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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 24-ft-long pole AB is placed in a hole and is guyed by three cables. Knowing that the tensions in cables BD and BE are 221 lb and 161 lb, respectively, determine(a) The tension in cable CD,(b) The reaction at A.
A follower ABCD is held against a circular cam by a stretched spring which exerts a force of 6 lb for the position shown. Knowing that the tension in rod BE is 4 lb, determine(a) The force exerted on the roller at A,(b) The reaction at bearing C.
Determine the reactions at A and B when en(a) α = 0,(b) α =90°,(c) α =30°.
Solve Prob. 4.17 assuming that the 330-N force is replaced with an 82.5-N m ‹… clockwise couple. Problem 4.17: Determine the reactions at A and B when(a) α = 0,(b) α =90°,(c) α =30°.
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 force to be exerted at A by lever ABC is 3 lb. Knowing that α =30° and that the spring has been stretched 1.2 in., determine(a) The constant k of the spring(b) The reaction at B.
The required force to be exerted at A by lever ABC is 3.6 lb. Knowing that the stretched spring exerts a 12-lb force at C, determine(a) The value of α,(b) The reaction at B.
A steel rod is bent to form a mounting bracket. For each of the mounting brackets and loading shown, determine the reactions at A and B.
A steel rod is bent to form a mounting bracket. For each of the mounting brackets and loading shown, determine the reactions at A and B.
A lever AB is hinged at C and is attached to a control cable at A. If the lever is subjected to a 60-lb vertical force at B, determine(a) The tension in the cable,(b) The reaction at C.
For the frame and loading shown, determine the reactions at A and F when(a) a = 2 in.,(b) a = 7.5 in.
A sign is hung by two chains from mast AB. The mast is hinged at A and is supported by cable BC. Knowing that the tensions in chains DE and FH are 225 N and 135 N, respectively, and that 0.39 d = m, determine(a) The tension in cable BC,(b) The reaction at A.
A sign is hung by two chains from mast AB. The mast is hinged at A and is supported by cable BC. Knowing that the tensions in chains DE and FH are 135 N and 90 N, respectively, and that 0.462 d = m, determine(a) The tension in cable BC,(b) The reaction at A.
Determine the tension in cable ABD and reaction at support C.
Neglecting friction and the radius of the pulley, determine the tension in cable BCD and the reaction at support A when 4 d = in.
Neglecting friction and the radius of the pulley, determine the tension in cable BCD and the reaction at support A when d = 7.2 in.
Neglecting friction and the radius of the pulley, determine(a) The tension in cable ADB,(b) The reaction at C.
Rod ABC is bent in the shape of a circular arc of radius R. Determine(a) The value of θ so that the magnitudes of the reactions at B and C are equal,(b) The corresponding reactions at B and C.
Rod ABC is bent in the shape of a circular arc of radius R. Determine(a) The value of θ which minimizes the magnitude of the reaction at C,(b) The corresponding reactions at B and C.
Neglecting friction, determine the tension in cable ABD and the reaction at C when 40 θ = °.
Neglecting friction, determine(a) The value of θ for which the tension in cable ABD is 3P/4,(b) The corresponding reaction at C.
A movable bracket is held at rest by a cable attached at C and by frictionless rollers at A and B. For the loading shown, determine(a) The tension in the cable,(b) The reactions at A and B.
To cross a crevasse, three mountain climbers position a 3.5-m-long ladder as shown. Neglecting friction at A and B and knowing that the hiker at A exerts a horizontal force P on the end of the ladder, determine(a) The reactions at A and B,(b) The force P.
Rod ABCD is bent in the shape of a circular arc of radius 4 in. and rests against frictionless surfaces at A and D. Knowing that the collar at B can move freely on the rod and that θ = 45°, determine(a) The tension in cord OB,(b) The reactions at A and D.
Rod ABCD is bent in the shape of a circular arc of radius 4 in. and rests against frictionless surfaces at A and D. Knowing that the collar at B can move freely on the rod, determine(a) The value of θ for which the tension in cord OB is as small as possible,(b) The corresponding value of the
A movable bracket is held at rest by a cable attached at E and by frictionless rollers. Knowing that the width of post FG is slightly less than the distance between the rollers, determine the force exerted on the post by each roller when α =20°.
