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mechanical engineering

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

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.
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 obtained by drawing the perpendicular from the point of contact to the x axis(b) For 1 a = m and b = 2 m, determine the
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.
Two 300-mm-diameter pulleys are mounted on line shaft AD. The belts B and C lie in vertical planes parallel to the yz plane. Replace the belt forces shown with an equivalent force-couple system at A.
A mechanic uses a crowfoot wrench to loosen a bolt at C. The mechanic holds the socket wrench handle at points A and B and applies forces at these points. Knowing that these forces are equivalent to a force-couple system at C consisting of the force (C = − 40 N)i+ (20 N)k and the couple MC = (40
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+ Ryj − (1.1 lb)k and the couple MR/A = Mxi
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 10-lb force at F lies in a plane parallel to the yz plane, determine(a) The angle α the
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 10-lb force at F lies in a plane parallel to the yz plane and that α = 60°, (a)
The head-and-motor assembly of a radial drill press was originally positioned with arm AB parallel to the z axis and the axis of the chuck and bit parallel to the y axis. The assembly was then rotated 25o about the y axis and 20o about the centerline of the horizontal arm AB, bringing it into the
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 300 R = N and M =37.5 N ⋅ m. Replace this force-couple system with an equivalent force-couple system at C.
Three children are standing on a 15 × 15- ft raft. If the weights of the children at points A, B, and C are 85 lb, 60 lb, and 90 lb, respectively, determine the magnitude and the point of application of the resultant of the three weights.
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 and the line
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 580-kN force is shoveled so that the this load acts at E, determine a and b knowing that the point of application of the resultant of the four
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. Determine the smallest load the students should
Solve Problem 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 0.6 × 0.6 × 0.6-mboxes and one 0.6 × 0.6 ×
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
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.
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
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
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.
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 y 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. Discuss.
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.
A worker tries to move a rock by applying a 360-N force to a steel bar as shown.(a) Replace that force with an equivalent force-couple system at D.(b) Two workers attempt to move the same rock by applying a vertical force at A and another force at D. Determine these two forces if they are to be
A worker tries to move a rock by applying a 360-N force to a steel bar as shown. If two workers attempt to move the same rock by applying a force at A and a parallel force at C, determine these two forces so that they will be equivalent to the single 360-N force shown in the figure.
A force and a couple are applied as shown to the end of a cantilever beam.(a) Replace this system with a single force F applied at point C, and determine the distance d from C to a line drawn through points D and E.(b) Solve part a if the directions of the two 360-N forces are reversed.
A crate of mass 80 kg is held in the position shown. Determine(a) The moment produced by the weight W of the crate about E,(b) The smallest force applied smallest force applied smallest force applied smallest force applied smallest force applied smallest force applied smallest force applied
A crate of mass 80 kg is held in the position shown. Determine(a) The moment produced by the weight W of the crate about E,(b) The smallest force applied at A which creates a moment of equal magnitude and opposite sense about E,(c) The magnitude, sense, and point of application on the bottom of the
A farmer uses cables and winch pullers B and E to plumb one side of a small barn. Knowing that the sum of the moments about the x axis of the forces exerted by the cables on the barn at points A and D is equal to 4728 lb ⋅ ft, determine the magnitude of TDE when TAB = 255 lb.
Solve Problem 3.147 when the tension in cable AB is 306 lb. Problem 3.147: A farmer uses cables and winch pullers B and E to plumb one side of a small barn. Knowing that the sum of the moments about the x axis of the forces exerted by the cables on the barn at points A and D is equal to 4728 lb ⋅
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.
Two parallel 60-N forces are applied to a lever as shown. Determine the moment of the couple formed by the two forces(a) By resolving each force into horizontal and vertical components and adding the moments of the two resulting couples,(b) By using the perpendicular distance between the two
A 32-lb motor is mounted on the floor. Find the resultant of the weight and the forces exerted on the belt, and determine where the line of action of the resultant intersects the floor.
To loosen a frozen valve, a force F of magnitude 70 lb is applied to the handle of the valve. Knowing that at θ = 25°, Mx = −61 lb ⋅ ft, and Mz = −43 lb ⋅ ft, determine θ and d.
When a force F is applied to the handle of the valve shown, its moments about the x and z axes are, respectively, Mx = − 77 lb ⋅ ft and Mz = − 81 lb ⋅ ft. For d = 27 in., determine the moment My of F about the y axis.
Determine the force in each member of the Gambrel roof truss shown. State whether each member is in tension or compression.
Determine the force in each member of the Howe roof truss shown. State whether each member is in tension or compression.
Determine the force in each member of the Fink roof truss shown. State whether each member is in tension or compression.
Determine the force in each member of the fan roof truss shown. State whether each member is in tension or compression.
Determine the force in each member of the roof truss shown. State whether each member is in tension or compression.
Determine the force in each member of the Gambrel roof truss shown. State whether each member is in tension or compression.
Determine the force in each member of the Pratt bridge truss shown. State whether each member is in tension or compression.
