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engineering
engineering mechanics statics 15th

Engineering Mechanics Statics 15th Edition Russell C. Hibbeler - Solutions

Determine the magnitude of the forces F and - F, so that the resultant couple moment is 400 N · m clockwise. 250 N 250 N 1 m -40% 600 N 600 N
The road exerts a torque of MA = 400 N · m and MB = 200 N · m on the brushes of the road sweeper. Determine the magnitude of the couple forces that are developed by the road on the rear wheels of the sweeper, so that the resultant couple moment on the sweeper is zero. What is the magnitude
If F = 125 lb, determine the resultant couple moment. 200 lb 1.5 ft 200 lb -2 ft- 1.25 ft 130° 130⁰ F
Two couples act on the beam. Determine the magnitude of F so that the resultant couple moment is 450 Ib · ft, counterclockwise. Where on the beam does the resultant couple moment act? 200 lb 1.5 ft -2 ft 200 lb 1.25 ft 130⁰ 130° F
The 25-kg bar has a center of mass at G. If it is supported by a smooth peg at C, a roller at A, and cord AB, determine the reactions at these supports. A DOD 0.5 m 0.2 m G 30° 15° 0.3 m C D B
The linkage supports a force of 500 lb and rides along the top and bottom flanges of the crane rail. Determine the force of each roller on the flange. -8 in.- B -3 in. 500 lb
If the crane has a mass of 800 kg and a center of mass at G, and the maximum rated force at its end is F = 15 kN, determine the reactions at its bearings. The bearing at A is a journal bearing and supports only a horizontal force, whereas the bearing at B is a thrust bearing that supports both
Determine the reactions at the roller B, the rocker C, and where the beam contacts the smooth plane at A. Neglect the thickness of the beam. 3 5 + A 4 m 500 N B -2 m- 800 N 60⁰ -6 m- C
The crane has a mass of 800 kg and a center of mass at G. The bearing at A is a journal bearing and can support a horizontal force, whereas the bearing at B is a thrust bearing that supports both horizontal and vertical components. Determine the maximum load F that can be suspended from its end if
The 10-kg lamp has a center of mass at G. Determine the horizontal and vertical components of reaction at A, and the force in the cable BC. 0.3 m 0.4 m 0.15 m A B -0.5 m- *G
The 2.5-Mg assembly has a center of mass at G and is hoisted with a constant velocity. Determine the force in each cable and the distance d for equilibrium. 3 m 1 m/ - 4 m P .G 4 m C B 4 m 1.25 m
If the beam is horizontal and the springs are upstretched when the load is removed, determine the angle of tilt of the beam when the load is applied. k₁= 1 kN/m 3 m 600 N/m 3m B kB = 1.5 kN/m D
The cantilevered jib crane is used to support the load of 780 lb. If x = 5, determine the reactions at the supports. Note that the supports are collars that allow the crane to rotate freely about the vertical axis. The collar at B supports a force in the vertical direction, whereas the one at A
The crane lifts the 400-kg load L. The primary boom AB has a mass of 1.20 Mg and a center of mass at G1, whereas the secondary boom BC has a mass of 0.6 Mg and a center of mass at G2. Determine the tension in the cable BD and the horizontal and vertical components of reaction at the pin A.
The bar of negligible weight is supported by two springs, each having a stiffness k = 100 N > m. If the springs are originally upstretched, determine the angle θ the bar makes with the horizontal when the 30-N force is applied to the bar. C -1m- 30 N B k 2 m- k
Determine the stiffness k of each spring so that the 30-N force causes the bar to tip θ = 15° when the force is applied. Originally the bar is horizontal and the springs are upstretched. Neglect the weight of the bar. 30 N 1m -00000 B 2 m. www.
