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The cable supports the three loads shown. Determine the sags y B and y D of points B and D. Take P 1 = 400 lb, P 2 = 250 lb. Combining Eqs. (1) & (2) Combining Eqs. (3) & (4) 4 ft A B P -12 ft-- -20... Determine the radiation efficiency of a half-wave dipole operating at 6 MHz. The wire is made of copper ( = 58 MS/m) and is 1.2 mm in radius. A short dipole antenna operates at the AM broadcast band at 1.2 MHz. To achieve a radiation resistance of 0.5, how long must the antenna be? Determine the product of inertia of the cross-sectional area of the member with respect to the x and y axes. 400 mm 20 mm C -100 mm- -100 mm- -20 mm 20 mm 400 mm -X 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 composite area about the y axis. T 3 in. 3 in. y -3 in. 6 in.. X (a) Write down the Hamiltonian for two noninteracting identical particles in the infinite square well. Verify that the fermion ground state given in Example 5.1 is an eigenfunction of H, with the... (a) At time t = 0 a large ensemble of spin-1/2 particles is prepared, all of them in the spin-up state (with respect to the z axis). They are not subject to any forces or torques. At time t 1 > 0... Determine the coordinate direction angles of the force. 2 45 -30 F = 75 lb In Example 4.3: (a) If you measured the component of spin angular momentum along the x direction, at time t, what is the probability that you would get +/2? (b) Same question, but for the y... Find the first three excited state energies (to five significant digits) for the harmonic oscillator, by wagging the dog (Problem 2.55). For the first (and third) excited state you will need to set u... Determine the resultant moment produced by the forces about point O. O -1m- 600 N -2 m 500 N 45 2.5 m 300 N 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. To tighten the screw, a... If a horizontal force of F = 50 N is applied perpendicular to the handle of the lever at E, determine the clamping force developed at G. The mean diameter and lead of the single square-threaded screw... Coherent states of the harmonic oscillator. Among the stationary states of the harmonic oscillator (Equation 2.68) only n = 0 hits the uncertainty limit ( x p = /2); in general, x p = (2n + 1) /2,... If it takes a vertical force of 60,000 lb to separate the two parts at A and C, determine the force P the hydraulic cylinder must exert on the wedge in order to push it forward. The coefficient of... The load bar of negligible weight is screwed in place between the walls of the truck bed in order to keep loads from shifting. Determine the torsional moment M that must be applied to the center of... Two blocks A and B, each having a mass of 6 kg, are connected by the linkage shown. If the coefficient of static friction at the contacting surfaces is s = 0.5 determine the largest vertical force P... The uniform 5-kg rod rests on the ground at B and against the wall at A. If the rod does not slip at B, determine the smallest coefficient of static friction at A which will prevent slipping at A. X... Two blocks A and B, each having a mass of 6 kg, are connected by the linkage shown. If the coefficients of static friction at the contacting surfaces are B = 0.8 and A = 0.2, determine the largest... The uniform crate resting on the dolly has a mass of 500 kg and mass center at G. If the front casters contact a high step, and the coefficient of static friction between the crate and the dolly is ... If a force of F = 50 lb is applied to the pads at A and C, determine the smallest dimension d required for equilibrium if the spring has an unstretched length of 1 ft. F A 1 ft 1 ft d B D 1 ft k= 150... If the vertical force P is applied to the two-bar mechanism, determine the equilibrium force F on the block. Plot this magnitude as a function of u, where 0 90. F B A P 1 / C If d = 0.75 ft and the spring has an unstretched length of 1 ft, determine the force F required for equilibrium. F A 1 ft 1 ft d B D 1 ft k= 150 lb/ft 1 ft C F If a force F = 350 N of is applied to the handle of the toggle clamp, determine the resulting clamping force at A. A -235 mm- 30 mm 30 mm, 70 mm -OC- B 30 F 30 275 mm E The machine shown is used for forming metal plates. It consists of two toggles ABC and DEF, which are operated by the hydraulic cylinder H.The toggles push the movable bar G forward, pressing the... The hoist supports the 125-kg engine.Determine the force this load creates along member DB and along member FB, which contains the hydraulic cylinder H. G A 1 m. F 2 m 