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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 steel plate is acted upon by two couples as shown. Determine(a) The moment of the couple formed by the two 40-N forces.(b) The value of α if the resultant of the two couples is 8 N m ⋅counterclockwise and d = 820mm,(c) The perpendicular distance between the two 24-N forces if the
A piece of plywood in which several holes are being drilled successively has been secured to a workbench by means of two nails. Knowing that the drill exerts a 12 N m ⋅ couple on the piece of plywood, determine the magnitude of the resulting forces applied to the nails if they are located(a)
The steel plate shown supports six 2-in. diameter idler rollers mounted on the plate as shown. Two flat belts pass around the rollers, and rollers A and D are adjusted so that the tension in each belt is 10-lb. Determine(a) The resultant couple acting on the plate if a = 8 in.(b) The value of a so
Two 2.4-in.-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 2.5-lb forces as indicated.(a) Determine the resulting couple acting on the plate when T = 9
The two shafts a speed-reducer unit are subjected to couples of magnitude M1 = 18 N ∙ m and M2 = 7.5 N ∙ m, respectively. 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 90 P = N, replace the three couples with a single equivalent couple, specifying its magnitude and the direction of its axis.
Knowing that 52.5 P = lb, 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.
A force P of magnitude 160 N is applied to a man€™s hand as shown. Replace P with an equivalent force-couple system(a) At the elbow B,(b) At the shoulder C.
A 135-N vertical force P is applied at A to the bracket shown, which is held by screws at B and C.(a) Replace P with an equivalent force couple system at B.(b) Find the two horizontal forces at B and C that are equivalent to the couple obtained 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 tugboat exerts a 2.8-kN force along its axis on a barge at point B. Replace the force applied at B with an equivalent system formed by two parallel forces applied at A and C.
A landscaper tries to plumb a tree by applying a 54-lb 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 54-lb force shown in the figure.
A landscaper tries to plumb the tree shown in Fig. P3.82 by applying a 54-lb force(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
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 150-lb forces are reversed.
Three workers trying to move a 1 × 1 × 1.2-m crate apply to the crate the three horizontal forces shown. (a) If P = 240 N, 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
To open an in-ground water valve, two workers apply the two horizontal forces shown to the handle of a valve wrench. Show that these forces are equivalent to a single force and specify, if possible, the point of application of the single force on handle ABC.
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
A force and a couple lying in the yz plane are applied to the end of a cantilevered wide-flange beam. This system is to be replaced with a single equivalent force.(a) For θ =15°, determine the magnitude and the line of action of the equivalent force,(b) Determine the value of θ if
A trapezoidal plate is acted upon by the force P and the couple shown. Determine(a) The point of application on the plate of the smallest force F that is equivalent to the given system,(b) The magnitude and direction of F.
An eccentric, compressive 250-kN force P is applied to the end of a column. 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 54 lb, 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 61 lb, replace the force exerted at C by rope CD with an equivalent force-couple system at O.
The jib crane shown is oriented so that its boom AD is parallel to the x axis and is used to move a heavy crate. Knowing that the tension in cable AB is 10.5Kn, replace the force exerted by the cable at A with an equivalent force-couple system at the center O of the base of the crane.
A plumber applies a 220-N force to the handle of a wrench as she removes a coupling from the end of a pipe. Knowing that the wrench and the force lie in a vertical plane parallel to the yz plane, replace the force with an equivalent force-couple system at the origin of the coordinate system
A 63-lb force F and 560- lb ⋅in. 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
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 = 0determine(a) The distance d,(b) F2 and M2.
A 5-m-long beam is subjected to a variety of loadings.(a) Replace each loading with an equivalent force-couple system at end B of the beam.(b) Which of the loadings are equivalent?
A 5-m-long beam is loaded as shown. Determine the loading of Prob 3.98 that is equivalent to this loading.
