In a sandy soil (' = 35; = 18.0 kN/m 3 , and sat = 20.0 kN/m 3 ), the water table is located at a depth of 6 m below the ground level. How deep would you drive a sheet pile to carry out an...

Use MuPAD to prove the following identities: a. sin 2 x = cos 2 x = 1 b. sin(x + y) = sin x cosy + cosx siny c. sin 2 x = 2 sin x cosx d. cosh 2 x - sinh 2 x = 1

A soil profile is shown in Figure P3.3 along with the standard penetration numbers in the clay layer. Use Eqs. (3.8b) and (3.9) to determine the variation of c u and OCR with depth. What is the...

The 20-N horizontal force acts on the handle of the socket wrench. What is the moment of this force about point B. Specify the coordinate direction angles , , of the moment axis. 20 N -200 mm- B A...

A standard penetration test was carried out in a normally consolidated sand at 7.62 m depth where the N 60 was determined to be 28. The unit weight of the sand is 17.29 kN/m 3 , and the grain-size...

Use the general bearing capacity equation [Eq. (6.28)] to solve the following: a. Problem 6.1a b. Problem 6.1b c. Problem 6.1c Eq. (6.28) qu = c'N,FeFcaFeci + qNFqsFqaFqi + >yBN,F,FyaFyi +...

Replace the loading system acting on the post by an equivalent resultant force and couple moment at point A. 650 N 500 N 30 300 N 1500 N m 60 B -3 m 5 m 2 m

The form is used to cast a concrete wall having a width of 5 m. Determine the equivalent resultant force the wet concrete exerts on the form AB if the pressure distribution due to the concrete can be...

A 1500 kN load was applied on two 20 m long and 500 mm diameter piles that were instrumented for measuring the load variation with depth. a. The variation of frictional resistance per unit area, f...

Determine the magnitude of force at the pin A and in the cable BC needed to support the 500-lb load. Neglect the weight of the boom AB. 8 ft 122 35

Redo Problem 12.3 using Coyle and Castellos methods for estimating both Q p and Q s . Problem 12.3 A 500 mm diameter and 20 m long concrete pile is driven into a sand where = 18.5 kN/m 3 and ' = 32....

Determine the force in each member of the truss and state if the members are in tension or compression. Set P1 = 10 kN, P2 = 8 kN. F E 2 m D. A B 2 m P2

Consider a 500 mm diameter pile having a length of 18 m in a clay. Given: = 20.0 kN/m 3 and c u = 60 kN/m 2 . a. Determine the maximum allowable load (Qall) with FS = 3. Use the a method and Table...

A concrete pile 20 m long having a cross section of 0.46 m 0.46 m is fully embedded in a saturated clay layer. For the clay, given: sat = 18 kN/m 3 , = 0, and c u = 80 kN/m 2 . Determine the...

The toggle clamp is subjected to a force F at the handle. Determine the vertical clamping force acting at E.

Consider a continuous flight auger pile in a sandy soil deposit 10 m long with a diameter of 0.45 m. Following is the variation of standard penetration resistance values (N 60 ) with depth. Depth (m)...

A concrete pile 406 mm 406 mm in cross section is shown in Figure P12.13. Calculate the ultimate skin friction resistance by using the a. method [use Eq. (12.61) and Table 12.11] b. method c. ...

The tractor has a weight of 16,000 lb and the coefficient of rolling resistance is a = 2 in. Determine the force P needed to overcome rolling resistance at all four wheels and push it forward. P 2...

The average values of the undrained shear strength (cu) with depth are given as follows: Depth (m) . c u (kN/m 2 ) 03 .. 20 38 .. 35 812 . 80 1216 . 95 If a CFA pile having a diameter of 0.6 m and...

A steel pile (H-section; HP 310 125; see Table 12.1a) is driven into a layer of sandstone. The length of the pile is 25 m. Following are the properties of the sandstone: unconfined compression...

Locate the centroid y of the shaded area. y 4 m 4 4 m

Figure P13.1 shows a drilled shaft in sand. Determine the maximum load that can be allowed on it. Assume ' = 0.6' and allow a factor of safety of 4. Use Berezantzev et al.s Eq. (13.18) for computing...

Locate the centroid y of the shaded area. y 4 m 1 y = 4 - 16 3D4 -8 m

A straight drilled shaft 1.0 m in diameter and 15.0 m long is installed in a sand where ' = 34 and = 18.0 kN/m 3 . a. Determine the load-carrying capacity at the base using the Chen and Kulhawy...

