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mechanical engineering

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

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.
A mechanic uses a piece of pipe AB as a lever when tightening an alternator belt. When he pushes down at A, a force of 580 N is exerted on the alternator B. Determine the moment of that force about bolt C if its line of action passes through O.
Form the vector products B × C and B′ × C, where B = B′, and use the results obtained to prove the identity
A line passes through the points (420 mm, −150 mm) and (−140 mm, 180 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 are equal to, respectively,(a) 4i − 2j + 3k and −2i + 6j − 5k,(b) 7i + j − 4k and −6i − 3k + 2k.
The vectors P and Q are two adjacent sides of a parallelogram. Determine the area of the parallelogram when(a) P = (8 in.)i + (2 in)j − (1 in.)k and Q = −(3 in.)i + (4 in)j + (2 in)k,(b) P = − (3 in.)i + (6 in)j + (4 in.)k and Q = (2 in.)i + (5 in)j − (3 in.)k.
Determine the moment about the origin O of the force F = −(5 N)i − (2 N)j + (3 N)k which acts at a point A. Assume that the position vector of A is(a) r = (4 m)i − (2 m)j − (1 m)k,(b) r = −(8 m)i + (3 m)j + (4 m)k,(c) r = (7.5 m)i + (3 m)j − (4.5 m)k.
Determine the moment about the origin O of the force F = − (1.5 lb)i + (3 lb)j − (2 lb)k which acts at a point A. Assume that the position vector of A is(a) r = (2.5 ft)i − (1 ft)j + (2 ft)k,(b) r = (4.5 ft)i − (9 ft)j + (6 ft)k,(c) r = (4 ft)i − (1 ft)j + (7 ft)k.
Before the trunk of a large tree is felled, cables AB and BC are attached as shown. Knowing that the tension in cables AB and BC are 777 N and 990 N, respectively, determine the moment about O of the resultant force exerted on the tree by the cables at B.
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 tension T in the rope is 124 N, determine the moment about O of the resultant force exerted on the pulley
An 8-lb 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.
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.
The ramp ABCD is supported by cables at corners C and D. The tension in each of the cables is 360 lb. Determine the moment about A of the force exerted by(a) The cable at D,(b) The cable at C.
The arms AB and BC of a desk lamp lie in a vertical plane that forms an angle of 30o with the xy plane. To reposition the light, a force of magnitude 8 N is applied at C as shown. Determine the moment of the force about O knowing that AB = 450 mm, BC = 325 mm, and line CD is parallel to the z axis.
In Problem 3.21, determine the perpendicular distance from point O to cable AB. Problem 3.21: Before the trunk of a large tree is felled, cables AB and BC are attached as shown. Knowing that the tension in cables AB and BC are 777 N and 990 N, respectively, determine the moment about O of the
In Problem 3.21, determine the perpendicular distance from point O to cable BC. Problem 3.21: Before the trunk of a large tree is felled, cables AB and BC are attached as shown. Knowing that the tension in cables AB and BC are 777 N and 990 N, respectively, determine the moment about O of the
In Problem 3.24, determine the perpendicular distance from point D to a line drawn through points A and B. Problem 3.24: 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 Problem 3.24, determine the perpendicular distance from point C to a line drawn through points A and B. Problem 3.24: 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 Problem 3.25, determine the perpendicular distance from point A to portion DE of cable DEF. Problem 3.25: The ramp ABCD is supported by cables at corners C and D. The tension in each of the cables is 360 lb. Determine the moment about A of the force exerted by(a) The cable at D,(b) The cable at
In Problem 3.25, determine the perpendicular distance from point A to a line drawn through points C and G. Problem 3.25: The ramp ABCD is supported by cables at corners C and D. The tension in each of the cables is 360 lb. Determine the moment about A of the force exerted by(a) The cable at D,(b)
In Problem 3.25, determine the perpendicular distance from point B to a line drawn through points D and E. Problem 3.25: The ramp ABCD is supported by cables at corners C and D. The tension in each of the cables is 360 lb. Determine the moment about A of the force exerted by(a) The cable at D,(b)
Determine the value of a which minimizes the perpendicular distance from point C to a section of pipeline that passes through points A and B.
Given the vectors P = 7i − 2j + 5k, Q = −3i − 4j + 6k, and S = 8i + j − 9k, compute the scalar ar products P⋅Q, P⋅S, and Q⋅S.
Form the scalar products B ⋅ C and B′ ⋅ C, where B=B′, and use the results obtained to prove the identity
Consider the volleyball net shown. Determine the angle formed by guy wires AB and AC.
Consider the volleyball net shown. Determine the angle formed by guy wires 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 330 N, 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 445 N, determine(a) The angle between EG and member BC,(b) The projection on BC of the force exerted by cable EG at point E.
