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A 50-cm 30-cm 20-cm block weighing 150 N is to be moved at a constant velocity of 1.10 m/s on an inclined surface with a friction coefficient of 0.27. (a) Determine the force F that needs to be... A 200-kg granite rock ( = 2700 kg/m 3 ) is dropped into a lake. A man dives in and tries to lift the rock. Determine how much force the man needs to apply to lift it from the bottom of the lake. Do... A 78-percent-efficient 12-hp pump is pumping water from a lake to a nearby pool at a rate of 1.2 ft 3 /s through a constant- diameter pipe. The free surface of the pool is 32 ft above that of the... The forming section of a plastics plant puts out a continuous sheet of plastic that is 1.2 m wide and 2 mm thick at a rate of 18 m/min. The sheet is subjected to airflow at a velocity of 4 m/s on... A 2.4-in-diameter smooth ball rotating at 500 rpm is dropped in a water stream at 60F flowing at 4 ft/s. Determine the lift and the drag force acting on the ball when it is first dropped in the water. A 7-ft-diameter spherical tank completely submerged in fresh water is being towed by a ship at 8 ft/s. Assuming turbulent flow, determine the required towing power. In the metal processing industry, heat treatment of metals is commonly done using electrically heated draw batch furnaces. Consider a furnace that is situated in a room with surrounding air... A turbine blade made of a metal alloy (k=17 W/mK) has a length of 5.3 cm, a perimeter of 11 cm, and a cross-sectional area of 5.13 cm 2 . The turbine blade is exposed to hot gas from the combustion... For the common-base network of Fig. 4.138 Fig. 4.143 a. Using the information provided determines the value of R C . b. Find the currents I B and I E . c. Determine the voltages V BC and V CE . 9.1 ... The in situ moisture content of a soil is 18%, and the moist unit weight is 105 lb/ft 3 . The specific gravity of soil solids is 2.75. This soil is to be excavated and transported to a construction... Refer to Figure 12.43. Given that B = 1 m, L = 3 m, and Q = 110 kN, calculate the primary consolidation settlement of the foundation. 1.5 m 1.5 m 2.5 m FIGURE 12.43 Load = Q BXL Sand Clay (normally... An earth dam section is shown in Figure 8.33. Determine the rate of seepage through the earth dam using Pavlovskys solution. Use k = 4 X 10 -5 mm/s. 3 m 32 m FIGURE 8.33 2.0 1 7 m Impermeable layer... A zinc alloy has a SDAS of 0.01 cm and m = 0.40. What is the solidification time? In Problem 1.19 we noted that the Wright brothers, in the design of their 1900 and 1901 gliders, used aerodynamic data from the Lilienthal table given in Figure 1.65. They chose a design angle of... What is the tempering of steels? Why is tempering necessary? Lefties and music In an experiment to see if left- and right-handed people have different abilities in music, subjects heard a tone and were then asked to identify which of several other tones... Where is B/t nonzero, in Figure 7.21(b) ?Exploit the analogy between Faradays law and Ampres law to sketch (qualitatively) the electric field. B (in) (a) B (in) (b) changing magnetic field FIGURE... Two positive point charges, qA and qB (masses mA and mB) are at rest, held together by a massless string of length a. Now the string is cut, and the particles fly off in opposite directions. How fast... For the airfoil in Problem 4.11, calculate the value of the circulation around the airfoil. Data from Problem 4.11: Consider again the NACA 2412 airfoil discussed in Problem 4.10. The airfoil is... Starting with Equations (1.7), (1.8), and (1.11), derive in detail Equations (1.15), (1.16), and (1.17). N' == TE -TE * (P, cos 0 + T sine) ds, + (p, cos 0 , sine) ds; (1.7) - TE TE - fort (- Pu... Pubs In England, a Leeds University researcher said that the local watering holes welcoming atmosphere helps men get rid of the stresses of modern life and is vital for their psychological... The Drake equation In 1961 astronomer Frank Drake developed an equation to try to estimate the number of extraterrestrial civilizations in our galaxy that might be able to communicate with us via... Depression and the Internet The September 1998 issue of the American Psychologist published an article by Kraut et al. that reported on an experiment examining the social and psychological impact of... Traffic Highway planners investigated the relationship between traffic Density (number of automobiles per mile) and the average Speed of the traffic on a moderately large city thoroughfare. The data... Name recognition, part II The advertising company described in is thinking about signing a WNBA star to an endorsement deal. In its poll, 27% of the respondents could identify her. 1. Fans who never... Fried PCs A computer company recently experienced a disastrous fire that ruined some of its inventory. Unfortunately, during the panic of the fire, some of the damaged computers were sent to another... If the magnitude of the resultant force acting on the bracket is to be 450 N directed along the positive u-axis. determine the magnitude of F 1 and its direction . 