Determine the single equivalent force and the distance from end A to its line of action for the beam and loading shown when(a) 200 B N, F= ↓ MB=100 N ∙ m,(b) B 100 N, F= ↑ MB = −600 N ∙ m,(c) B 100 N, F= ↓ MB = −200 N ∙ m.
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 = (2 lb)j and a couple of moment M=(48 lb ∙ in.)i + (32 lb ∙ in)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. Determine where a third child should 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 hikers are shown crossing a footbridge. Knowing that the weights of the hikers at points C, D, and E are 200 lb, 175 lb, and 135 lb, respectively, determine(a) The horizontal distance from A to the line of action of the resultant of the three weights when 3.3 α = ft,(b) The
By driving a truck over a scale, it was determined that the loads on the front and rear axles are 18 kN and 12 kN, respectively, when the truck is empty. Determine the weight and the location of the heaviest load that the truck can carry if the load on each axle is not to exceed 40 kN.
Fixture ABCD is used to apply forces to photo elastic models of mechanical components. For the model and forces shown, determine when α = 50°(a) The resultant of the applied forces,(b) The point where the line of action of the resultant intersects a line drawn through points F and G.
Fixture ABCD is used to apply forces to photo elastic models of mechanical components for the model and the forces shown. Determine(a) The value of α so that the line of action of the resultant of the applied forces passes through the model 100 mm to the right of the 40-N force,(b) The
When the couple M is applied to the link in a mechanism, the resulting forces exerted on the link from a guide and the connecting links are as shown. Determine(a) The values of M and α so that the applied forces and couple can be reduced to a single equivalent force whose line of action
The three forces and a couple shown are applied to an angle bracket.(a) Find the resultant of this system of forces.(b) Locate the points where the line of action of the resultant intersects line AB and line BC.
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 en α =45° and the point of
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
Pulleys A and B are mounted on bracket CDEF. The tension on each side of the two belts is as shown. Replace the four forces with a single equivalent force, and determine where its line of action intersects the bottom edge of the bracket.
Three forces and a couple act on crank ABC. For P = 25 N 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 point B and C.(c) Locate the point where the line of action
Three different drive belt profiles are to be studied. If at any given time each belt makes contact with one-half of the circumference of its pulley, determine the contact area between the belt and the pulley for each design.
As follower AB rolls along the surface of member C, it exerts a constant force F perpendicular to the surface.(a) Replace F with an equivalent force-couple system at the point D.(b) For b = 1 ft and h = 2 ft, determine the value of x for which the moment of the equivalent force couple system at D
A machine component is subjected to the forces shown, each of which is parallel to one of the coordinate axes. Replace these forces with an equivalent force-couple system at A.
As a block of wood is sanded, it exerts on the disk of the sander a force F of magnitude 1.8 lb. Knowing that the belt forces exerted on the 5-in.- diameter pulley lie in a plane parallel to yz plane, replace F and the belt forces with an equivalent force-couple system at O.
A car owner uses wrench ABC to loosen the lug nut at C. The length of the handle AB is 372 mm, and the owner applies forces A and B to the wrench. Knowing that these forces are equivalent to a force-couple system at O consisting of the force (R= −(10 N)i + (6 N)k and the couple MO = (60 N m)i
While using a pencil sharpener, a student applies the forces and couple shown.(a) Determine the forces exerted at B and C knowing that these forces and the couple are equivalent to a force-couple system at A consisting of the force R = (3.9 lb)i + Ry j ˆ’(1.1 lb)k and the couple MR/A =
A portion of the flue for a furnace is attached to the ceiling at A. While supporting the free end of the flue at F, a worker pushes in at E and pulls out at F to align end E with the furnace. Knowing that the 50-N force at F lies in a plane parallel to the yz plane, determine(a) The angle α
A portion of the flue for a furnace is attached to the ceiling at A. While supporting the free end of the flue at F, a worker pushes in at E and pulls out at F to align end E with the furnace. Knowing that the 50-N force at F lies in a plane parallel to the yz plane and that α = 60°,(a)
As an adjustable brace BC is used to bring a wall into plumb, the force couple system shown is exerted on the wall. Replace this force-couple system with an equivalent force-couple system at A knowing that 21.2 R = lb and M=13.25 lb ∙ ft.