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 and vertical components of reaction at the pin A. E 100 14 ft -8 ft B 80⁰ 12 ft
The cantilevered jib crane is used to support the load of 780 lb. If the trolley T can be placed anywhere between 1.5 ft < x < 7.5 ft determine the maximum magnitude of reaction at the supports A and B. Note that the supports are collars that allow the crane to rotate freely about the
The block has a mass of 80 kg and a center of mass at G. Determine the smooth reactions on the supporting platform at A, B, and C. 60° G. B 60⁰ 0.3 m -0.8 m
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 θ for equilibrium. The spring is upstretched when θ = 0, and has a stiffness of k = 60 N / m. k = 60 N/m -0.5 m 0 TELA А B 2 m 50 Nm
Calculate the tension in the cable at B required to support the load of 200 kg. The cable passes over a frictionless pulley located at C. Neglect the size of this pulley and weight of the boom. 60° B 1 m 4.5 m A 30° 200 kg
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 reaction at the rollers A and B. -3m- B h k A 2 m 2 m
The exercise machine consists of a rigid bar pin connected to the frame at A. As the woman pushes up on the bar it stretches the rubber band BC. If the stiffness of the rubber band is k = 500 lb/ft, determine the applied vertical force F needed to hold the bar in the position θ = 30°. The rubber
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 is to remain in the horizontal position as shown. The plug at A is circular. A -300 mm- -50 mm B 150
Determine the force in the cable as a function of θ, needed to support the 100-kg hatch door. P 2 m C 2 m B
A 10-kN load is suspended from the boom at D. Determine the force in the hydraulic cylinder BC and the pin reaction at A. 4 1.5 m C 45° B 3m 130° D 10 kN/m
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 pipe’s thickness in the calculation. 30° 45 lb 16 in. C A 90° в 20 in. 8 in.
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 θ for equilibrium, measured from the horizontal. Express the answer in terms of a and l. Neglect the weight of the rod. 2
The crane supports the load of 800 kg. Determine the reactions at the supports A and B as a function of position d of the trolley. Plot the reactions vs. d for 0.5 m < d < 3 m. 5 m A
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 smooth uniform rod has a mass m and is placed on the semicircular arch and against the wall. Show that for equilibrium the angle θ must satisfy 1 sin 0 = (V1 + 3 cos ²0) (d - I sin 0).
Determine the x, y, z components of reaction acting on the ball-and-socket at A, the reaction at the roller B, and the tension in the cord CD required for equilibrium of the plate. X C 40 lb/ft -5 ft- 100 lb-ft B B 2 ft
Determine the reaction at the ball supports B and C and the components of the reaction at the ball-and-socket A (not shown) for the uniformly loaded plate. X 4 ft -1 ft- -2 ft- Z 2 lb/ft² B 2 ft -y
Determine the normal floor reaction on each wheel of the engine stand. The engine weights 750 lb and has a center of gravity at G. X 2 ft C 2 ft 2 ft ita B Z 4 ft 4 ft y
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
Determine the components of reaction at the ball-and-socket B and the reaction at the rollers A and C due to the loading shown. x 0.4 m 0.4 m 600 N B Z 400 NA 800 N 0.3 m 0.3 m y
The bent rod is supported at A, B, and C by smooth journal bearings. Determine the components of reaction at the bearings if the rod is subjected to the force F = 800 N. The bearings are in proper alignment and exert only force reactions on the rod. X A 2 m 30° 60° F Z B 1 m C 2 m -0.75 m
The 100-lb door has its center of gravity at G. Determine the components of reaction at hinges A and B if hinge B resists only forces in the x and y directions and A resists forces in the x, y, z directions. B 24 in. 24 in. A 18 in. X Z CELL 18 in. 30° -y
The triangular plate, having a 90° angle at A, supports the 150-lb load. Determine the tension in cables BD and CD and the x, y, z components of reaction at the ball-and-socket joint at A. B - 4 ft X se bat antas personaltrans 150 lb 4 ft Z 1 ft A 6 ft C 2 ft
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 cause it to lift or topple off the frame. Specify the force location r and the smallest angle and
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 가 2 m 3Dİ +FBDK A Z 2 m -1m. 1'm •G D 1 m
Determine the reaction at fixed support A. A 6 m 0.5 kN/m -3 m- 3 kN 5 kN-m
The truss is supported by a pin at A and a roller at B. Determine the support reactions. 5 kN 4 m 45° 2 m 10 kN -2 m- -4 m-
Determine the components of reaction at the fixedsupport A. Neglect the thickness of the beam. 3m A 60° 200 N 200 N 200 N m- tim- 30° 400 N
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
