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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... 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... Locate the centroid y of the shaded area. y 4 m 4 4 m Locate the centroid y of the shaded area. y 4 m 1 y = 4 - 16 3D4 -8 m 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... 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 Locate the centroid z of the frustum of the right-circular cone. h R- y 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? 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... 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... 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... 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? 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... 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.... Find the percent overshoot, settling time, rise time, and peak time for 14.65 T(s) (s2 + 0.842s + 2.93)(s + 5) 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... 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. 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... 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... 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' ... 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... 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... An IPMC (ionic polymer-metal composite) is a Nafion sheet plated with gold on both sides. An IPMC bends when an electric field is applied across its thickness. IPMCs have been used as robotic... 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... 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... 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... 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 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 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 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... 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... 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,... 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 =... 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 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 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 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... 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.... The 4-oz slider has a speed v = 3 ft /sec as it passes point A of the smooth guide, which lies in a horizontal plane. Determine the magnitude R of the force which the guide exerts on the slider (a)... 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.... In the design of a space station to operate outside the earths gravitational field, it is desired to give the structure a rotational speed N which will simulate the effect of the earths gravity for... During a brake test, the rear-engine car is stopped from an initial speed of 100 km/h in a distance of 50 m. If it is known that all four wheels contribute equally to the braking force, determine the... The small spheres are free to move on the inner surface of the rotating spherical chambers shown in section with radius R = 200 mm. If the spheres reach a steady-state angular position = 45,... A child twirls a small 50-g ball attached to the end of a 1-m string so that the ball traces a circle in a vertical plane as shown. What is the minimum speed v which the ball must have when in... A small object A is held against the vertical side of the rotating cylindrical container of radius r by centrifugal action. If the coefficient of static friction between the object and the container... The hollow tube is pivoted about a horizontal axis through point O and is made to rotate in the vertical plane with a constant counterclockwise angular velocity = 3 rad /sec. If a 0.2-lb particle is... A Formula-1 car encounters a hump which has a circular shape with smooth transitions at both ends. (a) What speed vB will cause the car to lose contact with the road at the topmost point B? (b) For a... A 180-lb snowboarder has speed v = 15 ft/sec when in the position shown on the halfpipe. Determine the normal force on his snowboard and the magnitude of his total acceleration at the instant... The flatbed truck carries a large section of circular pipe secured only by the two fixed blocks A and B of height h. The truck is in a left turn of radius . Determine the maximum speed for which the... Calculate the necessary rotational speed N for the aerial ride in an amusement park in order that the arms of the gondolas will assume an angle = 60 with the vertical. Neglect the mass of the arms... Repeat the previous problem, only now the slotted arm is rotating with angular velocity = 3 rad /s, and this rate is increasing at 5 rad /s 2 . At the instant under consideration, the cable attached to the cart of mass m 1 is tangent to the circular path of the cart. If the upward speed of the cylinder of mass m 2 is v 2 = 1.2 m/s, determine... The configuration of Prob. 3/70 is now modified as shown in the figure. Use all the data of Prob. 3/70 and determine the forces applied to the slider B by both arm OA and the sides of the slot.... Determine the altitude h (in kilometers) above the surface of the earth at which a satellite in a circular orbit has the same period, 23.9344 h, as the earths absolute rotation. If such an orbit lies... A small coin is placed on the horizontal surface of the rotating disk. If the disk starts from rest and is given a constant angular acceleration = , determine an expression for the number of... The rotating drum of a clothes dryer is shown in the figure. Determine the angular velocity of the drum which results in loss of contact between the clothes and the drum at = 50. Assume that the... The spacecraft P is in the elliptical orbit shown. At the instant represented, its speed is v = 13,244 ft /sec. Determine the corresponding values of r, , r, and . Use g = 32.23 ft /sec 2 as the... The 2-kg collar is at rest in position A when the constant force P is applied as shown. Determine the speed of the collar as it passes position B if (a) P = 25 N (b) P = 40 N. The curved rod lies in... The 6-kg cylinder is released from rest in the position shown and falls on the spring, which has been initially precompressed 50 mm by the light strap and restraining wires. If the stiffness of the... Calculate the maximum velocity of slider B if the system is released from rest with x = y. Motion is in the vertical plane. Assume that friction is negligible. The sliders have equal masses, and the... A bead with a mass of 0.25 kg is released from rest at A and slides down and around the fixed smooth wire. Determine the force N between the wire and the bead as it passes point B. A 0.6 m B 45 0.15 m The 15 200-kg lunar lander is descending onto the moons surface with a velocity of 2 m/s when its retro-engine is fired. If the engine produces a thrust T for 4 s which varies with time as shown and... The 80-lb boy has taken a running jump from the upper surface and lands on his 10-lb skateboard with a velocity of 16 ft/sec in the plane of the figure as shown. If his impact with the skateboard has... The 6-kg sphere and 4-kg block (shown in section) are secured to the arm of negligible mass which rotates in the vertical plane about a horizontal axis at O. The 2-kg plug is released from rest at A... The 0.4-lb ball and its supporting cord are revolving about the vertical axis on the fixed smooth conical surface with an angular velocity of 4 rad /sec. The ball is held in the position b = 14 in.... The figure shows a centrifugal clutch consisting in part of a rotating spider A which carries four plungers B. As the spider is made to rotate about its center with a speed , the plungers move... The small car, which has a mass of 20 kg, rolls freely on the horizontal track and carries the 5-kg sphere mounted on the light rotating rod with r = 0.4 m. A geared motor drive maintains a constant... The carriage of mass 2m is free to roll along the horizontal rails and carries the two spheres, each of mass m, mounted on rods of length l and negligible mass. The shaft to which the rods are...
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