Solve Prob. 4.41 41 when α =30°. Problem 4.41: A movable bracket is held at rest by a cable attached at E and by frictionless rollers. Knowing that the width of post FG is slightly less than the distance between the rollers, determine the force exerted on the post by each roller when
A parabolic slot has been cut in plate AD, and the plate has been placed so that the slot fits two fixed, frictionless pins B and C. The equation of the slot is 2/y=x/4, where x and y are expressed in inches. Knowing that the input force P = 1 lb, determine(a) The force each pin exerts on the
A parabolic slot has been cut in plate AD, and the plate has been placed so that the slot fits two fixed, frictionless pins B and C. The equation of the slot is 2/y=x/4, where x and y are expressed in inches. Knowing that the maximum allowable force exerted on the roller at D is 2 lb, determine(a)
A 10-kg block can be supported in the three different ways shown, knowing that the pulleys have a 100-mm radius, determine the reaction at A in each case.
A belt passes over two 2-in.-diameter pulleys which are mounted on a bracket as shown. Knowing that 0 and 12 M = Ti = To = lb, determine the reaction at C.
A belt passes over two 2-in.-diameter pulleys which are mounted on a bracket as shown. Knowing that M = 8 lb ∙ in, and that Ti and To are equal to 16 lb and 8 lb, respectively, determine the reaction at C.
In a laboratory experiment, students hang the weights shown from a beam of negligible weight.(a) Determine the reaction at the fixed support A knowing that end D of the beam does not touch support E.(b) Determine the reaction at the fixed support A knowing that the adjustable support E exerts an
In a laboratory experiment, students hang the weights shown from a beam of negligible weight. Determine the range of values of the force exerted on the beam by the adjustable support E for which the magnitude of the couple at A does not exceed 20lb ⋅in.
The rig shown consists of a 5.4-kN horizontal member ABC and a vertical member DBE welded together at B. The rig is being used to raise a 16.2-kN crate at a distance x = 4.8 m from the vertical member DBE. If the tension in the cable is 18kN, determine the reaction at E assuming that the cable
The rig shown consists of a 5.4-kN horizontal member ABC and a vertical member DBE welded together at B and is used to raise a 16.2-kN crate. Determine(a) The required tension in cable ADCF if the maximum value of the couple at E is to be as small as possible as x varies from 0.6 m to 7 m,(b) The
A 160-kg utility pole is used to support at C the end of an electric wire. The tension in the wire is 540 N, and the wire forms an angle of 15° with the horizontal at C. Determine the largest and smallest allowable tensions in the guy cable BD if the magnitude of the couple at A cannot exceed
Uniform rod AB of length l and mass m lies in a vertical plane and is acted upon by a couple M. The ends of the rod are connected to small rollers which rest against frictionless surfaces.(a) Express the angle θ corresponding to equilibrium in terms of M, m, g, and l.(b) Determine the value
Rod AB of length l and negligible weight lies in a vertical plane and is pinned to blocks A and B. The weight of each block is W, and the blocks are connected by an elastic cord which passes over a pulley at C. Neglecting friction between the blocks and the guides, determine the value of θ
A thin, uniform ring of mass m and radius R is attached by a frictionless pin to a collar at A and rests against a small roller at B. The ring lies in a vertical plane, and the collar can move freely on a horizontal rod and is acted upon by a horizontal force P.(a) Express the angle θ
A uniform rod having a length of l m and mass of 2 kg is suspended from two cords AC and BC. Determine the angle θ corresponding to the equilibrium position when a couple M of magnitude 3 N ∙ m is applied to the rod.