Determine the force in each member of the Pratt bridge truss shown. State whether each member is in tension or compression. Assume that the load at G has been removed.
Determine the force in member DE and in each of the members located to the left of DE for the inverted Howe roof truss shown. State whether each member is in tension or compression.
Determine the force in each of the members located to the right of DE for the inverted Howe roof truss shown. State whether each member is in tension or compression.
Determine the force in each of the members located to the left of member FG for the scissor roof truss shown. State whether each member is in tension or compression.
Determine the force in member FG and in each of the members located to the right of member FG for the scissor roof truss shown. State whether each member is in tension or compression.
The portion of truss shown represents the upper part of a power transmission line tower. For the given loading, determine the force in each of the members located above HJ. State whether each member is in tension or compression.
For the tower and loading of Prob. 6.21 and knowing that 1.5 FCH =FEJ = kN C and FEH = 0, determine the force in member HJ and in each of the members located between HJ and NO. State whether each member is in tension or compression.
Determine the force in each member of the truss shown. State whether each member is in tension or compression.
Determine the force in each member of the truss shown. State whether each member is in tension or compression.
For the roof truss shown in Fig P6.25 and P6.26, determine the force in each of the members located to the left of member GH. State whether each member is in tension or compression.
Determine the force in member GH and in each of the members located to the right of GH for the roof truss shown. State whether each member is in tension or compression.
Determine whether the trusses of Probs. 6.13, 6.14, and 6.25 are simple trusses.
Determine whether the trusses of Probs. 6.19, 6.21, and 6.23 are simple trusses.
For the given loading, determine the zero-force members in the truss shown.
For the given loading, determine the zero-force members in the truss shown.
For the given loading, determine the zero-force members in the truss shown.
For the given loading, determine the zero-force members in the truss shown.
For the given loading, determine the zero-force members in the truss shown.
For the given loading, determine the zero-force members in the truss shown.
Determine the zero-force members in the truss of(a) Prob. 6.9,(b) Prob. 6.19.
The truss shown consists of six members and is supported by a ball and socket at B, a short link at C, and two short links at D. Determine the force in each of the members for P=(−5670 lb)j and Q = 0.
The truss shown consists of six members and is supported by a ball and socket at B, a short link at C, and two short links at D. Determine the force in each of the members for P = 0 and Q=(7420 lb)i.
The truss shown consists of six members and is supported by a short link at A, two short links at B, and a ball and socket at D. Determine the force in each of the members for the given loading.
The portion of a power line transmission tower shown consists of nine members and is supported by a ball and socket at B and short links at C, D, and E. Determine the force in each of the members for the given loading.
The truss shown consists of 18 members and is supported by a ball and socket at A, two short links at B, and one short link at G.(a) Check that this truss is a simple truss, that it is completely constrained, and that the reactions at its supports are statically determinate.(b) For the given
The truss shown consists of 18 members and is supported by a ball and socket at A, two short links at B, and one short link at G.(a) Check that this truss is a simple truss, that it is completely constrained, and that the reactions at its supports are statically determinate.(b) For the given
A Warren bridge truss is loaded as shown. Determine the force in members CE, DE, and DF.
A Warren bridge truss is loaded as shown. Determine the force in members EG, FG, and FH.
A parallel chord Howe truss is loaded as shown. Determine the force in members CE, DE, and DF.
A parallel chord Howe truss is loaded as shown. Determine the force in members GI, GJ, and HJ.
Using the method of joints, determine the force in each member of the truss shown. State whether each member is in tension or compression.
Determine the force in each member of the Gambrel roof truss shown. State whether each member is in tension or compression.
Determine the force in each member of the Howe roof truss shown. State whether each member is in tension or compression.
Determine the force in each member of the Fink roof truss shown. State whether each member is in tension or compression.
Determine the force in each member of the fan roof truss shown. State whether each member is in tension or compression.
Determine the force in each member of the roof truss shown. State whether each member is in tension or compression.
Determine the force in each member of the Gambrel roof truss shown. State whether each member is in tension or compression.
Using the method of joints, determine the force in each member of the truss shown. State whether each member is in tension or compression.
A floor truss is loaded as shown. Determine the force in members CF, EF, and EG.
A floor truss is loaded as shown. Determine the force in members FI, HI, and HJ.
A pitched flat roof truss is loaded as shown. Determine the force in members CE, DE, and DF.
A pitched flat roof truss is loaded as shown. Determine the force in members EG, GH, and HJ.
A Howe scissors roof truss is loaded as shown. Determine the force in members DF, DG, and EG.
A Howe scissors roof truss is loaded as shown. Determine the force in members GI, HI, and HJ.
A Fink roof truss is loaded as shown. Determine the force in members BD, CD, and CE.
A Fink roof truss is loaded as shown. Determine the force in members FH, FG, and EG.
A Fink roof truss is loaded as shown. Determine the force in members DF, DG, and EG.
A roof truss is loaded as shown. Determine the force in members FH, GJ, and GI.
A stadium roof truss is loaded as shown. Determine the force in members AB, AG, and FG.
A stadium roof truss is loaded as shown. Determine the force in members AE, EF, and FJ.
A vaulted roof truss is loaded as shown. Determine the force in members BE, CE, and DF.
A vaulted roof truss is loaded as shown. Determine the force in members HJ, IJ, and GI.

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