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engineering
mechanical engineering
Vector Mechanics For Engineers Statics And Dynamics 8th Edition Ferdinand Beer, E. Russell Johnston, Jr., Elliot Eisenberg, William Clausen, David Mazurek, Phillip Cornwell - Solutions
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 2.6 kN, determine the vertical force P exerted by the tower on the pin at A.
A 320-lb load of lumber is lifted using a triple leg sling. Knowing that at the instant shown the lumber is at rest determine the tension in each leg of the sling.
A load of lumber is lifted using a triple leg sling. Knowing that at the instant shown the lumber is at rest and that the tension in leg AD is 220 lb, determine the weight of the lumber.
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 16-kg triangular plate is supported by three wires as shown. Knowing that a = 150 mm, determine the tension in each wire.
A 16-kg triangular plate is supported by three wires as shown. Knowing that a = 200 mm, 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.
A derrick boom is guyed by cables AC and AD. A worker is lifting a 20-kg block by pulling on a rope that passes through the pulley at A. Knowing that the boom AB exerts a force at A that is directed from B to A. determine this force and the force in each of the two cables.
A horizontal circular plate weighing 62 lb is suspended as shown from three wires that are attached to a support D and that form 30° angles with the vertical. Determine the tension in each wire.
For the cone of Prob. 2.112, determine the range of values of P for which cord DG is taut if P is directed in the €“x direction.Problem 2.112: 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
In trying to move across a slippery icy surface, a 175-lb man uses two ropes AB and AC. Knowing that the force exerted on the man by the icy surface is perpendicular to that surface, determine the tension in each rope.
Solve Prob. 2.119 assuming that a friend is helping the man at A by pulling on him with a force P= −(45 lb)k. Problem 2.119: In trying to move across a slippery icy surface, a 175-lb man uses two ropes AB and AC. Knowing that the force exerted on the man by the icy surface is perpendicular to
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 10.5 N 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 10.5 N and that P = 0.5 N, determine the tension in each cord.
To lower a pack of weight W to the hiker at C, the hikers at A and B have passed a rope ADB through a ring attached to the pack at D. The hiker at C is 64 ft below A and guides the pack using rope CD. Knowing that at the instant shown the pack is at rest and that the tension in rope CD is 17 lb,
To lower a pack of weight W to the hiker at C, the hikers at A and B have passed a rope ADB through a ring attached to the pack at D. The hiker at C is 64 ft below A and guides the pack using rope CD. Knowing that W = 120 lb and that at the instant shown the pack is at rest, determine the tension
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 = 1400 N, 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 300 N, determine(a) The tension in AC,(b)
Collars A and B are connected by a 1-m-long wire and can slide freely on frictionless rods. If a force (680 P= 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 Prob. 2.127 assuming ng 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 at A, determine(a) The tension in the wire when y = 300 mm,(b) The magnitude of the force Q required to maintain the
Two forces are applied as shown to a hook support. Using trigonometry and knowing that the magnitude of P is 14 lb, determine(a) The required angle α if the resultant R of the two forces applied to the support is to be horizontal,(b) The corresponding magnitude of R.
Determine the x and y components of each of the forces shown.
The guy wire BD exerts on the telephone pole AC a force P directed along BD. Knowing that P has a 450-N component along line AC, determine(a) The magnitude of the force P,(b) Its component in a direction perpendicular to AC.
Knowing that α =25°, determine the tension(a) In cable AC,(b) In rope BC.
The cabin of an aerial tramway is suspended from a set of wheels that can roll freely on the support cable ACB and is being pulled at a constant speed by cable DE. Knowing that α = 42° and β = 32°, that the tension in cable DE is 20kN, and assuming the tension in
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 horizontal circular plate is suspended as shown from three wires which are attached to a support at D and that 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
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.
Find the magnitude and direction of the resultant of the two forces shown knowing that 500 P = lb and Q = 600 lb.