A vertical load P is applied at end B of rod BC. The constant of the spring is k, and the spring is unstretched when θ = 90o.(a) Neglecting the weight of the rod, express the angle θ corresponding to equilibrium in terms of P, k, and l.(b) Determine the value of θ corresponding to
Cable AB is wrapped around two drums as shown. Attached to drum A is a torsion spring for which M = kφ, where k = 58 N ˆ™ m/rad and φ is the angle of rotation in radians of the drum. Knowing that the mass of block E is 10 kg and that the torsion spring is unstretched
A vertical load P is applied at end B of rod BC. The constant of the spring is k and the spring is unstretched when θ = 0.(a) Neglecting the weight of the rod, express the angle θ corresponding to the equilibrium position in terms of P, k, and l.(b) Determine the value of θ
A slender rod AB of weight W is attached to blocks A and B which move freely in the guides shown. The constant of the spring is k, and the spring is unstretched d when θ = 0.(a) Neglecting the mass of the blocks, derive an equation in W, k, l, and θ which must be satisfied when the rod
The bracket ABC can be supported in the eight different ways shown. All connections consist of frictionless pins, rollers, or short links. In each case, determine whether(a) The plate is completely, partially, or improperly constrained,(b) The reactions are statically determinate or
Eight identical 20 30-× in. rectangular plates each weighing 50 lb are held in a vertical plane as shown. All connections consist of frictionless pins, rollers, or short links. For each case, answer the questions listed inProb. 4.61, and wherever possible, compute the reactions.
Horizontal and vertical links are hinged to a wheel, and forces are applied to the links as shown. Knowing that 75 a = mm, determine the value of P and the reaction at A.
Horizontal and vertical links are hinged to a wheel, and forces are applied to the links as shown. Determine the range of values of the distance a for which the magnitude of the reaction at A does not exceed 180 N.
Using the method of Sec. 4.7, Solve Prob. 4.21 Problem 4.21: The required force to be exerted at A by lever ABC is 3 lb. Knowing g that α =30° and that the spring has been stretched 1.2 in., determine(a) The constant k of the spring(b) The reaction at B.
Using the method of Sec. 4.7, Solve Prob. 4.33 Problem 4.33: Rod ABC is bent in the shape of a circular arc of radius R. Determine(a) The value of θ so that the magnitude of the reactions at B and C are equal,(b) The corresponding reactions at B and C.
A T-shaped bracket supports a 75-lb load as shown. Determine the reactions at A and C when(a) α =90°,(b) α =45°.
A uniform plate girder weighing 6000 lb is held in a horizontal position by two crane cables. Determine the angle α and the tension in each cable.
To remove a nail, a small block of wood is placed under a crowbar, and a horizontal force P is applied as shown. Knowing that l = 88 mm and P = 130 N, determine the vertical force exerted on the nail and the reaction at B.
To remove a nail, a small block of wood is placed under a crowbar, and a horizontal force P is applied as shown. Knowing that the maximum vertical force needed to extract the nail is 2600 N and that the horizontal force P is not to exceed 290 N, determine the largest acceptable value of distance l.
A worker is raising a 9.2-m-long ladder of mass 53 kg as shown. Knowing g a = 1.8 m and that the force exerted by the worker is perpendicular to the ladder, determine,(a) The force exerted by the worker,(b) The reaction at B.
A worker is raising a 9.2-m-long ladder of mass 53 kg as shown. Knowing that the force exerted by the worker is perpendicular to the ladder, determine(a) The smallest value of a for which the vertical component of the reaction at B is zero,(b) The corresponding force exerted by the worker.
To remove the lid from a 5-gallon pail, the tool shown is used to apply an upward and radially outward force to the bottom inside rim of the lid. Assuming that the rim rests against the tool at A and that a 20-lb force is applied as indicated to the handle, determine the force acting on the rim.
To remove the lid from a 5-gallon pail, the tool shown is used to apply an upward and radially outward force to the bottom inside rim of the lid. Assuming that the top and the rim of the lid rest against the tool at A and B, respectively, and that a 14-lb force is applied as indicated to the
A 20-kg roller of diameter 200 mm, which is to be used on a tile floor, is resting directly on the sub flooring as shown. Knowing that the thickness of each tile is 8 mm, determine the force P required to move the roller onto the tiles if the roller is pushed to the left.
A 20-kg roller of diameter 200 mm, which is to be used on a tile floor, is resting directly on the sub flooring as shown. Knowing that the thickness of each tile is 8 mm, determine the force P required to move the roller onto the tiles if the roller is pulled to the right.