2 m H B 1 m C E 2 m D 1 m The bent rod is supported at A, B, and C by smooth journal bearings. Determine the magnitude of F which will cause the positive x component of reaction at the bearing C to be C x = 50 N. The bearings... Determine the moment of inertia of the area about the x axis. 80 mm 20 mm = 1/3 (4 -(400 -x) X Determine the moment of inertia of the area about the x axis. y y = x 1 in. 1 in. X Determine the distance x to the center of gravity of the gas dehydrator assembly. The weight and the center of gravity of each of the various components are indicated. What are the vertical reactions... A large stone having a mass of 500 kg is moved along the incline using a series of 150-mm-diameter rollers for which the coefficient of rolling resistance is 3 mm at the ground and 4 mm at the bottom... The 5-kg skateboard rolls down the 5 slope at constant speed. If the coefficient of kinetic friction between the 12.5-mm-diameter axles and the wheels is k = 0.3, determine the radius of the wheels.... The 4-lb pulley has a diameter of 1 ft and the axle has a diameter of 1 in. If the coefficient of kinetic friction between the axle and the pulley is k = 0.20, determine the vertical force P on the... The corkscrew is used to remove the 15-mm-diameter cork from the bottle. Determine the smallest vertical force P that must be applied to the handle if the gauge pressure in the bottle is p = 175 kPa... If the coefficient of static friction at the cone clutch is s , determine the smallest force P that should be applied to the handle in order to transmit the torque M. B M P4 C b A tube has a total weight of 200 lb, length = 8 ft, and radius = 0.75 ft. If it rests in sand for which the coefcient of static friction is s = 0.23, determine the torque M needed to turn it.... A girl weighing 100 lb attempts to pull herself up a tree using a rope which is draped over the limb at B. If s = 0.4, determine the smallest force at which she must pull on the rope to lift... The choker sling is used to lift the smooth pipe that has a mass of 600 kg. If the coefficient of static friction between the loop at the end A of the sling and the rope is s = 0.3, determine the... A conveyer belt is used to transfer granular material and the frictional resistance on the top of the belt is F = 500 N. Determine the smallest stretch of the spring attached to the moveable axle of... Two boys have a tug-of-war using a rope. In the process the rope rubs against a post such that it is deflected 3 on each side of the post. If boy A weighs 60 lb and boy B weighs 50 lb, determine if... Two boys have a tug-of-war using a rope. In the process the rope rubs against a post such that it is deflected 3 on each side of the post. If boy A weighs 60 lb and boy B weighs 50 lb, determine if... If the force T 1 is applied to the rope at A, determine the force T 2 at B needed to pull the rope over the two fixed drums having the angles of contact and the coefficients of static friction shown.... Determine the minimum tension in the rope at points A and B that is necessary to maintain equilibrium. Take s = 0.3 between the rope and the fixed post D. 300 lb T D B 60 A A spin-1/2 particle with gyromagnetic ratio , at rest in a static magnetic field B 0 k, precesses at the Larmor frequency 0 = B 0 (Example 4.3). Now we turn on a small transverse radiofrequency so... In the photoelectric effect, light can ionize an atom if its energy () exceeds the binding energy of the electron. Consider the photoelectric effect for the ground state of hydrogen, where the... You could derive the spontaneous emission rate (Equation 11.63) without the detour through Einsteins A and B coefficients if you knew the ground state energy density of the electromagnetic field, 0... The first term in Equation 11.32 comes from the e it /2 part of Cos(t), and the second from e - it . Thus dropping the first term is formally equivalent to writing H' = (V/2)e - it , which is to say,... The uniform rod OA weighs 20 lb, and when the rod is in the vertical position, the spring is unstretched. Determine the position for equilibrium. Investigate the stability at the equilibrium... Consider the case of a symmetrical double well, such as the one pictured in Figure 9.14. We are interested in bound states with E < V(0). Figure 9.14: Symmetric double well; Problem 9.17. (a) Write... Determine the force in the spring required tokeep the 6-kg rod in equilibrium when = 30. The spring remains horizontal due to the roller guide. A k = 200 N/m wwwww 40 Nm 0.5 m The spring is unstretched when = 0. If P = 8 lb, determine the angle for equilibrium. Due to the roller guide, the spring always remains vertical. Neglect the weight of the links. 