While a sagging porch is leveled and repaired, a screw jack is used to support the front of the porch. As the jack is expanded, it exerts on the porch the force-couple system shown, where 60 R = lb and M = 22.5 lb ˆ™ ft. Replace this force-couple system with an equivalent force-couple
A concrete foundation mat in the shape of a regular hexagon with 3-m sides supports four column loads as shown. Determine the magnitude and the point of application of the resultant of the four loads.
A concrete foundation mat in the shape of a regular hexagon with 3-m sides supports four column loads as shown. Determine the magnitudes of the additional loads that must be applied at B and F if the resultant of all six loads is to pass through the center of the mat.
The forces shown are the resultant downward loads on sections of the flat roof of a building because of accumulated snow. Determine the magnitude and the point of application of the resultant of these four loads.
The forces shown are the resultant downward loads on sections of the flat roof of a building because of accumulated snow. If the snow represented by the 116-kip force is shoveled so that this load acts at E, determine a and b knowing that the point of application of the resultant of the four loads
A group of students loads a 2 ×4-m flatbed trailer with two 0.6×0.6×0.6-mboxes and one 0.6×0.6×1.2-m box. Each of the boxes at the rear of the trailer is positioned so that it is aligned with both the back and a side of the trailer.
Solve Prob. 3.127 if the students want to place as much weight as possible in the fourth box and that at least one side of the box must coincide with a side of the trailer. Problem 3.127: A group of students loads a 2 ×4-m flatbed trailer with two
A piece of sheet metal is bent into the shape shown and is acted upon by three forces. Replace the three forces with an equivalent wrench and determine(a) The magnitude and direction of the resultant R,(b) The pitch of the wrench,(c) The point where the axis of the wrench intersects the yz plane.
A block of wood is acted upon by three forces of the same magnitude P and having the directions shown. Replace the three forces with an equivalent wrench and determine(a) The magnitude and direction of the resultant R,(b) The pitch of the wrench,(c) The point where the axis of the wrench intersects
The forces and couples shown are applied to two screws as a piece of sheet metal is fastened to a block of wood. Reduce the forces and the couples to an equivalent wrench and determine(a) The resultant force R,(b) The pitch of the wrench,(c) The point where the axis of the wrench intersects the xz
In an automated manufacturing process, three holes are drilled simultaneously in an aluminum block as shown. Each drill exerts a 50-N force and a 0.100- N m ‹… couple on the block. Knowing that drill A rotates counterclockwise and drills B and C rotate clockwise (as observed from each
Two bolts A and B are tightened by applying the forces and couples shown. Replace the two wrenches with a single equivalent wrench and determine(a) The resultant R,(b) The pitch of the single equivalent wrench,(c) The point where the axis of the wrench intersects the yz plane.
Two bolts A and B are tightened by applying the forces and couple shown. Replace the two wrenches with a single equivalent wrench and determine(a) The resultant R,(b) The pitch of the single equivalent wrench,(c) The point where the axis of the wrench intersects the xz plane.
A flagpole is guyed by three cables. If the tensions in the cables have the same magnitude P, replace the forces exerted on the pole with an equivalent wrench and determine(a) The resultant force R,(b) The pitch of the wrench,(c) The point where the axis of the wrench intersects the xz plane.
Determine whether the force-and-couple system shown can be reduced to a single equivalent force R. If it can, determine R and the point where the line of action of R intersects the yz plane, if it cannot be so reduced, replace the given system with an equivalent wrench and determine its resultant,
Determine whether the force-and-couple system shown can be reduced to a single equivalent force R. If it can, determine R and the point where the line of action of R intersects the yz plane, if it cannot be so reduced, replace the given system with an equivalent wrench and determine its resultant,
Replace the wrench shown with an equivalent system consisting of two forces perpendicular to the z axis and applied respectively at A and B.
