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Vector Mechanics For Engineers Statics 7th Edition R.C.Hibbeler - Solutions

For the structure and loading of Problem 2.45, determine(a) The value of α for which the tension in cable BC is as small as possible,(b) The corresponding value of the tension.
Boom AB is supported by cable BC and a hinge at A. Knowing that the boom exerts on pin B a force directed along the boom and that the tension in rope BD is 70 lb, determine(a) The value of α for which the tension in cable BC is as small as possible,(b) The corresponding value of the tension.
Collar A shown in Figure P2.65 and P2.66 can slide on a frictionless vertical rod and is attached as shown to a spring. The constant of the spring is 660 N/m, and the spring is unstretched when h = 300 mm. Knowing that the system is in equilibrium when h = 400 mm, determine the weight of the collar.
The 40-N collar A can slide on a frictionless vertical rod and is attached as shown to a spring. The spring is unstretched when h = 300 mm. Knowing that the constant of the spring is 560 N/m, determine the value of h for which the system is in equilibrium.
A 280-kg crate is supported by several rope-and-pulley arrangements as shown. Determine for each arrangement the tension in the rope.
Solve parts b and d of Problem 2.67 assuming that the free end of the rope is attached to the crate. Problem 2.67: A 280-kg crate is supported by several rope-and-pulley arrangements as shown. Determine for each arrangement the tension in the rope.
A 350-lb load is supported by the rope-and-pulley arrangement shown. Knowing that β = 25°, determine the magnitude and direction of the force P which should be exerted on the free end of the rope to maintain equilibrium.
A 350-lb load is supported by the rope-and-pulley arrangement shown. Knowing that α = 35°, determine(a) The angle β,(b) The magnitude of the force P which should be exerted on the free end of the rope to maintain equilibrium.
A load Q is applied to the pulley C, which can roll on the cable ACB. The pulley is held in the position shown by a second cable CAD, which passes over the pulley A and supports a load P. Knowing that P = 800 N, determine(a) The tension in cable ACB,(b) The magnitude of load Q.
A 2000-N load Q is applied to the pulley C, which can roll on the cable ACB. The pulley is held in the position shown by a second cable CAD, which passes over the pulley A and supports a load P. Determine(a) The tension in the cable ACB,(b) The magnitude of load P.
Determine(a) The x, y, and z components of the 200-lb force,(b) The angles θx, θy, and θz that the force forms with the coordinate axes
Determine(a) The x, y, and z components of the 420-lb force,(b) The angles θx, θy, and θz that the force forms with the coordinate axes.
To stabilize a tree partially uprooted in a storm, cables AB and AC are attached to the upper trunk of the tree and then are fastened to steel rods anchored in the ground. Knowing that the tension in cable AB is 4.2kN, determine(a) The components of the force exerted by this cable on the tree,(b)
To stabilize a tree partially uprooted in a storm, cables AB and AC are attached to the upper trunk of the tree and then are fastened to steel rods anchored in the ground. Knowing that the tension in cable AC is 3.6kN, determine(a) The components of the force exerted by this cable on the tree,(b)
A horizontal circular plate is suspended as shown from three wires which are attached to a support at D and form 30° angles with the vertical. Knowing that the x component of the force exerted by wire AD on the plate is 220.6 N, determine(a) The tension in wire AD,(b) The angles θx, θy, and θz
A horizontal circular plate is suspended as shown from three wires which are attached to a support at D and form 30° angles with the vertical. Knowing that the z component of the force exerted by wire BD on the plate is –64.28 N, determine (a) The tension in wire BD, (b) The angles
A horizontal circular plate is suspended as shown from three wires which are attached to a support at D and form 30° angles with the vertical. Knowing that the tension in wire CD is 120 lb, determine(a) The components of the force exerted by this wire on the plate,(b) The angles θx, θy, and θz
A horizontal circular plate is suspended as shown from three wires which are attached to a support at D and form 30° angles with the vertical. Knowing that the x component of the forces exerted by wire CD on the plate is –40 lb, determine (a) The tension in wire CD, (b) The angles θx,
Determine the magnitude and direction of the force F= (800 lb) i + (260 lb) j − (320 lb) k.