12 13 F " 30 -X F = 200 N 5 F3 =... Learning math Developers of a new math curriculum called Accelerated Math compared performances of students taught by their system with control groups of students in the same schools who were taught... Resolve the force F 2 into components along the and axes and determine the magnitudes of the components. 75 30 30 F = 6 kN V F = 4 kN Determine the magnitude and direction of the resultant force. 250 N T 30 400 N 300 N X A magnetic disk drive requires a motor to position a read/write head over tracks of data on a spinning disk, as shown in Figure E4.4. The motor and head may be represented by the transfer function... Repeat 1.3-10 but use the method of sections to find member forces in AB and DC. (a) Find reaction force components B x , Bz , and O z . (b) Find the axial force in truss member AC. Problem 1.3-10... Two pipes (L 1 = 2.5 m and L 2 =1.5 m) are joined at B by flange plates (thickness t f =14 mm) with five bolts (d b f =13 mm) arranged in a circular pattern (see figure). Also, each pipe segment is... A simple beam AB is loaded as shown in the figure. (a) Calculate the required section modulus S if sallow 518,000 psi, L = 32 ft, P = 2900 lb, and q = 450 lb/ft. Then select a suitable I-beam (S... A cantilever beam AB is loaded by a uniform load q and a concentrated load P, as shown in the figure. (a) Select the most economical steel C shape from Table F-3(a) in Appendix F; use q 5 20 lb/ft... The 80-ft-long cable is attached to the boom at A. If x = 60 ft. determine the coordinates y and z to the end of cable B. Take z = 3y. A Z B Probs. 2-93/94 -y A simple beam of length L = 5 m carries a uniform load of intensity q = 5.8 kN/m and a concentrated load 22.5 kN (see figure). (a) Assuming sallow = 110 MPa, calculate the required section modulus S.... Determine the resultant force acting on the hook, and its direction measured clockwise from the positive x axis. S F = 800 N Prob. 2-55 60 X F = 500 N A sandwich beam having steel faces enclosing a plastic core is subjected to a bending moment M = 5 kN m. The thickness of each steel face is t = 3 mm with a modulus of elasticity E s = 200 GPa. The... A W 360 X 79 steel beam is fixed at A. The beam has a length of 2.5 m and is subjected to a linearly varying distributed load with maximum intensity q 0 = 500 N/m on segment AB and a uniformly... Express F 1 , F 2 and F 3 as Cartesian vectors. F = 60 lb 30% Probs. 2-50/51 20 F = 50 lb The 500-lb force is to be resolved into two components acting along the axis of the struts AB and AC. If the component of force along AC is required to be 300 lb, directed from A to C. determine the... Two forces act on the hook. Determine the magnitude of the resultant force. 15 30 lb 30 U Determine the maximum weight of the crate that can be suspended from cables AB, AC, and AD so that the tension developed in any one of the cables does not exceed 250 lb. X CGS 3 ft N 2 ft 3 ft- 36% B... Determine the components of reaction that the thrust bearing A and cable BC exert on the bar. N A 6 ft F = 80 lb D C 1.5 ft B 1.5 ft Determine the support reactions at the smooth journal bearings A, B, and C of the pipe assembly. 0.4 m 0.6 m, 0.6 m 0.6 m B 450 N The sign has a mass of 100 kg with center of mass at G. Determine the x, y, z components of reaction at the ball-and socket joint A and the tension in wires BC and BD. y 1m 2 m 3D +FBDK A Z 2 m -1m.... The 50-kg glass tabletop rests on the centrally located equilateral triangular frame which is supported by three legs. Determine the smallest vertical force P that, when applied to the glass, would... 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... 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 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... 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 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
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