Determine the surface area of the curb. Do not include the area of the ends in the calculation. 100 mm 150 mm 30 4 m 150 mm 150 mm

The plate has a thickness of 0.25 ft and a specific weight of = 180 lb/ft 3 . Determine the location of its center of gravity. Also, find the tension in each of the cords used to support it. 16 ft...

The top 5 m in a site consists of a clay with c u = 80 kN/m 2 . This is underlain by a thick clay deposit with c u = 150 kN/m 2 . A 1.0 m diameter and 15 m long straight drilled shaft is constructed...

Locate the centroid x of the shaded area. y 4 ft 4 ft

Locate the centroid y of the shaded area. 4 ft 4 ft

Locate the centroid y of the shaded area. y =x 100 mm 00 100 mm

Figure P16.8 shows a smooth vertical wall retaining a sandy backfill underlain by clay. Assuming that the entire soil is in the active state, determine the magnitude and location of the resultant...

In Problem 17.1, if there is a possibility that the soil in front of the wall will be removed sometime later, neglect the passive resistance and compute the factors of safety. Problem 17.1 Figure...

Locate the centroid z of the frustum of the right-circular cone. h R- y

It is required to design a cantilever retaining wall to retain a 5.0 m high sandy backfill. The consultant suggests the dimensions and soil properties shown in Figure P17.6 and requires that the wall...

Determine the moment of inertia for the shaded area about the x axis. y y =x/2 1m 1 m

Determine the moment of inertia of the composite area about the y axis. -3 in. 6 in. 3 in. 3 in.

Determine the moment of inertia I x of the shaded area about the x axis. |-100 mm--100 mm150 mm 150 mm 150 mm 75 mm

The following are the burning times of chemical flares of two different formulations. The design engineers are interested in both the mean and variance of the burning times. (a) Test the hypothesis...

In GD&T, which type of dimension should generally be directly toleranced with a plus/minus tolerance?

A spin coater is used to apply photoresist to a bare silicon wafer. This operation usually occurs early in the semiconductor manufacturing process, and the average coating thickness and the...

Complete this table for H 2 O: T, C , U, m/kg Phase description 140 0.035 550 Saturated liquid 125 750 300 0.140

A house is maintained at 1 atm and 24C, and warm air inside a house is forced to leave the house at a rate of 90 m 3 /h as a result of outdoor air at 5C infiltrating into the house through the...

An air-standard Stirling cycle operates with a maximum pressure of 600 psia and a minimum pressure of 10 psia. The maximum volume of the air is 10 times the minimum volume. The temperature during the...

A tube has another tube shrunk over it. The specifications are: Both tubes are made of a plain carbon steel. (a) Find the nominal shrink-fit pressure and the von Mises stresses at the fit surface....

Reconsider Prob. 1-58. Using appropriate software, investigate the effect of the spring force in the range of 0 to 500 N on the pressure inside the cylinder. Plot the pressure against the spring...

An ideal vapor-compression refrigeration cycle that uses refrigerant-134a as its working fluid maintains a condenser at 800 kPa and the evaporator at 20C. Determine this systems COP and the amount of...

For the system of Figure P2.12 find the transfer function, G(s) = X 1 (s)/F(s). K = 4 N/m -Xj K, = 5 N/m ft) = 3 N-s/mM1 =T'kg Jv2=3N-s/m M2 = 2 kg fva = 2 N-s/m %3D FIGURE P2.12

For the rotational system shown in Figure P2.21, find the transfer function, G(s) = 2 (s)=T(s). |N = 4 F = 2 kg-mHD =I N-m-s/rad N2 = 12in0 D2 = 2 N-m-s/rad 6,() 2 = 1 kg-m-=* K= 64 N-m/rad N4 = 16...

Find the transfer function, 1 (s)/T(s) , for the system shown in Figure P2.19. T(1) 0(1) 1 N-m/rad 1 N-m/rad 1 kg-m? 0000 1 kg-m? 1 N-m-s/rad FIGURE P2.19

For the system of Figure P8.8(a), sketch the root locus and find the following: a. Asymptotes b. Breakaway points c. The range of K for stability d. The value of K to yield a 0.7 damping ratio for...