2 ft 4 ft. k = 50... By appropriate modification of the hydrogen formula, determine the hyperfine splitting in the ground state of (a) Muonic hydrogen (in which a muonsame charge and g-factor as the electron, but 207... The linkage is subjected to a force of P = 6 kN. Determine the angle for equilibrium. The spring is unstretched at = 60. Neglect the mass of the links. A 0.9 m B 10 k = 20 kN/m wwwwwwwwww P = 6 kN... Locate the centroid (x, ) of the cross-sectional area of the beam. 6 in. 3 in. 6 in. - 3 in. 2 in. 1 Determine the location y of the centroid for the beams cross-sectional area. 15 mm 400 mm 15 mm -300 mm- - 15 mm -200 mm- The collar fits loosely around a fixed shaft that has a radius of 2 in. If the coefficient of kinetic friction between the shaft and the collar is k = 0.3, determine the force P on the horizontal... The corkscrew is used to remove the 15-mm-diameter cork from the bottle. Determine the smallest vertical force P that must be applied to the handle if the gauge pressure in the bottle is p = 175 kPa... A tube has a total weight of 200 lb, length l = 8 ft, and radius = 0.75 ft. If it rests in sand for which the coeffcient of static friction is s = 0.23, determine the torque M needed to turn it.... 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... If the force T 1 is applied to the rope at A, determine the force at T 2 at B needed to pull the rope over the two fixed drums having the angles of contact and the coefficients of static friction... 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... Two boys have a tug-of-war using a rope. In the process the rope rubs against a post such that it is deflected 3 on each side of the post. If boy A weighs 60 lb and boy B weighs 50 lb, determine if... If the coefficient of static friction between the axe and the wood is s = 0.2, determine the smallest angle of the blade which will cause the axe to be self-locking. Neglect the weight of the axe.... The uniform cylindrical tank has a mass of 250 kg. If the coefficient of static friction is s = 0.15, determine the force P applied to the rope needed to move the tank. 3m - 2m 45 MATERIALES P The blocks each have a weight of 50 lb. If the coefficient of static friction at A is s = 0.2 and between each block's = 0.4, determine how many blocks can be stacked as shown before they begin to... The 50-lb board is placed across the channel and a 100-lb girl attempts to walk across. If the coefficient of static friction at A and B is s = 0.4, determine if she can make the crossing; and if... The man has a mass of 60 kg and the crate has a mass of 100 kg. If the coefficient of static friction between his shoes and the ground is s = 0.4 and between the crate and the ground is c = 0.3,... If the coefficient of static friction at A and B is s = 0.6, determine the maximum angle so that the frame remains in equilibrium, regardless of the mass of the cylinder. Neglect the mass of the... The 800-lb concrete pipe is being lowered from the truck bed when it is in the position shown. If the coefficient of static friction at the points of support A and B is s = 0.4, determine where it... The car has a weight of 4000 lb and a center of gravity at G. If it pulls off the side of the road, determine the greatest angle of tilt it can have without slipping or tripping over. The... The man having a weight of 200 lb pushes horizontally on the crate. If the coefficient of static friction between the 450-lb crate and the floor is s = 0.3 and between his shoes and the floor ' s =... Determine the smallest force P that must be applied to begin moving the 150-lb uniform crate. The coefficent of static friction between the crate and the floor is s = 0.5. 3 ft -2 ft- P The double-block brake mechanism is used to prevent the wheel from turning when the wheel is subjected to the torque of M = 5 N m. If the coefficient of static friction between the blocks and the... Two blocks A and B have a weight of 10 lb and 6 lb, respectively. They are resting on the incline for which the coefficients of static friction are A = 0.15 and B = 0.25 Determine the incline angle... The friction pawl is pinned at A and rests against the wheel at B. It allows freedom of movement when the wheel is rotating counterclockwise about C. Clockwise rotation is prevented due to friction... The uniform thin pole has a weight of 30 lb and a length of 26 ft. If it is placed against