Determine the magnitude of F so that the resultant couple moment acting on the beam is 1.5 kN m clockwise. FA 0.9 m 2 kN Prob. F4-22 B -F 0.3 m 2 kN

Determine the moment of the force F about point A as a function of . Plot the result of M (ordinate) versus (abscissa) for 0 < < 180. 8 ft- 2 ft F = 40 lb

The handle of the hammer is subjected to the force of F = 20 Ib Determine the moment of this force about the point A. 18 in. 30 5 in. B

Two men exert forces of F = 80 Ib and P = 50 Ib on the ropes. Determine the moment of each force about A. Which way will the pole rotate, clockwise or counterclockwise? 12 ft 6 ft A C

If F = {100i-120j +75k} lb and F = {-200i+ 250j + 100k} lb, determine the resultant moment produced by these forces about point O. Express the result as a Cartesian vector. 3 ft 4 ft 5 ft F -y

Determine the moment of each of the three forces about point B. F = 250 N 30% A -2 m -3 mr B F2 = 300 N 60 4 m F3 = 500 N

An infinitely long conductor of radius a carries a uniform current with J = J o a z . Show that the magnetic vector potential for r < a is A = 1 Hopa=

The members of a truss are pin connected at joint O. Determine the magnitude of and its angle for equilibrium. Set F 2 = 6 kN. 5 kN 7 kN 5 30 y 70 0 F F X

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

Determine the coordinate direction angles of the force. 2 45 -30 F = 75 lb

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...

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 ...

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...

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 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...

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...

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

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...

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...

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-

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 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...

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...

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)...

(a) Place two charges +q at two diagonal corners of a square (a,a, 0) and two minus charges q at the two other diagonals of the square (a,a, 0). Evaluate the primitive quadrupole moment components Q...

The parallel plates of a microchannel plate electron multiplier are segmented into conducting strips of width b so the potential can be fixed on the strips at staggered values. We model this using...

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 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 truck has rear-wheel drive while the front wheels are free to roll, and (b) the truck has...

Determine the normal force, shear force, and moment at points C and D. A 2 ft 6 ft C 45% 3 ft D 2 kip/ft 3 ft B

The disk rolls without slipping such that it has an angular acceleration of = 4 rad/s 2 and angular velocity of = 2 rad/s at the instant shown. Determine the acceleration of points A and B on the...

Determine the velocity of the center of gravity G of the connecting rod at the instant shown. Piston is moving upward with a velocity of 300 in./s. Up = 300 in./s G 30 P O B. 5 in. 2.75 in. 1.45 in.

If the motor turns gear A with an angular acceleration of A = 3 rad/s when the angular velocity is A = 60 rad/s, determine the angular acceleration and angular velocity of gear D. A B -100 mm C 40...

The center of the wheel is moving to the right with a speed of 2 ft/s. If no slipping occurs at the ground, A, determine the velocity of points B and C. 1.5 ft C A 30 2 ft/s B

If P = 30 lb, determine the angular acceleration of the 50-lb roller. Assume the roller to be a uniform cylinder and that no slipping occurs. P 30 1.5 ft

Determine the angular acceleration of the 25-kg diving board, and the horizontal and vertical components of reaction at the pin A, the instant the man dives off. Assume that the board is uniform and...

If the carts mass is 30 kg and it is subjected to a horizontal A force of P = 90 N, determine the tension in cord AB and the horizontal and vertical components of reaction on end C of the uniform...

The gear is pinned at A and has a mass of 0.3 kg and a radius of gyration of k A = 25 mm. The gear rack has mass of 0.5 kg. If has spring is stretched 50 mm and released from rest, determine the...

The slender rod has a mass of 10 kg and is released from rest when it is in the vertical position. Determine its angular velocity at the instant it becomes horizontal. The attached block at D has a...

The assembly consists of a 3-kg pulley A and 10-kg pulley B. If a 2-kg block is suspended from the cord, determine the distance the block must descend, starting from rest, in order to cause B to have...

A force of P = 20 N is applied to the cable, which causes the 175-kg reel to turn without slipping on the two rollers A and B of the dispenser. Determine the angular velocity of the reel after it has...

The assembly consists of a 3-kg pulley A and 10-kg pulley B. If a 2-kg block is suspended from the cord, determine the blocks speed after it descends 0.5 m starting from rest. Neglect the mass of the...

If the 50-lb bucket C is released from rest, determine its velocity after it has fallen a distance of 10 ft. The windlass A can be considered as a 30-lb cylinder, while the spokes are slender rods,...

The rotary screen S is used to wash limestone. When empty it has a mass of 800 kg and a radius of gyration of k G = 1.75 m. Rotation is achieved by applying a torque of M = 280 N m about the drive...

The 10-g bullet having a velocity of 800 m/s is fired into the 5-kg disk as shown. Determine the angular velocity of the disk just after the bullet becomes embedded. Also, calculate the angle the...

Repeat Problem 3-88 with T = 900 lbf in, a = 6 in, b = 5 in, c = 10 in, d = 1.375 in, e = 4 in, f = 10 in, and g = 6 in. Data in Problem 3-88 A torque T = 100 N m is applied to the shaft EFG, which...

