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.

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 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...

A rotating step shaft is loaded as shown, where the forces F A and FB are constant at 600 lbf and 300 lbf, respectively, and the torque T alternates from 0 to 1800 lbf in. The shaft is to be...

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....

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...

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...

On doubling the concentration of reactant, the rate of reaction triples. Find the reaction order.

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...

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?...

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...

Repeat Example 9.2, but with a feed pressure of 5.0 MPa. Compare your results to those obtained at a feed pressure of 1.0 \(\mathrm{MPa}\). Data From Example 9.2:- Air can be separated into...

In the mechanism shown in Fig.2.14(a), the crank \(O_{1} A\) rotates at a uniform speed of \(650 \mathrm{rpm}\). Determine the linear velocity of the slider \(C\) and the angular speed of the link...

An unknown sample of Ni 2+ gave a current of 2.36 A in an electrochemical analysis. When 0.500 mL of solution containing 0.028 7 M Ni 2+ was added to 25.0 mL of unknown, the current increased to 3.79...

Calculate the pH when 25.0 mL of 0.020 0 M 2-aminophenol have been titrated with 10.9 mL of 0.015 0 M HClO 4 .

A large piece of dry rock has a mass of 2450 kg and volume of 0.925 m 3 . The specific gravity of the rock mineral is 2.80. Determine the porosity of the rock.

The bulk density of a compacted soil specimen (Gs = 2.70) and its water content are 2060 kg/m 3 and 15.3%, respectively. If the specimen is soaked in a bucket of water for several days until it is...

Determine the magnitude of the resultant force and its direction, measured counterclockwise from the positive x axis. F = 8 kN F2 = 5 kN 60 45 F = 4 kN

If the roller at A and the pin at B can support a load up to 4 kN and 8 kN, respectively, determine the maximum intensity of the distributed load w, measured in kN/m, so that failure of the supports...

Determine the location of the centroid C for the loop of the lemniscate, r 2 = 2a cos2, (-45 45). 12 = 2a? cos 20

A free-headed drilled shaft is shown in Figure P13.10. Let Q g = 260 kN, M g = 0, = 17.5 kN/m 3 , ' = 35, c' = 0, and E p = 22 10 6 kN/m 2 . Determine a. The ground line deflection, xo b. The...

Three different washing solutions are being compared to study their effectiveness in retarding bacteria growth in 5-gallon milk containers. The analysis is done in a laboratory, and only three trials...

An aluminum master alloy manufacturer produces grain refiners in ingot form. The company produces the product in four furnaces. Each furnace is known to have its own unique operating characteristics,...

Air is expanded from 1000 kPa and 600C at the inlet of a steady-flow turbine to 100 kPa and 200C at the outlet. The inlet area and velocity are 0.1 m 2 and 30 m/s, respectively, and the outlet...

Repeat Prob. 51 by first plotting the failure loci in the A , B plane to scale; then, for each stress state, plot the load line and by graphical measurement estimate the factors of safety. A...

Consider the reaction 2H 2 O 2H 2 + O 2 at 4000 K and 10 kPa. Will the amount of hydrogen gas produced be increased when the reaction occurs at 100 kPa rather than 10 kPa?

A mixture of 2 mol of CO 2 and 1 mol of O 2 is heated to 2800 K at a pressure of 4 atm. Determine the equilibrium composition of the mixture, assuming that only CO 2 , CO, O 2 , and O are present.

Name three applications for feedback control systems.

A 0.40-m 3 insulated pistoncylinder device initially contains 1.3 kg of air at 30C. At this state, the piston is free to move. Now air at 500 kPa and 70C is allowed to enter the cylinder from a...

A two-stage compression refrigeration system with an adiabatic liquid-vapor separation unit like that in Fig. P11 60 uses refrigerant-134a as the working fluid. The system operates the evaporator at...

Find the transfer function, G(s) = V o (s)/V i (s), for each network shown in Figure P2.5. Solve the problem using mesh analysis. + V(1)- 1 H 1 H 10 2 H 3 H vi(1) 12 vi(1) 1F Volt) (a) (b) FIGURE...

Represent the following transfer function in state space. Give your answer in vector-matrix form. s(s + 2) T(s) (s+ 1Xs + 2s + 5)

Given the dc servomotor and load shown in Figure P3.11, represent the system in state space, where the state variables are the armature current, i a , load displacement, L , and load angular...

Refer to the Journal of Engineering, Computing and Architecture (Vol. 3., 2009) study of cell phone handoff behavior, Exercise 3.15. Recall that the different color codes accessed by two different...