Determine the force developed in the short link BD, and the tension in the cords CE and CF, and the reactions of the ball-and-socket joint A on the block. 3 m D 6 kN E 9 kN 1.5 m 4m
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
The file cabinet contains four uniform drawers, each 2.5 ft long and weighing 30 lb/ft. If the empty cabinet (without drawers) has a weight of 40 lb and a center of mass at G, determine how many of the drawers can be fully pulled out and the extension x of the last drawer that will cause the
The disk has a mass of 10 kg. If it is suspended from a spring having an unstretched length of 400 mm, determine the angle θ for equilibrium. k = 600 N/m 200 mm
The mechanism shown was thought by its inventor to be the perpetual-motion machine. It consists of stand A, two smooth idler wheels B and C, and in between a uniform hollow cylindrical ring D suspended in the manner shown. The ring has a weight W and it was expected to revolve in the direction
The hold-down clamp exerts a compressive force of 400 N on the wood block at C. If the clamp is loosely bolted to the bench using two symmetrically placed bolts B, one of which is shown, determine the force along the axis of each bolt and the vertical reaction of the bench on the clamp at A. -150
The rod is supported by smooth journal bearings at A, B, and C and is subjected to the two forces. Determine the reactions at these supports. X A N 0.6 m B 0.6 m A600N 400 N D 0.6 m 0.4 m -y
Determine the reactions at the roller support A, the joint D, and the tension in cable BC for ball-and-socket the plate. 0.4 m X 0.6 m 0.6 m 0.6 m B 450 N
The 30-kg block is supported by two springs having the stiffness shown. Determine the un stretched length of each spring after the block is removed. C -0.6 m KAC = 1.5 kN/m A -0.4 m- B 0.5 m KAB = 1.2 kN/m
Determine the magnitude of forces F1. F2, F3. so that the particle is held in equilibrium. F3 = 600 lb ab W F₂ = 400 lb F₁ = 700 lb 30°
The lift sling is used to hoist a container having a mass of 500 kg. Determine the force in each of the cables AB and AC as a function of θ. If the maximum tension allowed in each cable is 5 kN, determine the shortest lengths of cables AB and AC that can be used for the lift. The center of gravity
In. Determine the tension developed in cables AB, AC, and AD. y 325 N 13 12 5 45° 600 N Prob. F2-10 F X
Determine the stretch in each spring for equilibrium of the 2-kg block. The springs are shown in the equilibrium position. 3 m Ans. -3 m- wwwwww KAC = 20 N/m D -4m- wwwwwww KAD = 40 N/m B KAB = 30 N/m
Determine the tension in cables AB, AC., and AD needed to support the 150-lb crate. 90 lb 45° Prob. F2-11 50 lb U1 -X
The spring has a stiffness of k = 800 N/m and an unstretched length of 200 mm. Determine the force in cables BC and BD when the spring is held in the position shown. k = 800 N/m B www 500 mm -400 mm D 400 mm 300 mm
The unstretched length of spring AB is 3 m. If the block is held in the equilibrium position shown, determine the mass of the block at D. 3 m -3 m- KAC = 20 N/m D A -4 m- B www. KAB = 30 N/m
Each cord can sustain a maximum tension of 20 lb. Determine the largest weight of the lamp that can be supported. Also, determine θ of cord DC for equilibrium. E 30° B 60° A C 750 D
Determine the stretch of each spring for equilibrium of the 20-kg cylinder. D A KAD=400 N/m B KAB = 300 N/m KAC = 200 N/m -3 m- 4 m 3 m
The lamp has a weight of 15 lb and is supported by the six cords connected together as shown. Determine the tension in each cord and the angle θ for equilibrium. Cord BC is horizontal. E 30° B A C 45° E D
If the cords suspend the two buckets in the equilibrium position, determine the weight of bucket B. Bucket A has a weight of 60 lb. E 40° A 20° 20° B D 65°
The 30-kg pipe is supported at A by a system of five cords. Determine the force in each cord for equilibrium. G B 60° A H D E
If the mass of the block at A is 20 kg, determine the mass of the block at B and at C for equilibrium. Also, determine the angles u and f. A D 3 m B E -4 m C 3 m
Each cord can sustain a maximum tension of 500 N. Determine the largest mass of pipe that can be supported. FM E H B 60° 1 Y H D E 25
Determine the tension developed in cables AB and AC and the force developed along strut AD for equilibrium of the 400-lb crate. 3 5.5 ft 2 ft Z D 2 ft B 6 ft. 4 ft A 2.5 ft y
If the bucket and its contents have a mass of 10 kg and are suspended from the cable by means of a small pulley at C, determine the location x of the pulley for equilibrium. The cable is 6 m long. 4 m B ד 1m |
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 6 ft 12 ft 3 ft D 4 ft
The 25-kg flowerpot is supported at A by the three cords. Determine the force acting in each cord. x D N 60° 30° 30° B 45°