the smooth wall and on the rough floor in the position d = 10, will it remain in this position when it is... The car has a mass of 1.6 Mg and center of mass at G. If the coefficient of static friction between the shoulder of the road and the tires is s = 0.4, determine the greatest slope the shoulder can... The uniform crate resting on the dolly has a mass of 500 kg and mass center at G. If the front casters contact a high step, and the coefficient of static friction between the crate and the dolly is ... Determine the angle at which the applied force P should act on the pipe so that P is as small as possible for pulling the pipe up the incline. What is the corresponding value of P? The pipe weighs W... The cylinder is confined by the brake, where s = 0.4. Determine the required compression in the spring in order to resist a torque of 800 N m on the cylinder. The spring has a stiffness of k = 3... The man has a mass of 40 kg. He plans to scale the vertical crevice using the method shown. If the coefficient of static friction between his shoes and the rock is s = 0.4 and between his backside... Determine the maximum force P that can be applied without causing the two 50-kg crates to move. The coefficient of static friction between each crate and the ground is s = 0.25. A B 30 The automobile jack is subjected to a vertical load of F = 8 kN. If a square-threaded screw, having a lead of 5 mm and a mean diameter of 10 mm, is used in the jack, determine the force that must be... (a) Evaluate the relevant part of the integral to find the interaction energy V E between two identical insulating spheres, each with radius R and charge Q distributed uniformly over their surfaces.... The friction pawl is pinned at A and rests against the wheel at B. It allows freedom of movement when the wheel is rotating counterclockwise about C. Clockwise rotation is prevented due to friction... Assume that (r) and |G(r)| both go to zero faster than 1/r as r . (a) Let F = and G = 0. Show that d 3 r F G = 0. (b) Let F = and G = 0. Show that d 3 r F G = 0. (c) Begin with the vector... Show that D(x) = lim m sin mx/x is a representation of (x) by showing that dxf (x)D(x) = (0). Use the Levi-Civit`a symbol to prove that (a) (A B) (C D) = (A C)(B D) (A D)(B C). (b) (f g) = g ( f) f ( g). (c) (A B) (C D) = (A C D)B (B C D)A. (d) The 2 2 Pauli matrices x... Car B is traveling a distance d ahead of car A. Both cars are traveling at 60 ft/s when the driver of B suddenly applies the brakes, causing his car to decelerate at 12 ft/s. It takes the driver of... Use the method of Lagrange multipliers to show that, among all functions D(r) which satisfy D = f , the minimum (not merely the extremum) of: Occurs when D(r) = E(r). Assume that n D takes... Application 6.3 modeled a meson (a quark-antiquark pair) as a finite dipole placed at the center of a spherical cavity with radius R and unit dielectric constant scooped out of an infinite medium... The text used Poissons equation to show that the charge density of a point electric dipole with moment p located at the point r 0 is D (r) = p (r r 0 ). (a) Derive the given formula for D (r)... For a short time, the 250-kg roller-coaster car with passengers is traveling along the spiral track at a constant speed of v = 8 m/s. If the track descends d = 12 m for every full revolution, = 2... The 150-lb man lies against the cushion for which the coefficient of static friction s = 0.5 is Determine the resultant normal and frictional forces the cushion exerts on him due to rotation about... The z-axis runs down the center of an infinitely long heating duct with a square cross section. For a real metal duct (not a perfect conductor), the electrostatic potential (x, y) varies linearly... A large stone having a mass of 500 kg is moved along the incline using a series of 150-mm-diameter rollers for which the coefficient of rolling resistance is 3 mm at the ground and 4 mm at the bottom... Determine the minimum tension in the rope at points A and B that is necessary to maintain equilibrium. Take s = 0.3 between the rope and the fixed post D. 300 lb T D B 60 A The tongs are used to suspend the 80-kg plate. Determine the smallest coefficient of static friction to prevent slipping of the plate. 150 mm C 20 mm, A P -150 mm 200 mm B 150 mm 150 mm Solve Prob. 826 if the truck and crate are resting on an upward 10 incline. Prob. 826 The truck has a mass of 1.25 Mg and a center of mass at G. Determine the greatest load it can move if (a) the...
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