Refer to the IEICE Transactions on Information & Systems (Jan. 2005) study of impedance to leg movement, Exercise 2.46. Recall that Korean engineers attached electrodes to the ankles and knees of...

The velocity of a particle is given by v = 25t 2 80t 200, where v is in feet per second and t is in seconds. Plot the velocity v and acceleration a versus time for the first 6 seconds of motion and...

The sprinter begins from rest at position A and accelerates along the track. If the stationary tracking camera at O is rotating counterclockwise at the rate of 12.5 deg/s when the sprinter passes the...

Motion of the sliding block P in the rotating radial slot is controlled by the power screw as shown. For the instant represented, = 0.1 rad/s, = 0.04 rad /s2, and r = 300 mm. Also, the screw turns...

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 collar of mass m is released from rest while in position A and subsequently travels with negligible friction along the vertical-plane circular guide. Determine the normal force (magnitude and...

The system is released from rest with no slack in the cable and with the spring stretched 200 mm. Determine the distance s traveled by the 4-kg cart before it comes to rest (a) If m approaches zero...

Reduce the block diagram shown in Figure P5.9 to a single transfer function, T(s) = C(s)/R(s). Figure P5.9 G1 C(s) R(s) G2 G5 G6 G3 G4 G7

Find the equivalent transfer function, T(s) = C(s)/R(s), for the system shown in Figure P5.3. G1 R(s) + G5 G6 C(s) G2 G3 G4 G7 FIGURE P5.3

Refer to the Journal of Waterway, Port, Coastal, and Ocean Engineering (March/April, 2013) study of coastal sea level rise, Exercise 5.6. Recall that the acceleration Y in sea level rise...

The HIV infection linearized model developed in Problem 84, Chapter 4, can be shown to have the transfer function It is desired to develop a policy for drug delivery to maintain the virus count at...

End A of the slender pole is given a velocity v A to the right along the horizontal surface. Show that the magnitude of the velocity of end B equals v A when the midpoint M of the pole comes in...

The 30,000-lb concrete pipe section is being transported on a flatbed truck. Five inextensible cables are passed across the top of the pipe and tightened securely to the flatbed with an initial...

An external force F = F 0 sin wt is applied to the cylinder as shown. What value w c of the driving frequency would cause excessively large oscillations of the system? k 2m m YF

The system of Figure P7.12 is to have the following specifications: K v = 20; = 0.7. Find the values of K 1 and K f required for the specifications of the system to be met. O(s) + A(s) K1 s(s + 2)...

What is the approximate mass in units of slugs for a. A 2-liter bottle of water? b. A typical adult male? c. A typical automobile?

Apply the grid method to calculate the cost in U.S. dollars to operate a pump for one year. Th e pump power is 20 hp. The pump operates for 20 hr/day, and electricity costs $0.10 per kWh.

This problem involves a cylinder falling inside a pipe that is filled with oil, as depicted in the figure. The small space between the cylinder and the pipe is lubricated with an oil film that has...

If for a binary solution one starts with an expression for M (or M R or M E ) as a function of x 1 and applies Eqs. (10.15) and (10.16) to find M 1 and M 2 (or M R 1 and M R 2 or M E 1 and M E 2 )...

Consider a binary mixture for which the excess Gibbs energy is given by G E /RT = 2.1x 1 x 2 (x 1 + 2x 2 ). For each of the following overall compositions, determine whether one or two liquid phases...

A room in the lower level of a cruise ship has a 40-cm-diameter circular window. If the midpoint of the window is 2 m below the water surface, determine the hydrostatic force acting on the window,...

Determine the magnitude and coordinate direction angles of the resultant force acting on the bracket. X N 45 60 F = 450 N 45. 30 F = 600 N -y

Determine the resultant of the two forces and express the result as a Cartesian vector. x F= 180 lb 60 60 24. 135 25 F = 50 lb

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

Express the following vectors in rectangular coordinates: (a) A = sin a + cos a 2za z (b) B = 4r cos a r + r a

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...

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

The weights of the various components of the truck are shown. Replace this system of forces by an equivalent resultant force and specify its location measured from B. B 3 ft 3500 lb 8 5500 lb A -14...

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

Locate the centroid, y, and determine the orientation of the principal centroidal axes for the composite area. What are the moments of inertia with respect to these axes? -8 in.. 2 in. 2 in. + 8 in.....

