Determine the components of reaction acting at the balland-socket A, roller B, and cord CD. X B 400 N 2m 2 m N D 300 N 2 m C 1 m y

The smooth uniform rod has a mass m and is placed on the semicircular arch and against the wall. Show that for equilibrium the angle must satisfy 1 sin 0 = (V1 + 3 cos 0) (d - I sin 0).

The cable of the tower crane is subjected to a force of 840 N. Determine the x, y, z components of reaction at the fixed base A. 24 m A B 2 m F = 840 N 3 m X -10 m 15 m

The rod BC is supported by two cords, each of length a, which are attached to the pin at A. If weights W and 2W are suspended from the ends of the rod, determine the angle for equilibrium, measured...

The smooth pipe rests against the wall at the points of contact A, B, and C. Determine the reactions at these points needed to support the vertical force of 45 lb. Neglect the pipes thickness in the...

The check valve is used to regulate pressure in the pipe. If the stiffness of the spring is k = 80 kN/m and its uncompressed length is 120 mm, determine the maximum pressure in the tank if the lever...

The assembly is used to support the 120-kg container having a center of mass at G. If the spring has an upstretched length of 250 mm and stiffness of k = 300 kN/m, determine its height h and the...

The 10-kg uniform rod is pinned at end A. If it is subjected to a couple moments of 50 N m, determine the smallest angle for equilibrium. The spring is upstretched when = 0, and has a stiffness of...

The davit is used to suspend the lifeboat over the side of a ship. If the boat exerts a force of 800 lb on the chain at D, determine the force acting on the hydraulic cylinder BC, and the horizontal...

Determine the stiffness k of each spring so that the 30-N force causes the bar to tip = 15 when the force is applied. Originally the bar is horizontal and the springs are upstretched. Neglect the...

Determine the moment of force F about an axis extending between O and A. Express the result as a Cartesian vector. X 0.6 m N 0.8 m F = {80i-40j - 120k} N 0.3 m -y

Determine the magnitude of the equivalent resultant force of the distributed load and specify its location on the beam measured from point A. W 420 lb/ft w = (5 (x-8) +100) lb/ft 100 lb/ft. 8 ft- 120...

Determine the magnitude of the equivalent resultant force of the distributed loading and specify its location on the beam measured from point A. -4.5 ft- 2 kip/ft -6 ft- 1.5 kip/ft

Replace the force system acting on the beam by an equivalent resultant force and couple moment at point A. A B 30 in. 30 250 lb 12 in. to 16 in. 3 in. -10 in.- 14 in. 45 260 lb 13 12 5 300 lb

The theory of scattering generalizes in a pretty obvious way to arbitrary localized potentials (Figure 2.21). To the left (Region I), V (x) = 0, so To the right (Region III), V (x) is again zero, so...

One way to obtain the allowed energies of a potential well numerically is to turn the Schrdinger equation into a matrix equation, by discretizing the variable x. Slice the relevant interval at evenly...

The spring has an unstretched length of 0.3 m. Determine the angle for equilibrium if the uniform bars each have a mass of 20 kg. A k = 150 N/m 2m B

The foot pump is used to fill the tire. If the force required to develop the necessary pressure in the cylinder is 70 lb, determine the vertical force P that must be applied to the pedal. The...

Suppose where is some positive constant with the appropriate dimensions. Wed like to find the bound statessolutions to the time-independent Schrdinger equation with negative energy (E < 0). (a) Lets...

Suppose (a) Solve the (time-independent) Schrdinger equation for this potential. by letting z x and y(z) (1/) (x) (the a is just so y (z) is normalized with respect to z when (x) is normalized...

The Boltzmann equation gives the probability of finding a system in the state n (with energy E n ), at temperature T(k B is Boltzmann's constant). The probability here refers to the random thermal...

The double link grip is used to lift the beam. If the beam weighs 4 kN, determine the horizontal and vertical components of force acting on the pin at A and the horizontal and vertical components of...