Determine the magnitude and direction of the force F = (400 N) i – (1200 N) j + (300 N) k.
A force acts at the origin of a coordinate system in a direction defined by the angles θx = 64.5° and θz = 55.9°. Knowing that the y component of the force is –200 N, determine (a) The angle θy, (b) The other components and the magnitude of the force.
A force acts at the origin of a coordinate system in a direction defined by the angles θx = 75.4° and θy = 132.6°. Knowing that the z component of the force is –60 N, determine (a) The angle θz, (b) The other components and the magnitude of the force.
A force F of magnitude 400 N acts at the origin of a coordinate system. Knowing that θx = 28.5°, Fy = –80 N, and Fz > 0, determine (a) The components Fx and Fz,(b) The angles θy and θz.
A force F of magnitude 600 lb acts at the origin of a coordinate system. Knowing that Fx = 200 lb, θz = 136.8°, Fy < 0, determine(a) The components Fy and Fz,(b) The angles θx and θy.
A transmission tower is held by three guy wires anchored by bolts at B, C, and D. If the tension in wire AB is 2100 N, determine the components of the force exerted by the wire on the bolt at B.
A transmission tower is held by three guy wires anchored by bolts at B, C, and D. If the tension in wire AD is 1260 N, determine the components of the force exerted by the wire on the bolt at D.
A rectangular plate is supported by three cables as shown. Knowing that the tension in cable AD is 195 lb, determine the components of the force exerted on the plate at D.
A rectangular plate is supported by three cables as shown. Knowing that the tension in cable AD is 195 lb, determine the components of the force exerted on the plate at D.
A steel rod is bent into a semicircular ring of radius 0.96 m and is supported in part by cables BD and BE which are attached to the ring at B. Knowing that the tension in cable BD is 220 N, determine the components of this force exerted by the cable on the support at D.
A steel rod is bent into a semicircular ring of radius 0.96 m and is supported in part by cables BD and BE which are attached to the ring at B. Knowing that the tension in cable BE is 250 N, determine the components of this force exerted by the cable on the support at E.
Find the magnitude and direction of the resultant of the two forces shown knowing that 500 P = N and Q = 600 N.
Find the magnitude and direction of the resultant of the two forces shown knowing that P = 600 N and Q = 400 N.
Knowing that the tension is 850 N in cable AB and 1020 N in cable AC, determine the magnitude and direction of the resultant of the forces exerted at A by the two cables.
Assuming that in Problem 2.95 the tension is 1020 N in cable AB and 850 N in cable AC, determine the magnitude and direction of the resultant of the forces exerted at A by the two cables.
For the semicircular ring of Problem 2.91, determine the magnitude and direction of the resultant of the forces exerted by the cables at B knowing that the tensions in cables BD and BE are 220 N and 250 N, respectively.
To stabilize a tree partially uprooted in a storm, cables AB and AC are attached to the upper trunk of the tree and then are fastened to steel rods anchored in the ground. Knowing that the tension in AB is 920 lb and that the resultant of the forces exerted at A by cables AB and AC lies in the yz
To stabilize a tree partially uprooted in a storm, cables AB and AC are attached to the upper trunk of the tree and then are fastened to steel rods anchored in the ground. Knowing that the tension in AC is 850 lb and that the resultant of the forces exerted at A by cables AB and AC lies in the yz
For the plate of Problem 2.89, determine the tension in cables AB and AD knowing that the tension if cable AC is 27 lb and that the resultant of the forces exerted by the three cables at A must be vertical.
The support assembly shown is bolted in place at B, C, and D and supports a downward force P at A. Knowing that the forces in members AB, AC, and AD are directed along the respective members and that the force in member AB is 146 N, determine the magnitude of P.