The clamp shown is used to hold the rough work piece C. Knowing that the maximum allowable compressive force on the work piece is 40 lb and neglecting the effect of friction at A, determines the corresponding(a) Reaction at B,(b) Reaction at A,(c) Tension in the bolt.
A small hoist is mounted on the back of a pickup truck and is used to lift a 260-lb crate. Determine(a) The force exerted on the hoist by the hydraulic cylinder BC,(b) The reaction at A.
The L-shaped member ACB is supported by a pin and brackets at C and by an inextensible cord attached at A and B and passing over a frictionless pulley at D. Determine(a) The tension in the cord,(b) The reaction at C.
Member ABCD is supported by a pin and bracket at C and by an inextensible cord attached at A and D and passing over frictionless pulleys at B and E. Neglecting the size of the pulleys, determine the tension in the cord and the reaction at C.
A modified peavey is used to lift an 8-in.-diameter log weighing 80 lb. Knowing that θ = 45° and that the force exerted at C by the worker is perpendicular to the handle of the peavey, determine(a) The force exerted at C,(b) The reaction at A.
A modified peavey is used to lift an 8-in.-diameter log weighing 80 lb. Knowing that θ =60° and that the force exerted at C by the worker is perpendicular to the handle of the peavey, determine(a) The force exerted at C,(b) The reaction at A
Using the method of Sec. 4.7, solve Prob. 4.17c. Problem 4.17: Determine the reactions at A and B when (a) α = 0,(b) α =90°,(c) α =30°.
Using the method of Sec. 4.7, solve 4.25 Problem 4.25: A lever AB is hinged at C and is attached to a control cable at A. If the lever is subjected to a 60-lb vertical force at B, determine(a) The tension in the cable,(b) The reaction at C.
The uniform rod AB of mass m and length L is attached to two blocks which slide freely in circular slots as shown. Knowing that the rod is in equilibrium and that at L = 2R, determine (a) The angle α that the rod forms with the horizontal, (b) The reactions at A and B.
The uniform rod AB of mass m and length L is attached to two blocks which slide freely in circular slots as shown. Knowing that 45 α = °, determine(a) The largest value of L for which the rod is in equilibrium,(b) The corresponding reactions at A and B.
The total weight of a wheelbarrow filled with gravel is 120 lb. If the wheelbarrow is held on an 18° incline in the position shown, determine the magnitude and direction of(a) The force exerted by the worker on each handle,(b) The reaction at C.
Solve Prob. 4.87 assuming that the slope of the incline is 18° downward. Problem 4.87: The total weight of a wheelbarrow filled with gravel is 120 lb. If the wheelbarrow is held on an 18° incline in the position shown, determine the magnitude and direction of(a) The force exerted by the
A uniform slender rod 10 in. long and weighing 0.01 lb is balanced on a glass of inner diameter 2.8 in. Neglecting friction, determine the angle θ corresponding to equilibrium.
A slender rod of length L and weight W is attached to collars which can slide freely along the guides shown. Knowing that the rod is in equilibrium, derive an expression for the angle θ in terms of the angle β.
A 10-kg slender rod of length L is attached to collars which can slide freely along the guides shown. Knowing that the rod is in equilibrium and that t β =25°, determine(a) The angle θ that the rod forms with the vertical,(b) The reactions at A and B.
A slender rod of length L is lodged between peg C and the vertical wall. It supports a load P at end A. Neglecting friction and the weight of the rod; determine the angle θ corresponding to equilibrium.
An athlete is doing push-ups on an inclined board. Neglecting friction between his shoes and the board, determine the value of θ if he wants to limit the magnitude of the total force exerted on his hands to 80 percent of his weight.
A uniform slender rod of length 2L and weight W rests against a. Knowing that t L = 8in., determine(a) The angle θ,(b) The length a.
A uniform slender rod of mass m and length 4r rests on the surface shown and is held in the given equilibrium position by the force P. Neglecting the effect of friction at A and C,(a) Determine the angle θ(b) Derive an expression for P in terms of m and g.