If d = 0.75 and the spring has an upstretched 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

Five coins are stacked in the smooth plastic container shown. If each coin weighs 0.0235 lb, determine the normal reactions of the bottom coin on the container at points A and B. + U 3 A Brunc B 3 3

Determine the force that must be developed in the hydraulic cylinder AB in order to develop a normal force of 4 MN in the grip. Also, determine the magnitude of the force developed in the pin at C. 4...

The gin-pole derrick is used to lift the 300-kg stone with constant velocity. If the derrick and the block and 0tackle are in the position shown, determine the horizontal and vertical components of...

The clamp is used to hold the smooth strut S in place. If the tensile force in the bolt GH is 300 N, determine the force exerted at the smooth surface at A and B. H G S B E A 20 mm- 60 - 250 mm 45 20...

Determine the force in the hydraulic cylinders EF and AD in order to hold the shovel in the position shown. The load has a mass of 125 Mg and a center of gravity at G. All joints are pin connected....

The two ends of the spanner wrench fit loosely into the smooth slots of the bolt head. Determine the required force P on the handle in order to develop a torque of M = 50 N m on the bolt. Also, what...

Determine the compressive force exerted on the stone by a vertical load of 50 N applied to the toggle press. 400 mm- 50 N BY 90 mm 400 mm-

The double tree AB is used to support the loadings applied to each of the single trees. Determine the total load that must be supported by the chain EG and its placement d for AB to remain...

The picture frame is glued together at its corners and held in place by the 4-corner clamp. If the tension in the adjusting screw is 14 N, determine the horizontal and vertical components of the...

The two ends of the spanner wrench fit loosely into the smooth slots of the bolt head. Determine the torque M on the bolt and the resultant force on the pin at B when a force of P = 80 N is applied...

The bridge frame consists of three parts which can be considered pinned at A, D, and E, rocker supported at C and F, and roller supported at B. Determine the horizontal and vertical components of...

Determine the horizontal and vertical components of force that pins A and C exert on the two-member frame. 3 m C -3 m 400 N/m 500 N/m B 600 N/m

Determine the resultant forces at pins B and Con member ABC of the four-member frame. F -2 ft- E 5 ft. -5 ft- Prob. R6-8 B -2 ft 150 lb/ft C D 4 ft

Determine the force in each member of the truss and state if the members are in tension or compression. Set P 1 = 8 kN, P 2 = 10 kN. AQ P -2 m- D P B C 2 m

Determine the force in member GJ and GC of the truss and state if the members are in tension or compression. 1000 lb A go 000 1000 lb 130 B -10 ft- H -10 ft- 1000 lb G -10 ft- Prob. R6-3 D 1000 lb...

Determine the force in each member of the truss and state if the members are in tension or compression. Set P 1 = 2 kN and P 2 = 1.5 kN. A 30 - 3 m B D P 30 3 m C P

Determine the force in each member of the truss. State if the members are in tension or compression. A -4 ft- B D -4 ft- 450 lb 4 ft

The hanger H is used to support the end of the floor beam B. If the loading on the hanger consists of two couples, determine the magnitude of the horizontal forces F and - F so that the resultant...

Determine the moment of each force about point A. Add these moments and calculate the magnitude and coordinate direction angles of the resultant moment. X 0.8 m F = {30i+20j - 30k} N A 1.20 m 0.4 m y...

Determine the moment about point O of each force acting on the pipe assembly. Add these moments and calculate the magnitude and coordinate direction angles of the resultant moment. 0.8 m Z F = {30i +...

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 operator is defined not just by its action (what it does to the vector it is applied to) but its domain (the set of vectors on which it acts). In a finite-dimensional vector space the domain is...

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=

Supersymmetry. Consider the two operators for some function W (x) . These may be multiplied in either order to construct two Hamiltonians: V 1 and V 2 are called supersymmetric partner potentials....

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

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 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 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 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...

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...

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...

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...

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,...

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