The support assembly shown is bolted in place at B, C, and D and supports a downward force P at A. Knowing that the forces in members AB, AC, and AD are directed along the respective members and that P = 200 N, determine the forces in the members.
Three cables are used to tether a balloon as shown. Determine the vertical force P exerted by the balloon at A knowing that the tension in cable AB is 60 lb.
Three cables are used to tether a balloon as shown. Determine the vertical force P exerted by the balloon at A knowing that the tension in cable AC is 100 lb.
The crate shown in Figure P2.105 and P2.108 is supported by three cables. Determine the weight of the crate knowing that the tension in cable AB is 3kN.
For the crate of Problem 2.105, determine the weight of the crate knowing that the tension in cable AD is 2.8kN. Problem 2.105: The crate shown in Figure P2.105 and P2.108 is supported by three cables. Determine the weight of the crate knowing that the tension in cable AB is 3kN.
For the crate of Problem 2.105, determine the weight of the crate knowing that the tension in cable AC is 2.4kN. Problem 2.105: The crate shown in Figure P2.105 and P2.108 is supported by three cables. Determine the weight of the crate knowing that the tension in cable AB is 3kN.
A 750-kg crate is supported by three cables as shown. Determine the tension in each cable.
A force P is applied as shown to a uniform cone which is supported by three cords, where the lines of action of the cords pass through the vertex A of the cone. Knowing that P = 0 and that the tension in cord BE is 0.2 lb, determine the weight W of the cone.
A force P is applied as shown to a uniform cone which is supported by three cords, where the lines of action of the cords pass through the vertex A of the cone. Knowing that the cone weighs 1.6 lb, determine the range of values of P for which cord CF is taut.
A transmission tower is held by three guy wires attached to a pin at A and anchored by bolts at B, C, and D. If the tension in wire AB is 3.6kN, determine the vertical force P exerted by the tower on the pin at A.
A transmission tower is held by three guy wires attached to a pin at A and anchored by bolts at B, C, and D. If the tension in wire AC is 2.6kN, determine the vertical force P exerted by the tower on the pin at A.
A rectangular plate is supported by three cables as shown. Knowing that the tension in cable AC is 15 lb, determine the weight of the plate.
A rectangular plate is supported by three cables as shown. Knowing that the tension in cable AD is 120 lb, determine the weight of the plate.
A horizontal circular plate having a mass of 28 kg is suspended as shown from three wires which are attached to a support D and form 30Â° angles with the vertical. Determine the tension in each wire.
A transmission tower is held by three guy wires attached to a pin at A and anchored by bolts at B, C, and D. Knowing that the tower exerts on the pin at A an upward vertical force of 8 kN, determine the tension in each wire.
For the rectangular plate of Problems 2.113 and 2.114, determine the tension in each of the three cables knowing that the weight of the plate is 180 lb.
For the cone of Problem 2.110, determine the range of values of P for which cord DG is taut if P is directed in the -x direction.
A force P is applied as shown to a uniform cone which is supported by three cords, where the lines of action of the cords pass through the vertex A of the cone. Knowing that the cone weighs 2.4 lb and that P = 0, determine the tension in each cord.
A force P is applied as shown to a uniform cone which is supported by three cords, where the lines of action of the cords pass through the vertex A of the cone. Knowing that the cone weighs 2.4 lb and that P = 0.1 lb, determine the tension in each cord.
Using two ropes and a roller chute, two workers are unloading a 200-kg cast-iron counterweight from a truck. Knowing that at the instant shown the counterweight is kept from moving and that the positions of points A, B, and C are, respectively, A(0, –0.5 m, 1 m), B(–0.6 m, 0.8 m, 0), and C(0.7
Solve Problem 2.121 assuming that a third worker is exerting a force (180 P= − N)i on the counterweight. Problem 2.121: Using two ropes and a roller chute, two workers are unloading a 200-kg cast-iron counterweight from a truck. Knowing that at the instant shown the counterweight is kept from
A piece of machinery of weight W is temporarily supported by cables AB, AC, and ADE. Cable ADE is attached to the ring at A, passes over the pulley at D and back through the ring, and is attached to the support at E. Knowing that W = 320 lb, determine the tension in each cable.