The crate shown is supported by three cables. Determine the weight of the crate knowing that the tension in cable AB is 3 kN.
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 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 in the position shown. Knowing that W = 1200 N, determine P and Q.
A 90-N force is applied to the control rod AB as shown. Knowing that the length of the rod is 225 mm, determine the moment of the force about point B by resolving the force into components along AB and in a direction perpendicular to AB.
A 90-N force is applied to the control rod AB as shown. Knowing that the length of the rod is 225 mm, determine the moment of the force about point B by resolving the force into horizontal and vertical components.
A 3-lb force P is applied to the lever which controls the auger of a snow blower. Determine the moment of P about A when α is equal to 30°.
The force P is applied to the lever which controls the auger of a snow blower. Determine the magnitude and the direction of the smallest force P which has a 19.5- lb ⋅in. counterclockwise moment about A.
A 2.9-lb force P is applied to the lever which controls the auger of a snow blower. Determine the value of α knowing that the moment of P about A is counterclockwise and has a magnitude of 17 lb ⋅in.
A sign is suspended from two chains AE and BF. Knowing that the tension in BF is 200 N, determine(a) The moment about A of the force exerted by the chain at B,(b) The smallest force applied at C which creates the same moment about A.
A sign is suspended from two chains AE and BF. Knowing that the tension in BF is 200 N, determine(a) The moment about A of the force exerted by the chain at B,(b) The magnitude and sense of the vertical force applied at C which creates the same moment about A,(c) The smallest force applied at B
An athlete is exercising while wearing a 5-lb ankle weight at A as shown. Determine(a) The moment of the weight about the knee joint at B,(b) The magnitude of the muscular force P which creates a moment of equal magnitude about B,(c) The smallest force F applied at C which creates the same moment
A winch puller AB is used to straighten a fence post. Knowing that the tension in cable BC is 260 lb, length a is 8 in., length b is 35 in., and length d is 76 in., determine the moment about D of the force exerted by the cable at C by resolving that force into horizontal and vertical components
It is known that a force with a moment of 7840 lb ⋅in. about D is required to straighten the fence post CD. If a = 8 in., b = 35 in., and d = 112 in., determine the tension that must be developed in the cable of winch puller AB to create the required moment about point D.
It is known that a force with a moment of 1152 N m ⋅ about D is required to straighten the fence post CD. If the capacity of the winch puller AB is 2880 N, determine the minimum value of distance d to create the specified moment about point D knowing that a = 0.24 m and b = 1.05 m.
It is known that the connecting rod AB exerts on the crank BC a 2.5-kN force directed down and to the left along the centerline of AB. Determine the moment of that force about C.
It is known that the connecting rod AB exerts on the crank BC a 2.5-kN force directed down and to the left along the centerline of AB. Determine the moment of that force about C.
A 64-mm-diameter circular follower B is held against cam A as shown. Knowing that the cam exerts on the follower a force of magnitude 80 N directed along the common normal BC, determine the moment of the force about the pin at D.
Form the vector products B × C and B€² × C, where B = B€², and the use results obtained to prove the identity sin α cos β = ½ sin (α + β) + ½ sin (α €“
A line passes through the points (630 mm, −255 mm) and (−210 mm, 270 mm). Determine the perpendicular distance d from the line to the origin O of the system of coordinates.
A plane contains the vectors A and B. Determine the unit vector normal to the plane when A and B equal to, respectively, (a) 12 a i−6j+9k and −3i+9j−7.5k, (b) −14i−2j+8k and 3i+1.5j−k
The vectors P and Q are two adjacent sides of a parallelogram. Determine the area of the parallelogram when (a) (3 in.) (7 in.) (a P= i+ j−2 in.)k and Q= −(5 in.)i + (1 in.)j + (3 in.)k (b) P = (2 in.)i − (4 in.)j −(3 in.)k (4 in.)j and Q=(6 in.)i−(1 in.)j+ (5
Determine the moment about the origin O of the force (7.5 N) (3 N) (4.5 F= i+ j − N)k which acts at a point A. Assume that the position vector of A is (a) r= −(6 m)i+ (3 m)j + (1.5 m)k, (b) r=(2 m)i−(0.75 m)j−(1 m)k, (c) r= −(2.5 m)i −(1 m)j+(1.5 m)k.