Repeat Problem 13 for the following transfer function: Data from Problem 13: Use MATLAB to generate the transfer function: in the following ways: a. The ratio of factors; b. The ratio of polynomials....

Represent the translational mechanical system shown in Figure P3.5 in state space, where x 1 (t) is the output. x2(1) M3 = 1 kg x3(1) K = 1 N/m fv, = 1 N-s/m M2 = 2 kg fv, = 1 N-s/m f(1). X1(1) K2 =...

What factors influence the choice of state variables in any system?

A linear, time-invariant model of the hypothalamic pituitary-adrenal axis of the endocrine system with five state variables has been proposed as follows (Kyrylov, 2005): where each of the state...

Use MATLAB to find the transfer function, G(s)=Y(s)/R(s), for each of the following systems represented in state space: a) b) 01 1 5 x+ 1 8 -9 -2 -3 2 y = [1 3 6 6]x 1.

According to the Union of Concerned Scientists (www.ucsusa.org), as of November 2012, there were 502 low Earth orbit (LEO) and 432 geosynchronous orbit (GEO) satellites in space. Each satellite is...

Process Safety Progress (Sept. 2004) reported on an emergency response system for incidents involving toxic chemicals in Taiwan. The system has logged over 250 incidents since being implemented in...

The reliability of a computer system is measured in terms of the life length of a specified hardware component (e.g., the hard disk drive). To estimate the reliability of a particular system, 100...

Find the percent overshoot, settling time, rise time, and peak time for 14.65 T(s) (s2 + 0.842s + 2.93)(s + 5)

A brewery utilizes two bottling machines, but they do not operate simultaneously. The second machine acts as a backup system to the first machine and operates only when the first breaks down during...

Use MATLAB to plot the capacitor voltage in Problem 12. Data from Problem 12: Write the general form of the capacitor voltage for the electrical network shown in Figure P4.4. R = 10 k2 vit) = u(t) R2...

Solve for y(t) for the following system represented in state space, where u(t) is the unit step. Use the Laplace transform approach to solve the state equation. -3 1 01 X = |0 -6 1 x+1 u(t) 0 0 -5 y...

Figure P4.9 shows five step responses of an automatic voltage regulation system as one of the system parameters varies (Gozde, 2011). Assume for all five responses that they are those of a second...

Although the use of fractional calculus in control systems is not new, in the last decade there is increased interest in its use for several reasons. The most relevant are that fractional calculus...

If the tennis player serves the ball horizontally ( = 0), calculate its velocity v if the center of the ball clears the 0.9-m net by 150 mm. Also fi nd the distance s from the net to the point where...

A projectile is launched from point A with the initial conditions shown in the figure. Determine the slant distance s which locates the point B of impact. Calculate the time of flight t. vo = 120 m/s...

A projectile is launched from point A with an initial speed v 0 = 100 ft/sec. Determine the minimum value of the launch angle for which the projectile will land at point B. vo = 100 ft/sec A/a 80' ...

An earth satellite which moves in the elliptical equatorial orbit shown has a velocity v in space of 17 970 km/h when it passes the end of the semi minor axis at A. The earth has an absolute surface...

As it passes the position shown, the particle P has a constant speed v = 100 m/s along the straight line shown. Determine the corresponding values of r, , r, and . y v = 100 m/s P 30 80 ml 9. 80 m...

Determine the steady-state angle if the constant force P is applied to the cart of mass M. The pendulum bob has mass m and the rigid bar of length L has negligible mass. Ignore all friction....

For a given horizontal force P, determine the normal reaction forces at A and B. The mass of the cylinder is m and that of the cart is M. Neglect all friction. m A 60 B 60 P M

The system of the previous problem is now placed on the 15 incline. What force P will cause the normal reaction force at B to be zero? m M A B 60 P 60 15

The drive system of the 350-ton tugboat causes an external thrust P = 7000 lb to be applied as indicated in the figure. If the tugboat pushes an 800-ton coal barge starting from rest, what is the...

The inexperienced driver of an all-wheel-drive car applies too much throttle as he attempts to accelerate from rest up the slippery 10-percent incline. The result is wheel spin at all four tires,...

The 300-Mg jet airliner has three engines, each of which produces a nearly constant thrust of 240 kN during the takeoff roll. Determine the length s of runway required if the takeoff speed is 220 km...