A piece of machinery of weight W is temporarily supported by cables AB, AC, and ADE. Cable ADE is attached to the ring at A, passes over the pulley at D and back through the ring, and is attached to the support at E. Knowing that the tension in cable AB is 68 lb, determine(a) The tension in AC,(b)
A container of weight W is suspended from ring A. Cable BAC passes through the ring and is attached to fixed supports at B and C. Two forces P = Pi and Q = Qk are applied to the ring to maintain the container is the position shown. Knowing that W = 1200 N, determine P and Q.
For the system of Problem 2.125, determine W and P knowing that Q = 160 N. Problem 2.125: A container of weight W is suspended from ring A. Cable BAC passes through the ring and is attached to fixed supports at B and C. Two forces P= Pi and Q = Qk are applied to the ring to maintain the container
Collars A and B are connected by a 1-m-long wire and can slide freely on frictionless rods. If a force (P= 680 N)j is applied at A, determine(a) The tension in the wire when y = 300 mm,(b) The magnitude of the force Q required to maintain the equilibrium of the system.
Solve Problem 2.127 assuming y = 550 mm. Problem 2.127: Collars A and B are connected by a 1-m-long wire and can slide freely on frictionless rods. If a force P= (680 N)j is applied atA, determine(a) The tension in the wire when y = 300 mm,(b) The magnitude of the force Q required to maintain the
Member BD exerts on member ABC a force P directed along line BD. Knowing that P must have a 300-lb horizontal component, determine(a) The magnitude of the force P,(b) Its vertical component.
A container of weight W is suspended from ring A, to which cables AC and AE are attached. A force P is applied to the end F of a third cable which passes over a pulley at B and through ring A and which is attached to a support at D. Knowing that W = 1000 N, determine the magnitude of P.
A container of weight W is suspended from ring A, to which cables AC and AE are attached. A force P is applied to the end F of a third cable which passes over a pulley at B and through ring A and which is attached to a support at D. Knowing that the tension in cable AC is 150 N, determine(a) The
Two cables tied together at C are loaded as shown. Knowing that Q = 60 lb, determine the tension(a) In cable AC,(b) In cable BC.
Two cables tied together at C are loaded as shown. Determine the range of values of Q for which the tension will not exceed 60 lb in either cable.
A welded connection is in equilibrium under the action of the four forces shown. Knowing that at FA = 8kN and FB = 16kN, determine the magnitudes of the other two forces.
A welded connection is in equilibrium under the action of the four forces shown. Knowing that t FA = 5kN and FD = 6kN, determine the magnitudes of the other two forces.
Collar A is connected as shown to a 50-lb load and can slide on a frictionless horizontal rod. Determine the magnitude of the force P required to maintain the equilibrium of the collar when(a) x = 4.5 in.,(b) x = 15 in.
Collar A is connected as shown to a 50-lb load and can slide on a frictionless horizontal rod. Determine the distance x for which the collar is in equilibrium when P = 48 lb.
A frame ABC is supported in part by cable DBE which passes through a frictionless ring at B. Knowing that the tension in the cable is 385 N, determine the components of the force exerted by the cable on the support at D.
A frame ABC is supported in part by cable DBE which passes through a frictionless ring at B. Determine the magnitude and direction of the resultant of the forces exerted by the cable at B knowing that the tension in the cable is 385 N.
A steel tank is to be positioned in an excavation. Using trigonometry, determine(a) The magnitude and direction of the smallest force P for which the resultant R of the two forces applied at A is vertical,(b) The corresponding magnitude of R.
The boom on a 4300-kg truck is used to unload a pallet of shingles of mass 1600 kg. Determine the reaction at each of the two(a) Rear wheels B,(b) Front wheels C.
