5t) for R 3 = 20 k. c. Determine the...

For the fixed-bias configuration of Fig. 7.75 : a. Sketch the transfer characteristics of the device. b. Superimpose the network equation on the same graph. c. Determine I DQ and V DSQ . d. Using...

The stagnation temperature on the Apollo vehicle at Mach 36 as it entered the atmosphere was 11,000 K, a much different value than predicted in Problem 8.17 for the case of a calorically perfect gas...

A unity feedback system has the loop transfer function Determine the relationship between the steady-state error to a ramp input and the gain K and system parameter b. For what values of K and b can...

Extreme temperature changes result in many failures of electronic circuits. Temperature control feedback systems reduce the change of temperature by using a heater to overcome outdoor low...

A T-frame structure is composed of prismatic beam ABC and non prismatic column DBF that are joined at B by a frictionless pin connection. The beam has sliding support at A and the column is pin...

A simply supported beam is subjected to a linearly varying distributed load q(x) 0 maximum intensity q 0 at B. The beam has a length L = 4 m and a rectangular cross-section with a width of 200 mm and...

Determine the magnitude of the resultant force F R = F 1 + F 2 and its orientation , measured counter clockwise from the positive x axis. F3 = 250 N F = 360 N 30% 45% 30 F = 400 N X

Determine the tension developed in cables OD and OB and the strut OC, required to support the 50-kg crate.The spring OA has an unstretched length of 0.8 m and a stiffness The force in the strut acts...

Determine the tension in the cables in order to support the 100-kg crate. x- C B 2 m N 2.5 m m D 2 m 1 m -y

The 25-kg flowerpot is supported at A by the three cords. Determine the force acting in each cord. x D N 60 30 30 B 45

If the bucket and its contents have a mass of 10 kg and are suspended from the cable by means of a small pulley at C, determine the location x of the pulley for equilibrium. The cable is 6 m long. 4...

Each cord can sustain a maximum tension of 500 N. Determine the largest mass of pipe that can be supported. FM E H B 60 1 Y H D E 25

If the mass of the block at A is 20 kg, determine the mass of the block at B and at C for equilibrium. Also, determine the angles u and f. A D 3 m B E -4 m C 3 m

The 30-kg pipe is supported at A by a system of five cords. Determine the force in each cord for equilibrium. G B 60 A H D E

Let P = 2a x 4a y + a z and Q = a x + 2a y . Find R which has magnitude 4 and is perpendicular to both P and Q.

Determine the force developed in the short link BD, and the tension in the cords CE and CF, and the reactions of the ball-and-socket joint A on the block. 3 m D 6 kN E 9 kN 1.5 m 4m

The davit is used to suspend the lifeboat over the side of a ship. If the boat exerts a force of 800 lb on the chain at D, determine the force acting on the hydraulic cylinder BC, and the horizontal...

Determine the magnitude of the moment of the force F = {50i - 20j - 80k} N about the baseline BC of the tripod. X 1.5 m 2 m 2m C 0.5 m B D F N 1 m 4 m A 2.5 m y

The curved pipe has a radius of 5 ft. If a force of 80 lb acts at its end as shown, determine the moment of this force about point C. Solve the problem by using two different position vectors. X 75-...

Using a ring collar the 75-N force can act in the vertical plane at various angles . Determine the magnitude of the moment it produces about point A, plt the result of M (ordinate) versus (abscissa)...

Replace the loading system acting on the post by an equivalent resultant force and couple moment at point O. 60 lb 3 4 P O 30 lb 1 ft 3 ft 2 ft 40 lb X

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 20 kN acting vertically downward at point O and a...

Replace the force and couple moment system acting on the beam by an equivalent resultant force and couple moment at point O. 0.2 m -1.5m 30 500 N -2m 15 -1.5 m- 200 N 200 N-m X

Replace the forces acting on the gear by an equivalent resultant force and couple moment acting at point O. 2.25 kN 175 mm 41 60 3 kN 20 175 mm w X

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 in each member of the truss. State if the members are in tension or compression. 600 16 450 lb YE A -3 ft- D B 30 -3 ft

Determine the force in each member of the truss and state if the members are in tension or compression. Set P 1 = 2 kN and P 2 = 1.5 kN. A 30 - 3 m B D P 30 3 m C P