If couple forces of F = 10 lb are applied perpendicular to the lever of the clamp at A and B, determine the clamping force on the boards. The single square-threaded screw of the clamp has a mean...

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 of s = 0.3. If the clamping force in...

Determine the centroid (x, ) of the area. 1m -y=x -1m- Prob. F9-1 X

A vector function Z(r) satisfies Z = 0 and Z = 0 everywhere in a simply-connected volume V bounded by a surface S. Modify the proof of the Helmholtz theorem in the text and show that Z(r) can be...

Evaluate the following expressions which exploit the Einstein summation convention. (a). ii. (b). ij ijk. (c). ijk jk. (d). ijk ijk.

Find the electric dipole moment of: (a) A ring with charge per unit length = 0 cos where is the angular variable in cylindrical coordinates. (b) A sphere with charge per unit areas = 0 cos ...

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

By modern standards, the shaft design of Problem 5-76 is poor because it is so long. Suppose it is redesigned by halving the length dimensions. Using the same material and design factor as in Problem...

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...

(a) Show that the magnetic dipole moment of a magnetized body can be written where (r) = M(r) is the density of fictitious magnetic charge.(b) Let B 1 and B 2 be the magnetic fields produced by...

Show that the following scheme proposed by R. Ogg, J. Chem. Phys., 15,337 (1947) is consistent with, and can explain, the observed first-order decomposition of N 2 0 5 . k NO5NO + NO** k NO NO* + NO...

How much would you need to save annually to be willing to invest $1.75 million in a process improvement? The internal hurdle rate for process improvements is 18% before taxes over eight years.

To examine this issue, imagine that banks can charge any borrower 150 basis points above the interest rate at which the bank would break even (in an expected value sense) on that borrower. This is a...

Fill in the blanks. (a) If you double the frequency of electromagnetic radiation, you __________ the energy. (b) If you double the wavelength, you _________ the energy. (c) If you double the...

The absorbance of a 2.31 10 -5 M solution of a compound is 0.822 at a wavelength of 266 nm in a 1.00-cm cell. Calculate the molar absorptivity at 266 nm.

For each of the following systems, give two examples of how a mechanical engineer would be involved in its manufacture. (a) Graphite-epoxy skis, tennis racket, or golf club (b) Elevator (c) Blu-ray...

One U.S. gallon is equivalent to 0.1337 ft 3 , 1 ft is equivalent to 0.3048 m, and 1000 L are equivalent to 1 m 3 . By using those definitions, determine the conversion factor between gallons and...

A robotic-wheeled vehicle that contains science instruments is used to study the geology of Mars. The rover weighs 408 lb on Earth. (a) In the USCS dimensions of slugs and lbm, what is the rovers...

A 1-Mg container hangs from a 15-mm-diameter steel cable. What is the stress in the cable?

A two-tier system to repair bridge infrastructures is supported by two steel cables for each platform (Figure P5.15). All the support cables have a diameter of 0.50 in. Assume the applied loads are...

The Boeing 787 Dreamliner is billed to be 20% more fuel efficient than the comparable Boeing 767 and will fly at Mach 0.85. The midsize Boeing 767 has a range of 12,000 km, a fuel capacity of 90,000...

A plastic pipe carries deionized water in a microelectronics clean room, and one end of it is capped (Figure P5.25). The water pressure is p 0 = 50 psi, and the cap is attached to the end of the pipe...

A 500 m long levee made of compacted clay impounds water in a reservoir as shown in Figure P2.8. There is a 1 m thick (measured in the direction perpendicular to the seam) sand seam continuing along...

Express the force F in Cartesian vector form if it acts at the midpoint B of the rod. A 4 m B 4 m F = 600 N 3 m 6 m D

For the following cases, determine the allowable gross vertical load bearing capacity of the foundation. Use Terzaghis equation and assume general shear failure in soil. Use F S = 4. Part D; c'...

A square foundation is shown in Figure P6.19. Use FS = 6, and determine the size of the foundation. Use Prakash and Saran's method [Eq. (6.59)]. Figure P6.19. 450 kN 70 kN-m y = 16 kN/m3 c' = 0 o'=...

In Problem 7.3, if no bedrock was present for at least 4 m below the foundation, determine the ultimate bearing capacity. Problem 7.3 A 1.5 m 2.0 m rectangular foundation is placed at 1.0 m depth in...

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...

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...

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...

Two missing values in a randomized block. Suppose that in Problem 4-1 the observations for chemical type 2 and bolt 3 and chemical type 4 and bolt 4 are missing. (a) Analyze the design by iteratively...

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