Slider P can move along rod OA. An elastic cord PC is attached to the slider and to the vertical member BC. Knowing that the distance from O to P is 0.12 m and the tension in the cord is 30 N, determine(a) The angle between the elastic cord and the rod OA,(b) The projection on OA of the force
Slider P can move along rod OA. An elastic cord PC is attached to the slider and to the vertical member BC. Determine the distance from O to P for which cord PC and rod OA are perpendicular.
Determine the volume of the parallelepiped of Figure 3.25 when(a) P = − (7 in.)i − (1 in.)j + (2 in)k, Q = (3 in.)i − (2 in.)j + (4 in)k, and S = − (5 in.)i + (6 in)j − (1 in)k,(b) P = (1 in.)i + (2 in)j − (1 in.)k, Q = − (8 in.)i − (1 in.)j + (9 in)k, and S = (2 in.)i + (3 in)j +
Given the vectors P = 4i − 2j + Pzk, Q = i + 3j − 5k, and S = −6i + 2j − k, determine the value of Pz for which the three vectors are coplanar.
The 0.732 × 1.2-m lid ABCD of a storage bin is hinged along side AB and is held open by looping cord DEC over a frictionless hook at E. If the tension in the cord is 54 N, determine the moment about each of the coordinate axes of the force exerted by the cord at D.
The 0.732 × 1.2-m-m lid ABCD of a storage bin is hinged along side AB and is held open by looping cord DEC over a frictionless hook at E. If the tension in the cord is 54 N, determine the moment about each of the coordinate axes of the force exerted by the cord at C.
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 −66 N · m, determine the magnitude de TCD when TBA = 56 N.
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 212 N · m, determine the magnitude of TBA when TCD = 33 N.
To lift a heavy crate, a man uses a block and tackle attached to the bottom of an I-beam at hook B. Knowing that the moments about the y and z axes of the force exerted at B by portion AB of the rope are, respectively, 100 lb ⋅ft and −400 lb ⋅ ft , determine the distance a.
To lift a heavy crate, a man uses a block and tackle attached to the bottom of an I-beam at hook B. Knowing that the man applies a 200-lb force to end A of the rope and that the moment of that force about the y axis is 175 lb ⋅ ft, determine the distance a.
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 230 lb Mx = ⋅ in., My = −200 lb ⋅ in., and Mz = −35 lb ⋅ in., determine the magnitude of P and the values of φ and θ.
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 My = − 180 lb ⋅ in. and Mz = − 30 lb ⋅ in., determine the moment Mx of P about the x axis when θ = 60°.
The triangular plate ABC is supported by ball-and-socket joints at B and D and is held in the position shown by cables AE and CF. If the force exerted by cable AE at A is 220 lb, determine the moment of that force about the line joining points D and B.
The triangular plate ABC is supported by ball-and-socket joints at B and D and is held in the position shown by cables AE and CF. If the force exerted by cable CF at C is 132 lb, determine the moment of that force about the line joining points D and B.
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 66 N, 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 61.5 N, determine the moment of that force about the line joining points D and I.
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 Problem 3.57 to determine the perpendicular distance between edges OA and BC.
The 8-ft-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 5400 lb, determine the moment of that force about edge AD.
The 8-ft-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 4800 lb, determine the moment of that force about edge AD.
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.
In Problem 3.53, determine the perpendicular distance between cable AE and the line joining points D and B. Problem 3.53: The triangular plate ABC is supported by ball-and-socket joints at B and D and is held in the position shown by cables AE and CF. If the force exerted by cable AE at A is 220
In Problem 3.54, determine the perpendicular distance between cable CF and the line joining points D and B. Problem 3.54: The triangular plate ABC is supported by ball-and-socket joints at B and D and is held in the position shown by cables AE and CF. If the force exerted by cable CF at C is 132
In Problem 3.55, determine the perpendicular distance between cable EF and the line joining points D and I. Problem 3.55: 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 66 N, determine the moment
In Problem 3.56, determine the perpendicular distance between cable EG and the line joining points D and I. Problem 3.56: 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 61.5 N, determine the
In Problem 3.41, determine the perpendicular distance between post BC and the line connecting points O and A. Problem 3.41: Slider P can move along rod OA. An elastic cord PC is attached to the slider and to the vertical member BC. Knowing that the distance from O to P is 0.12 m and the tension in
In Problem 3.45, determine the perpendicular distance between cord DE and the y axis. Problem 3.45: The 0.732 × 1.2 -m lid ABCD of a storage bin is hinged along side AB and is held open by looping cord DEC over a frictionless hook at E. If the tension in the cord is 54 N, determine the moment
A plate in the shape of a parallelogram is acted upon by two couples. Determine(a) The moment of the couple formed by the two 21-N forces,(b) The perpendicular distance between the 12-N forces if the resultant of the two couples is zero,(c) The value of α if the resultant couple is 71.8 N m ⋅
A couple M of magnitude 10 lb ⋅ft is applied to the handle of a screwdriver to tighten a screw into a block of wood. Determine the magnitudes of the two smallest horizontal forces that are equivalent to M if they are applied(a) At corners A and D,(b) At corners B and C,(c) Anywhere on the block.