Determine the tension in the cables in order to support the 100-kg crate. x- C B 2 m N 2.5 m m D 2 m 1 m -y
The 9500-lb pipe is supported by three cables. Determine the force in each cable for equilibrium of the hook at A B C 9500 lb A 135° -1 ft 135° 2.4 ft D
Determine the force in each of the three cables needed to lift the machine that has a weight of 10 kN. x 1 m 3 m 2 m 10 KN A B C 1.25 m 1.25 m
Determine the tension developed in cables OD and OB and the strut OC, required to support the 50-kg crate.The spring OA has an unstretched length of 0.8 m and a stiffness The force in the strut acts along the axis of a the strut. 2 m KOA = 1.2 kN/m 4 m x- 4 m m B N 4 m 4m D 3 m 4 m m
If the tension developed in either cable AB or AC cannot exceed 1000 lb, determine the maximum tension that can be developed in cable AD when it is tightened by the turnbuckle. Also, what is the force developed along the antenna tower at point A? Determine the force in each of the three cables
Determine the force in each of the three cables needed to support the tractor tread assembly, which has a mass of 8 Mg. 1.25 m B X 1.25 m N 3 m D 2 m 1m
Three 10-lb balls and one 15-lb ball are suspended from the pulley-and-cable system. If the pulleys are frictionless and the centers of all of them lie in the same horizontal plane, determine the sag s for equilibrium of the system. S 10 lb 20 in. 20 in. 10 lb 15 lb 20 in. 10 lb
The four concentric forces act on the post. Determine the resultant force and its direction, measured counterclockwise from the positive x-axis. F₁ = 250 N 60°. F₂ = 600 N 12 13 5 30⁰° F3 = 450 N Prob. 2-52 F₁ = 300 N X
Using the SI system of units, show that Equation is a dimensionally homogeneous equation that gives F in newtons. Determine three significant figures the gravitational force acting between two spheres that are touching each other. The mass of each sphere is 200 kg and the radius is 300 mm.
If a car is traveling at 55 mi/h, determine its speed in kilometers per hour and meters per second.
Determine the magnitude of the resultant force FR = F1 + F2, and its orientation θ, measured counter clock wise-axis from the positive x axis. А AG F 30° 45° C
Two forces act on the hook. Determine the magnitude of the resultant force. 15° 30 lb 30° U
Resolve the force into components along the u and y axes and determine the magnitudes of these components. V 105⁰ F = 250 N 30° "
Determine the magnitude of the resultant force F'R = F1 - F2, and its orientation θ, measured counterclockwise from the positive x axis. F₁ = 260 lb 45° F₂= 310 lb 12 5 13 X
Determine the magnitude of the resultant force acting on the gusset plate. 1000 000 F₁ = 300 lb 00 Do 00 O |F3 = 300 lb Prob. R2-3 F₁ = 200 lb F₂ = 400 lb
Resolve the 30-lb force into components along the u and y axes, and determine the magnitude of each of these components. 40° 500 N 30° 200 N Prob. F2-2
The cable exerts a force of 250 lb on the crane boom. Express this force as a Cartesian vector. 30° z Prob. R2-4 70° F = 250 lb
Determine the magnitudes of the two components of F along members AB and AC. Set F = 500 N. А AG F 30° 45° C
Determine the magnitude of the resultant force FR = F1 + F2 and its orientation θ, measured counter clockwise from the positive x axis. F3 = 250 N F₂ = 360 N 30% 45% 30° F₁ = 400 N X
Determine the angle θ for connecting member A to the plate sop that the resultant force of FA and FB is directed horizontally to the right. Also what is the magnitude if the resultant force? -40° FA = 8 KN BFB = 6 KN
Determine the magnitude of the resultant force and its direction O, measured counterclockwise from the positive x-axis. F₁ = 15 kN F₂ = 20 kN 00 F3 = 15 kN ·X
Express the force as a Cartesian vector. F = 500 N 45° 60⁰-
If the resultant force acting on the support is to be 1200 lb, directed horizontally to the right, determine the force F in rope A and the corresponding angle θ. G -60° B 900 lb
Express the force as a Cartesian vector. Z 60° F = 500 N 60° -y
The plate is subjected to the forces acting on members A and B. If θ = 600. determine the magnitude of the resultant of these forces and its direction measured clockwise from the positive x-axis. FA = 400 lb -30% A ge B X FB = 500 lb
The plate is subjected to the two forces at A and B. If θ = 600°, determine the magnitude of the resultant force and its direction measured from the positive x axis. -40° FA = 8 KN X BFB=6 kN
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 magnitude of the force acting along AB and the angle θ of the 500-lb force. B 60° A F = 500
If FB = 3 kN and θ = 45°. determine the magnitude of the resultant force and its direction measured clockwise from the positive x axis. F₁ = 2 kN 30° FB O B -X

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