The 750,000-lb jetliner A has four engines, each of which produces a nearly constant thrust of 40,000 lb during the takeoff roll. A small commuter aircraft B taxis toward the end of the runway at a...

cesium-ion engine for deep-space propulsion is designed to produce a constant thrust of 2.5 N for long periods of time. If the engine is to propel a 70-Mg spacecraft on an interplanetary mission,...

A toy train has magnetic couplers whose maximum attractive force is 0.2 lb between adjacent cars. What is the maximum force P with which a child can pull the locomotive and not break the train apart...

A worker develops a tension T in the cable as he attempts to move the 50-kg cart up the 20 incline. Determine the resulting acceleration of the cart if (a) T = 150 N and (b) T = 200 N. Neglect all...

The wheeled cart of Prob. 3 /19 is now replaced with a 50-kg sliding wooden crate. The coefficients of static and kinetic friction are given in the figure. Determine the acceleration of the crate if...

The 5-oz pinewood-derby car is released from rest at the starting line A and crosses the finish line C 2.75 sec later. The transition at B is small and smooth. Assume that the net retarding force is...

The coefficient of static friction between the flat bed of the truck and the crate it carries is 0.30. Determine the minimum stopping distance s which the truck can have from a speed of 70 km / h...

If the truck of Prob. 3/24 comes to a stop from an initial forward speed of 70 km / h in a distance of 50 m with uniform deceleration, determine whether or not the crate strikes the wall at the...

Determine the vertical acceleration of the 60-lb cylinder for each of the two cases. Neglect friction and the mass of the pulleys. 60 lb 40 lb 60 lb 40 lb (a) (b)

The rack has a mass m = 50 kg. What moment M must be exerted on the gear wheel by the motor in order to accelerate the rack up the 60 incline at a rate a = g/4? The fixed motor which drives the gear...

A jet airplane with a mass of 5 Mg has a touchdown speed of 300 km / h, at which instant the braking parachute is deployed and the power shut off. If the total drag on the aircraft varies with...

During its final approach to the runway, the aircraft speed is reduced from 300 km / h at A to 200 km / h at B. Determine the net external aerodynamic force R which acts on the 200-Mg aircraft during...

Determine the range of applied force P over which the block of mass m 2 will not slip on the wedge-shaped block of mass m 1 . Neglect friction associated with the wheels of the tapered block. m2 Hs =...

A heavy chain with a mass per unit length is pulled by the constant force P along a horizontal surface consisting of a smooth section and a rough section. The chain is initially at rest on the rough...

The sliders A and B are connected by a light rigid bar of length l = 0.5 m and move with negligible friction in the slots, both of which lie in a horizontal plane. For the position where x A = 0.4 m,...

The sliders A and B are connected by a light rigid bar and move with negligible friction in the slots, both of which lie in a horizontal plane. For the position shown, the velocity of A is 0.4 m /s...

The design of a lunar mission calls for a 1200-kg spacecraft to lift off from the surface of the moon and travel in a straight line from point A and pass point B. If the spacecraft motor has a...

Two iron spheres, each of which is 100 mm in diameter, are released from rest with a center-to-center separation of 1 m. Assume an environment in space with no forces other than the force of mutual...

The small 2-kg block A slides down the curved path and passes the lowest point B with a speed of 4 m /s. If the radius of curvature of the path at B is 1.5 m, determine the normal force N exerted on...

A spring-loaded device imparts an initial vertical velocity of 50 m/s to a 0.15-kg ball. The drag force on the ball is F D = 0.002v 2 , where F D is in newtons when the speed v is in meters per...

The system is released from rest in the configuration shown at time t = 0. Determine the time t when the block of mass m 1 contacts the lower stop of the body of mass m 2 . Also, determine the...

The system of Prob. 3/43 is reconsidered here, only now the interface between the two bodies is not smooth. Use the values s = 0.10 and k = 0.08 between the two bodies. Determine the time t when m...

The rod of the fixed hydraulic cylinder is moving to the left with a speed of 100 mm /s, and this speed is momentarily increasing at a rate of 400 mm/s each second at the instant when s A = 425 mm....

The particle of mass m is attached to the light rigid rod, and the assembly rotates about a horizontal axis through O with a constant angular velocity = . Determine the tension T in the rod as a...

If the 180-lb ski-jumper attains a speed of 80 ft /sec as he approaches the takeoff position, calculate the magnitude N of the normal force exerted by the snow on his skis just before he reaches A....