Two 60-mm-diameter pegs are mounted on a steel plate at A and C, and two rods are attached to the plate at B and D. A cord is passed around the pegs and pulled as shown, while the rods exert on the plate 10-N forces as indicated.(a) Determine the resulting couple acting on the plate when T = 36
The steel plate shown will support six 50-mm-diameter idler rollers mounted on the plate as shown. Two flat belts pass around the rollers, and rollers A and D will be adjusted so that the tension in each belt is 45 N. Determine(a) The resultant couple acting on the plate if a = 0.2 m,(b) The value
The shafts of an angle drive are acted upon by the two couples shown. Replace the two couples with a single equivalent couple, specifying its magnitude and the direction of its axis.
Knowing that P = 0, replace the two remaining couples with a single equivalent couple, specifying its magnitude and the direction of its axis.
Knowing that P = 0, replace the two remaining couples with a single equivalent couple, specifying its magnitude and the direction of its axis.
Knowing that P = 5 lb, replace the three couples with a single equivalent couple, specifying its magnitude and the direction of its axis.
Knowing that P = 210 N, replace the three couples with a single equivalent couple, specifying its magnitude and the direction of its axis.
In a manufacturing operation, three holes are drilled simultaneously in a work piece. Knowing that the holes are perpendicular to the surfaces of the work piece, replace the couples applied to the drills with a single equivalent couple, specifying its magnitude and the direction of its axis.
The tension in the cable attached to the end C of an adjustable boom ABC is 1000 N. Replace the force exerted by the cable at C with an equivalent force-couple system(a) At A,(b) At B.
The 20-lb horizontal force P acts on a bell crank as shown.(a) Replace P with an equivalent force-couple system at B.(b) Find the two vertical forces at C and D which are equivalent to the couple found in part a.
A 700-N force P is applied at point A of a structural member. Replace P with(a) An equivalent force-couple system at C,(b) An equivalent system consisting of a vertical force at B and a second force at D.
A landscaper tries to plumb a tree by applying a 240-N force as shown. Two helpers then attempt to plumb the same tree, with one pulling at B and the other pushing with a parallel force at C. Determine these two forces so that they are equivalent to the single 240-N force shown in the figure.
A landscaper tries to plumb a tree by applying a 240-N force as shown.(a) Replace that force with an equivalent force-couple system at C.(b) Two helpers attempt to plumb the same tree, with one applying a horizontal force at C and the other pulling at B. Determine these two forces if they are to be
A dirigible is tethered by a cable attached to its cabin at B. If the tension in the cable is 250 lb, replace the force exerted by the cable at B with an equivalent system formed by two parallel forces applied at A and C.
Three workers trying to move a 3 × 3 × 4-ft crate apply to the crate the three horizontal forces shown. (a) If P = 60 lb, replace the three forces with an equivalent force-couple system at A. (b) Replace the force-couple system of part a with a single force, and determine where it
A force and a couple are applied to a beam.(a) Replace this system with a single force F applied at point G, and determine the distance d.(b) Solve part a assuming that the directions of the two 600-N forces are reversed.
Three cables attached to a disk exert on it the forces shown.(a) Replace the three forces with an equivalent force-couple system at A.(b) Determine the single force which is equivalent to the force-couple system obtained in part a, and specify its point of application on a line drawn through points
While tapping a hole, a machinist applies the horizontal forces shown to the handle of the tap wrench. Show that these forces are equivalent to a single force, and specify, if possible, the point of application of the single force on the handle.
A rectangular plate is acted upon by the force and couple shown. This system is to be replaced with a single equivalent force. (a) For α = 40°, specify the magnitude and the line of action of the equivalent force.(b) Specify the value of α if the line of action of the equivalent force is to
A hexagonal plate is acted upon by the force P and the couple shown. Determine the magnitude and the direction of the smallest force P for which this system can be replaced with a single force at E.
An eccentric, compressive 270-lb force P is applied to the end of a cantilever beam. Replace P with an equivalent force-couple system at G.