Determine the moment about the origin O of the force (3 lb) (6 lb) (F= i− j+4 lb) k which acts at a point A. Assume that the position vector of A is (a) r = −(7.5 ft)i + (3 ft)j − (6 ft)k, (b) r = −(0.75 ft)i + (1.5 ft)j − (1 ft)k, (c) r = − (8 ft)I +(2
A small boat hangs from two davits, one of which is shown in the figure. The tension in line ABAD is 369 N. Determine the moment about C of the resultant force RA exerted on the davit at A.
A 36-N force is applied to a wrench to tighten a showerhead knowing that the centerline of the wrench is parallel to the x axis. Determine the moment of the force about A.
Before a telephone cable is strung, rope BAC is tied to a stake at B and is passed over a pulley at A. Knowing that portion AC of the rope lies in a plane parallel to the xy plane and that the magnitude of the tension T in the rope is 62 lb, determine the moment about O of the resultant force
A precast concrete wall section is temporarily held by two cables as shown. Knowing that the tensions in cables BD and FE are 900 N and 675 N, respectively, determine the moment about point O of the force exerted by(a) Cable BD,(b) Cable FE.
In an arm wrestling contest, a 150-lb force P is applied to the hand of one of the contestants by his opponent. Knowing that AB = 15.2 in. and BC = 16 in., determine the moment of the force about C.
A wooden board AB, which is used as a temporary prop to support a small roof, exerts at point A of the roof a 228-N force directed along BA. Determine the moment about C of that force.
In Prob. 3.21, determine the perpendicular distance from point C to portion AD of the line ABAD. Problem 3.21: A small boat hangs from two davits, one of which is shown in the figure. The tension in line ABAD is 369 N. Determine the moment about C of the resultant force RA exerted on the davit at A.
In Prob. 3.23, determine the perpendicular distance from point O to portion AC of rope BAC. Problem 3.23: Before a telephone cable is strung, rope BAC is tied to a stake at B and is passed over a pulley at A. Knowing that portion AC of the rope lies in a plane parallel to the xy plane and that the
In Prob. 3.23, determine the perpendicular distance from point O to portion AB of rope BAC. Problem 3.23: Before a telephone cable is strung, rope BAC is tied to a stake at B and is passed over a pulley at A. Knowing that portion AC of the rope lies in a plane parallel to the xy plane and that the
In Prob. 3.24, determine the perpendicular distance from point C to cable BD. Problem 3.24: A precast concrete wall section is temporarily held by two cables as shown. Knowing that the tensions in cables BD and FE are 900 N and 675 N, respectively, determine the moment about point O of the force
In Prob. 3.25, determine the perpendicular distance from point C to the action of force P. Problem 3.25: In an arm wrestling contest, a 150-lb force P is applied to the hand of one of the contestants by his opponent. Knowing that AB = 15.2 in. and BC = 16 in., determine the moment of the force
In Prob. 3.26, determine the perpendicular distance from point D to a line drawn through points A and B. Problem 3.26: A wooden board AB, which is used as a temporary prop to support a small roof, exerts at point A of the roof a 228-N force directed along BA. Determine the moment about C of that
In Prob. 3.26, determine the perpendicular distance from point C to a line drawn through points A and B. Problem 3.26: A wooden board AB, which is used as a temporary prop to support a small roof, exerts at point A of the roof a 228-N force directed along BA. Determine the moment about C of that
A gardener wishes to connect a water supply pipe from point C on the foundation of a 30-ft-long greenhouse to a water main that passes through points A and B. Determine(a) The value of L which minimize the length of supply pipe needed,(b) The length of pipe needed.