Two children are standing on a diving board of mass 65 kg. Knowing that the masses of the children at C and D are 28 kg and 40 kg, respectively, determine(a) The reaction at A,(b) The reaction at B.
Two crates, each weighing 250 lb, are placed as shown in the bed of a 3000-lb pickup truck. Determine the reactions at each of the two(a) Rear wheels A,(b) Front wheels B.
Solve Problem 4.3 assuming that crate D is removed and that the position of crate C is unchanged. P4.3 The boom on a 4300-kg truck is used to unload a pallet of shingles of mass 1600 kg. Determine the reaction at each of the two(a) Rear wheels B,(b) Front wheels C
A T-shaped bracket supports the four loads shown. Determine the reactions at A and B if(a) 100 a = mm,(b) a = 70 mm.
For the bracket and loading of Problem 4.5, determine the smallest distance a if the bracket is not to move. P4.5 A T-shaped bracket supports the four loads shown. Determine the reactions at A and B if(a) 100 a = mm,(b) a = 70 mm.
A hand truck is used to move two barrels, each weighing 80 lb. Neglecting the weight of the hand truck, determine(a) The vertical force P which should be applied to the handle to maintain equilibrium when α = 35o,(b) The corresponding reaction at each of the two wheels.
Solve Problem 4.7 when α = 40o. P4.7 A hand truck is used to move two barrels, each weighing 80 lb. Neglecting the weight of the hand truck, determine(a) The vertical force P which should be applied to the handle to maintain equilibrium when α = 35o,(b) The corresponding reaction at each of the
Four boxes are placed on a uniform 14-kg wooden plank which rests on two sawhorses. Knowing that the masses of boxes B and D are 4.5 kg and 45 kg, respectively, determine the range of values of the mass of box A so that the plank remains in equilibrium when box C is removed.
A control rod is attached to a crank at A and cords are attached at B and C. For the given force in the rod, determine the range of values of the tension in the cord at C knowing that the cords must remain taut and that the maximum allowed tension in a cord is 180 N.
The maximum allowable value of each of the reactions is 360N. Neglecting the weight of the beam, determine the range of values of the distance d for which the beam is safe.
Solve Problem 4.11 assuming that the 100-N load is replaced by a 160-N load P4.11 the maximum allowable value of each of the reactions is 360 N. Neglecting the weight of the beam, determine the range of values of the distance d for which the beam is safe.
For the beam of Sample Problem 4.2, determine the range of values of P for which the beam will be safe knowing that the maximum allowable value of each of the reactions is 45 kips and that the reaction at A must be directed upward.
For the beam and loading shown, determine the range of values of the distance a for which the reaction at B does not exceed 50 lb downward or 100 lb upward.
A follower ABCD is held against a circular cam by a stretched spring, which exerts a force of 21 N for the position shown. Knowing that the tension in rod BE is 14 N, determine(a) The force exerted on the roller at A,(b) The reaction at bearing C.
A 6-m-long pole AB is placed in a hole and is guyed by three cables. Knowing that the tensions in cables BD and BE are 442 N and 322 N, respectively, determine(a) The tension in cable CD,(b) The reaction at A.
Determine the reactions at A and C when(a) α = 0,(b) α = 30o.
Determine the reactions at A and B when(a) h = 0,(b) h = 8in.
The lever BCD is hinged at C and is attached to a control rod at B. If 200 P = N, determine(a) The tension in rod AB,(b) The reaction at C.
The lever BCD is hinged at C and is attached to a control rod at B. Determine the maximum force P which can be safely applied at D if the maximum allowable value of the reaction at C is 500 N.
The required tension in cable AB is 800 N. Determine(a) The vertical force P which must be applied to the pedal,(b) The corresponding reaction at C.
Determine the maximum tension which can be developed in cable AB if the maximum allowable value of the reaction at C is 1000 N.

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