Two workers use blocks and tackles attached to the bottom of an I-beam to lift a large cylindrical tank. Knowing that the tension in rope AB is 324 N, replace the force exerted at A by rope AB with an equivalent force-couple system at E.
Two workers use blocks and tackles attached to the bottom of an I-beam to lift a large cylindrical tank. Knowing that the tension in rope CD is 366 N, replace the force exerted at C by rope CD with an equivalent force-couple system at O.
To keep a door closed, a wooden stick is wedged between the floor and the doorknob. The stick exerts at B a 45-lb force directed along line AB. Replace that force with an equivalent force-couple system at C.
A 25-lb force acting in a vertical plane parallel to the yz plane is applied to the 8-in.-long horizontal handle AB of a socket wrench. Replace the force with an equivalent force-couple system at the origin O of the coordinate system.
A 315-N force F and 70-N · m couple M are applied to corner A of the block shown. Replace the given force-couple system with an equivalent force-couple system at corner D.
The hand piece of a miniature industrial grinder weighs 2.4 N, and its center of gravity is located on the y axis. The head of the hand piece is offset in the xz plane in such a way that line BC forms an angle of 25° with the x direction. Show that the weight of the hand piece and the two couples
A 20-lb force F1 and a 40- lb ⋅ ft couple M1 are applied to corner E of the bent plate shown. If F1 and M1 are to be replaced with an equivalent force-couple system (F2, M2) at corner B and if (M2)z = 0, determine(a) The distance d, (b) F2 and M2.
A 4-ft-long beam is subjected to a variety of loadings.(a) Replace each loading with an equivalent force-couple system at end A of the beam.(b) Which of the loadings are equivalent?
A 4-ft-long beam is loaded as shown. Determine the loading of Problem 3.98 which is equivalent to this loading.
Determine the single equivalent force and the distance from point A to its line of action for the beam and loading of(a) Problem 3.98b,(b) Problem 3.98d,(c) Problem 3.98e.Problem 3.98: A 4-ft-long beam is subjected to a variety of loadings. (a) Replace each loading with an equivalent force-couple
Five separate force-couple systems act at the corners of a metal block, which has been machined into the shape shown. Determine which of these systems is equivalent to a force F = (10 N)j and a couple of moment M= (6 N ⋅ m)i+(4 N ⋅ m)k located at point A.
The masses of two children sitting at ends A and B of a seesaw are 38 kg and 29 kg, respectively. Where should a third child sit so that the resultant of the weights of the three children will pass through C if she has a mass of?(a) 27 kg,(b) 24 kg.
Three stage lights are mounted on a pipe as shown. The mass of each light is 1.8 Ma = mB= kg and mC = 1.6 kg.(a) If d = 0.75 m, determine the distance from D to the line of action of the resultant of the weights of the three lights.(b) Determine the value of d so that the resultant of the weights
Three hikers are shown crossing a footbridge. Knowing that the weights of the hikers at points C, D, and E are 800 N, 700 N, and 540 N, respectively, determine(a) The horizontal distance from A to the line of action of the resultant of the three weights when a = 1.1 m,(b) The value of a so that the
Gear C is rigidly attached to arm AB. If the forces and couple shown can be reduced to a single equivalent force at A, determine the equivalent force and the magnitude of the couple M.
To test the strength of a 25 20-× in. suitcase, forces are applied as shown. If P = 18lb, (a) Determine the resultant of the applied forces, (b) Locate the two points where the line of action of the resultant intersects the edge of the suitcase.
Solve Problem 3.106 assuming that 28 P = lb. Problem 3.106: To test the strength of a 25 × 20-in. suitcase, forces are applied as shown. If P = 18 lb, (a) Determine the resultant of the applied forces, (b) Locate the two points where the line of action of the resultant intersects the
As four holes are punched simultaneously in a piece of aluminum sheet metal, the punches exert on the piece the forces shown. Knowing that the forces are perpendicular to the surfaces of the piece, determine (a) The resultant of the applied forces when α = 45° and the point of intersection
As four holes are punched simultaneously in a piece of aluminum sheet metal, the punches exert on the piece the forces shown. Knowing that the forces are perpendicular to the surfaces of the piece, determine(a) The value of α so that the resultant of the applied forces is parallel to the 10.5 N
A truss supports the loading shown. Determine the equivalent force acting on the truss and the point of intersection of its line of action with a line through points A and G.
Three forces and a couple act on crank ABC. . For P = 5 lb and α = 40°,(a) Determine the resultant of the given system of forces,(b) Locate the point where the line of action of the resultant intersects a line drawn through points B and C,(c) Locate the point where the line of action of the
Three forces and a couple act on crank ABC. Determine the value of d so that the given system of forces is equivalent to zero at(a) Point B,(b) Point D

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