Given the vectors 4 P = − i + 8j − 3k, Q = 9i − j − 7k, and S = 5i − 6j + 2k, compute the scalar products P⋅Q, P⋅S, and Q⋅S.
Form the scalar products B‹…C and B€²‹…C, where B = B€², and use the results obtained to prove the identity cos α cos β = 1/2 cos (α + β) +1/2cos (α ˆ’ β).
Three cables are used to support a container as shown. Determine the angle formed by cables AB and AD.
Three cables are used to support a container as shown. Determine the angle formed by cables AC and AD.
Steel framing members AB, BC, and CD are joined at B and C and are braced using cables EF and EG. Knowing that E is at the midpoint of BC and that the tension in cable EF is 110 lb, determine(a) The angle between EF and member BC,(b) The projection on BC of the force exerted by cable EF at point E.
Steel framing members AB, BC, and CD are joined at B and C and are braced using cables EF and EG. Knowing that E is at the midpoint of BC and that the tension in cable EG is 178 lb, determine(a) The angle between EG and member BC,(b) The projection on BC of the force exerted by cable EG at point E.
Shown are a mast and a portion of the rigging of a schooner. Members CD and EF lie in the same plane, and CD is of length 7.5 m and forms an angle of 45°with a vertical line drawn through C. Knowing that when θ =15°the tension in rope AB is 230 N, determine(a) The angle between ropes
Shown are a mast and a portion of the rigging of a schooner. Members CD and EF lie in the same plane, and CD is of length 7.5 m and forms an angle of 45°with a vertical line drawn through C. Knowing that when θ =10°the tension in rope BD is 250 N, determine(a) The angle between
Determine the volume of the parallelopiped of Fig. 3.25 when(a) P = (3 in).i − (4 in.)j + (1 in.) k, Q = − (7 in.)i + (6 in.)j − (8 in.)k, S = (9 in.)i − (2 in.)j − (3 in.)k,(b) P= − (5 in.)i − (7 in.) j + (4 in.) k, Q = (6 in.)i − (2 in.)j + (5 in.) k, S= − (4 in.)i + (8 in.) j
Given the vectors 3 P = − i − 7j + 5 k, Q = − 2i + j − 4k, and S = 8i + Sy j − 6k, determine the value of Sy for which the three vectors are coplanar.
The rectangular platform is hinged at A and B and is supported by a cable that passes over a frictionless hook at E. Knowing that the tension in the cable is 1349 N, determine the moment about each of the coordinate axes of the force exerted by the cable at C.
The rectangular platform is hinged at A and B and is supported by a cable that passes over a frictionless hook at E. Knowing that the tension in the cable is 1349 N, determine the moment about each of the coordinate axes of the force exerted by the cable at D.
A fence consists of wooden posts and a steel cable fastened to each post and anchored in the ground at A and D. Knowing that the sum of the moments about the z axis of the forces exerted by the cable on the posts at B and C is 48 lb − ⋅ft, determine the magnitude of TCD when TBA = 14 lb.
A fence consists of wooden posts and a steel cable fastened to each post and anchored in the ground at A and D. Knowing that the sum of the moments about the y axis of the forces exerted by the cable on the posts at B and C is 156 lb ⋅ft, determine the magnitude of TBA when TCD = 7.5 lb.
Given the vectors 3 P= −i− 7j + 5k, Q= −2i + j − 4k, and S = 8i + Sy j − 6k, determine the value of Sy for which the three vectors are coplanar. A force P is applied to the lever of an arbor press. Knowing that P lies in a plane parallel to the yz plane and that 26 Mx=
A force P is applied to the lever of an arbor press. Knowing that P lies in a plane parallel to the yz plane and that 20 My = − N⋅m and Mz = −3.5 N⋅m, determine the moment Mx of P about the x axis when θ = 60°.
Utility pole BC is guyed by cable AB as shown. Knowing that the magnitude of the force exerted by the cable at B is 70 lb and that the moment of that force about the x axis is 763 lb − ⋅ft, determine the length of the pole.