Show that, in general, a wrench can be replaced with two forces chosen in such a way that one force passes through a given point while the other force lies in a given plane.
Show that a wrench can be replaced with two perpendicular forces one of which is applied at a given point.
Show that a wrench can be replaced with two forces one of which has a prescribed line of action.
It is known that a vertical force of 800 N is required to remove the nail at C from the board. As the nail first starts moving, determine(a) The moment about B of the force exerted on the nail,(b) The magnitude of the force P which creates the same moment about B if α = 10°,(c) The
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.
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.
Consider the volleyball net shown. Determine the angle formed by guy wires AC and AD.
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 ˆ™ ft and ˆ’400 lb ˆ™ ft , determine the
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.
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.
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.
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.
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.
As plastic bushings are inserted into a 3-in.-diameter cylindrical sheet metal container, the insertion tool exerts the forces shown on the enclosure. Each of the forces is parallel to one of the coordinate axes. Replace these forces with an equivalent force-couple system at C.
Three children are standing on a 15 × 15-ft raft. The weights of the children at points A, B, and C are 85 lb, 60 lb, and 90 lb, respectively. If a fourth child of weight 95 lb climbs onto the raft, determine where she should stand if the other children remain in the positions shown
Two children are standing on a diving board that weighs 146 lb. Knowing that the weights of the children at C and D are 63 lb and 90 lb, respectively, determine(a) The reaction at A,(b) The reaction at B.
The boom on a 9500-lb truck is used to unload a pallet of shingles of weight 3500 lb, determine the reaction at each of the two(a) Rear wheels B,(b) Front wheels C.
A load of lumber weighing ng W = 25 kN is being raised by a mobile crane. The weight of the boom ABC and the combined weight of the truck and driver are as shown. Determine the reaction at each of the two(a) Front wheels H,(b) Rear wheels K.
A load of lumber er weighing W = 25 kN is being raised as shown by a mobile crane. Knowing that the tension is 25kN in all portions of cable AEF and that the weight of boom ABC is 3kN, determine(a) The tension in rod CD,(b) The reaction at pin B.
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 =35°,(b) The corresponding reaction at each of the two wheels.
Solve Prob. 4.5 when α =40°. Problem 4.5: 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 =35°,(b) The corresponding
When cars C and D stop on a two-lane bridge, the forces exerted by their tires on the bridge are as shown. Determine the total reactions at A and B when(a) ) A = 2.9 m,(b) A = 8.1 m.
When cars C and D stop on a two-lane bridge, the forces exerted by their tires on the bridge are as shown. When both cars are on the bridge, determine(a) The value of a for which the total reaction at A is maximum,(b) The corresponding total reactions at A and B.
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 36 lb.
Three loads are applied as shown to a light beam supported by cables attached at B and D. Neglecting the weight of the beam, determine the range of values of Q for which neither cable becomes slack when P = 0.
Three loads are applied as shown to a light beam supported by cables attached at B and D. Knowing that the maximum allowable tension in each cable is 12 kN and neglecting the weight of the beam, determine the range of values of Q for which the loading is safe when 5 P = kN.
Four boxes are placed on a uniform 28-lb wooden plank which rests on two sawhorses. Knowing that the weights of boxes B and D are 9 lb and 90 lb, respectively, determine the range of values of the weight of box A so that the plank remains in equilibrium when box C is removed.
For the beam and loading shown, determine the range of values of the distance a for which the reaction at B does not exceed 250 N downward or 500 N upward.
For the given loading of the beam AB, determine the range of values of the mass of the crate for which the system will be in equilibrium, knowing that the maximum allowable value of the reactions at each support is 2.5 kN and that the reaction at E must be directed downward.
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