Express the moment of the couple acting on the pipe assembly in Cartesian vector form. What is the magnitude of the couple moment? X Z 3 ft 1.5 ft X 1 ft. 20 lb. B 20 lb 1 ft 2 ft

If F = 80N, determine the magnitude and coordinate direction angles of the couple moment. The pipe assembly lies in the xy plane. X F 3 in. 3 in. 4 in. 10 lb Z -F 10 lb 30 -P 6 in. y

Three couple moments act on the pipe assembly. Determine the magnitudes of M 2 and M 3 so that the resultant couple moment is zero. My 0-2 120 120 120* M M-80N m

The hanger H is used to support the end of the floor beam B. If the loading on the hanger consists of two couples, determine the magnitude of the horizontal forces F and - F so that the resultant...

The cable exerts a 140-N force on the telephone pole. Determine the moment of this force about point A. Solve the problem using two different position vectors. F = 140 N/ 3 m B Z 6 m 2m -y

The force F = {6i + 8j + 10k} creates a moment about point O of M O = {-14i + 8j + 2k} N m. If the force passes through a point having an x coordinate of 1 m, determine the y and z coordinates of...

A force of F = {6i - 2j + 1k} k N produces a moment M O = {4i + 5j - 14k} of about the origin of coordinates, point O. If the force acts at a point having an x coordinate of x = 1 m, determine the y...

The pipe assembly is subjected to the 80-N force. Determine the moment of this force about point B. + 200 mm 30 N F = 80 N 400 mm 40 250 mm 300 mm 200 mm y

Determine the moment of the force of F = 600 N about point A. X 6 m B 45 4 m F N A 4 m 6 m

Determine the moment of the force F about point P. Express the result as a Cartesian vector. P X 2 m -3 m- 0 3 m- T A 1 m F = {2i + 4j6k) kN 3 m

The man pulls on the rope with a force of F = 20 N. Determine the moment of this force about the base of the pole at O. Solve the problem two ways, i.e., by using a position vector from O to A, then...

Determine the moment of the force F about point P. Express the result as a Cartesian vector. F = (-6i+4j+ 8k) kN 6 m x A -2 m- O N 4 m 1m P 3 m

Determine the smallest force F that must be applied to the rope in order to create a moment of M = 900 N m at point O. x B 1.5 m m F A 10.5 m

Determine the couple moment acting on the pipe assembly and express the result as a Cartesian vector. x B FA = 450 N 0.4 m 35 4 5 0.3 m 0 FB = 450 N C

The force F = {400i - 100j - 700} Ib acts at the end of the beam. Determine the moment of this force about point A. T 1.5 ft B -0.25 ft 8 ft N

A force of 80 N acts on the handle of the paper cutter at A. Determine the moment created by this force about the hinge at O, if = 60 At what angle should the force be applied so that the moment it...

If the man at B exerts a force of p = 30 Ib on his rope, determine the magnitude of the force F the man at C must exert to prevent the pole from rotating, i.e., so the resultant moment about A of...

Determine the moment of the force F about point O. Express the result as a Cartesian vector. F = (-6i+4j+ 8k) kN 6 m X -2 m- N 4 m 1m P 3 m

The cable exerts a force of P = 6 kN at the end of the 8-m-long crane boom. If = 30, determine the placement x of the hook at B so that this force creates a maximum moment about point O. What is...

If F B = 30 and F c = 45 Ib determine the resultant moment about the bolt located at A. 2.5 ft 20 FB 0.75 ft 30 Fc

The man exerts the wo forces on the handle of the shovel. Determine the resultant moment of these forces about the blade at A. 800 mm 65 450 mm F = 12 N F = 30 N 30 20

Region 1 is defined by x y + 2z > 5 with 1 = 2 o , while region 2 is defined by x y + 2z < 5 with 2 = 5 o . If H 1 = 40a x + 20a y 30a z A/m, find (a) H 1n , (b) H 2t ,

Determine the moment of inertia of the area about the x axis. -3 in.3 in. 2 in. 6 in. 4 in. X

Determine the moment of inertia of the Z section with respect to the x and y centroidal axes. 1 in. 4 in.- 4 in.- 1 in. T-4 in. -1 in. 8 in. X 1 in.

Draw the free-body diagram for the following problems. a) The beam in Prob. 510. b) The beam in Prob. 511. c) The beam in Prob. 512. d) The beam in Prob. 514.