Utility pole BC is guyed by cable AB as shown. Knowing that the moments about the x and z axes of the force exerted by the cable at B are 900 ˆ’ lb‹…ft and ˆ’315 lb‹…ft, respectively, determine the length of the pole.
The frame ACD is hinged at A and D and is supported by a cable that passes through a ring at B and is attached to hooks at G and H. Knowing that the tension in the cable is 1125 N, determine the moment about the diagonal AD of the force exerted on the frame by portion BH of the cable.
The frame ACD is hinged at A and D and is supported by a cable that passes through a ring at B and is attached to hooks at G and H. Knowing that the tension in the cable is 1125 N, determine the moment about the diagonal AD of the force exerted on the frame by portion BG of the cable.
The 2.4-m-wide portion ABCD of an inclined, cantilevered walkway is partially supported by members EF and GH. Knowing that the compressive force exerted by member EF on the walkway at F is 24.3kN, determine the moment of that force about edge AD of the walkway.
The 2.4-m-wide portion ABCD of an inclined, cantilevered walkway is partially supported by members EF and GH. Knowing that the compressive force exerted by member GH on the walkway at H is 21.3 kN, determine the moment of that force about edge AD of the walkway.
A rectangular tetrahedron has six edges of length a. A force P is directed as shown along edge BC. Determine the moment of P about edge OA.
A rectangular tetrahedron has six edges of length a.(a) Show that two opposite edges, such as OA and BC, are perpendicular to each other.(b) Use this property and the result obtained in Prob. 3.57 to determine the perpendicular distance between edges OA and BC.
A mast is mounted on the roof of a house using bracket ABCD and is guyed by cables EF, EG, and EH. Knowing that the force exerted by cable EF at E is 29.7 lb, determine the moment of that force about the line joining points D and I.
A mast is mounted on the roof of a house using bracket ABCD and is guyed by cables EF, EG, and EH. Knowing that the force exerted by cable EG at E is 24.6 lb, determine the moment of that force about the line joining points D and I.
Two forces F1 and F2 in space have the same magnitude F. Prove that the moment of F1 about the line of action of F2 is equal to the moment of F2 about the line of action of F1. Discuss.
In Prob. 3.53, determine the perpendicular distance between portion BH of the cable and the diagonal AD. Problem 3.53: The frame ACD is hinged at A and D and is supported by a cable that passes through a ring at B and is attached to hooks at G and H. Knowing that the tension in the cable is 1125 N,
In Prob. 3.54, determine the perpendicular distance between portion BG of the cable and the diagonal AD. Problem 3.54: The frame ACD is hinged at A and D and is supported by a cable that passes through a ring at B and is attached to hooks at G and H. Knowing that the tension in the cable is 1125 N,
In Prob. 3.59, determine the perpendicular distance between cable EF and the line joining points D and I. Problem 3.59: A mast is mounted on the roof of a house using bracket ABCD and is guyed by cables EF, EG, and EH. Knowing that the force exerted by cable EF at E is 29.7 lb, determine the moment
In Prob. 3.60, determine the perpendicular distance between cable EG and the line joining points D and I. Problem 3.60: A mast is mounted on the roof of a house using bracket ABCD and is guyed by cables EF, EG, and EH. Knowing that the force exerted by cable EG at E is 24.6 lb, determine the moment
In Prob. 3.55, determine the perpendicular distance between member EF and edge AD of the walkway. Problem 3.55: The 2.4-m-wide portion ABCD of an inclined, cantilevered walkway is partially supported by members EF and GH. Knowing that the compressive force exerted by member EF on the walkway at F
In Prob. 3.56, determine the perpendicular distance between member GH and edge AD of the walkway. Problem 3.56: The 2.4-m-wide portion ABCD of an inclined, cantilevered walkway is partially supported by members EF and GH. Knowing that the compressive force exerted by member GH on the walkway at H
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