For Figure A-15-1, let w = 2 in, d = 0.3 in, and estimate K t . Use 1/4 symmetry and 1/8-in-thick 2-D elements. K 3.0 2.8 2.6 2.4 2.2 2.0 0 Figure A-15-1 0.1 0.2 F 0.3 0.4 d/w d 0.5 0.6 0.7 0.8

Consider a pistoncylinder assembly containing 0.12 kg of nitrogen initially at 700 K and 300 kPa (state 1). The piston moves such that the final volume of the nitrogen (state 2) is three times larger...

Determine the reactions at B and C when a = 30 mm. 60 mm 40 mm A 250 N B C 100 mm 60 mm D

A 50-lb sign is supported by a pin and bracket at A and by a cable BC. Determine the reaction at A and the tension in the cable. C A 30 50 lb -3 ft 3 ft B 4 ft

Determine the range of values of for which the semicircular rod shown can be maintained in equilibrium by the small wheel at D and the rollers at B and C. P B 45 45 D

For the boom and loading shown, determine (a) The tension in cord BD, (b) The reaction at C. A 12 in. + 3 kips 16 in. B -32 in. D C 32 in.

A traffic-signal pole may be supported in the three ways shown; in part c, the tension in cable BC is known to be 1950 N. Determine the reactions for each type of support shown. 7.2 m B 3 m- 2.1 m...

Shafts A and B connect the gear box to the wheel assemblies of a tractor, and shaft C connects it to the engine. Shafts A and B lie in the vertical yz plane, while shaft C is directed along the x...

The two couples shown are to be replaced with a single equivalent couple. Determine (a) The couple vector representing the equivalent couple, (b) The two forces acting at B and C that can be used to...

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. B A E -20 in.. Fig. P15.131 and P15.133...

The 15-kg rear hatch of a vehicle opens as shown and can be modeled as a uniform 0.6-m long slender rod. Knowing that the tailgate is released from rest in the position shown, determine the angular...

Evaluate the matrix elements (or expectation values) given below. If any vanishes, explain why it vanishes using simple symmetry (or other) arguments. [In (a) and (b), |nlm stands for the energy...

Determine the output voltage for an integrator with a single-pulse input, as shown in Figure 1556. For repetitive pulses, how long will it take this circuit to reach steady state? 8 V 0 1 ms O...

Repeat Prob. 246 for a volume expansion of 1.5 percent for water. Data from Problem 46 A water tank is completely filled with liquid water at 20C. The tank material is such that it can withstand...

See Figure P123. The shaft rotating at 480 rpm carries two 4-in-diameter sheaves at D and E that each deliver 3 hp to mating sheaves as shown. Compute the torque delivered by the shaft to each sheave...

Consider a flat plate of thickness t, width w into the page, and length b submerged in water, as in Fig. P390. The depth of water from the surface to the center of the plate is H, and angle is...

Determine the force in each member of the truss and state whether it is in tension or compression. A D 3 m 0.0 B 10 kN 3 m

Consider the flow field produced by a hair dryer (Fig. P1050C). Identify regions of this flow field that can be approximated as irrotational, and those for which the irrotational flow approximation...

Consider the slipper-pad bearing of Prob. 1023. (a) Generate a characteristic scale for v, the y-component of velocity. (b) Perform an order-of-magnitude analysis to compare the inertial terms to the...

Suppose the pump of Fig. P1419C is situated between two large water tanks with their free surfaces open to the atmosphere. Explain qualitatively what would happen to the pump performance curve if a...

A flow process that operates with steam has one inlet stream (A) and two outlet streams (B and C). Stream A is at 20 bar, 25 C, and has a mass flow rate of 10 kg/s; stream B is saturated liquid at 20...

a) An ideal gas (C P = 30 J/mole) is throttled from 20 bar, 25 C to 1 bar. What is the temperature at the exit? b) Water is throttled from 20 bar, 25 C to 1 bar. What is the temperature at the exit?...

A thermally insulated turbine generates 750 kW of power by expanding steam from 500 C and 3.5 MPa to 200 C and 0.3 MPa. a) What is the mass flow rate of steam through the turbine? b) Because of...

Using the data on equipment costs given in this chapter or commercial cost-estimating software, estimate the cost of the following equipment: 1. A shell and tube heat exchanger, heat transfer area 50...

The maximum allowable temperature for a reactor is 800 K. At present our operating set point is 780 K, the 20-K margin of safety to account for fluctuating feed, sluggish controls, etc. Now, with a...

Every May 22 I plant one watermelon seed. I water it, I fight slugs, I pray, I watch my beauty grow, and finally the day comes when the melon ripens. I then harvest and feast. Of course, some years...

The kinetics of a particular catalytic reaction A R are studied at temperature T in a basket reactor (batch-solids and mixed flow of gas) in which the gas composition is kept unchanged, despite...

A reaction has the stoichiometric equation A + B = 2R. What is the order of reaction?

In the mid-nineteenth century the entomologist Henri Fabre noted that French ants (garden variety) busily bustled about their business on hot days but were rather sluggish on cool days. Checking his...