Two transmission belts pass over a double-sheaved pulley that is attached to an axle supported by bearings at A and D. The radius of the inner sheave is 125 mm and the radius of the outer sheave is 250 mm. Knowing that when the system is at rest the tension is 90 N in both portions of belt B and
Gears A and B are attached to a shaft supported by bearings at C and D. The diameters of gears A and B are 6 in. and 3 in., respectively, and the tangential and radial forces acting on the gears are as shown. Knowing that the system rotates at a constant rate, determine the reactions at C and D.
Solve Prob. 4.97 assuming that for gear A the tangential and radial forces are acting at E, so that (FA= (265 lb) j+ (96 lb) k. Problem 4.97: Gears A and B is attached to a shaft supported by bearings at C and D. The diameters of gears A and B are 6 in. and 3 in., respectively, and the tangential
A 1.2 2.4 × m sheet of plywood having a mass of 18 kg has been temporarily propped against column CD. It rests at A and B on small wooden blocks and against protruding nails. Neglecting friction at all surfaces of contact, determine the reactions at A, B, and C.
For the portion of a machine shown, the 100-mm-diameter pulley A and wheel B are fixed to a shaft supported by bearings at C and D. The spring of constant 366 N/m is unstretched when θ = 0, and the bearing at C does not exert any axial force. Knowing that θ = 180° and that the
Solve Prob. 4.100 100 for θ = 90°. Problem 4.100: For the portion of a machine shown, the 100-mmdiameter pulley A and wheel B are fixed to a shaft supported by bearings at C and D. The spring of constant 366 N/m is unstretched when θ = 0, and the bearing at C does not exert any
A stack of several sheets of drywall of mass 170 kg rests on three wooden blocks placed under the edges of the stack. Determine the force exerted on each block.
A stack of several sheets of drywall of mass 170 kg rests on three wooden blocks placed under the edges of the stack. Determine the mass and the location of the lightest bucket of sand so that when placed on the top sheet of drywall the forces exerted on the three blocks are equal.
Two steel pipes AB and BC each having a weight per unit length of 5 lb/ft are welded together at B and are supported by three wires. Knowing that 1.2a = 5 ft, determine the tension in each wire.
For the pipe assembly of Prob. 4.104, determine(a) The largest permissible value of a if the assembly is not to tip,(b) The corresponding tension in each wire. Problem 4.104: Two steel pipes AB and BC each having a weight per unit length of 5 lb/ft is welded together at B and is supported by three
A camera weighing 0.53 lb is mounted on a small tripod weighing 0.44 lb, assuming that the weight of the camera is uniformly distributed and that the line of action of the weight of the tripod passes through D, determine(a) The vertical components of the reactions at A, B, and C when θ =
A uniform brass rod of weight W and length 3L is bent into an equilateral triangle and then is hung from three wires as shown. Determine the tension in each wire.
A uniform brass rod of weight W and length 3L is bent into an equilateral triangle and then is hung from three wires as shown. A small collar of weight W is placed on side BD of the triangle and is positioned so that the tensions in the wires at A and B are equal. Determine(a) The tensions in the
A square steel sign is attached to frame ABC as shown. Knowing that the direction of the wind is perpendicular to the sign and that the wind exerts a force FW of magnitude 135 N at the center of the front of the sign, determine(a) The value of l for which the horizontal components of the reactions
An opening in a floor is covered by a 4.5 6-× ft sheet of plywood weighing 27 lb. The sheet is hinged at A and B and is maintained in a position slightly above the floor by a small block C. Determine the vertical component of the reaction(a) at A,(b) at B,(c) at C.
Solve Prob. 4.110 assuming that the small block C is moved and placed under edge DE at a point 0.75 ft from corner E. Problem 4.110: An opening in a floor is covered by a 4.5 × 6-ft sheet of plywood weighing 27 lb. The sheet is hinged at A and B and is maintained in a position slightly
The 10-ft flagpole AC forms an angle of 30° with the z axis. It is held by a ball-and-socket joint at C and by two thin braces BD and BE. Knowing that the distance BC is 3 ft, determine the tension in each brace and the reaction at C.
A 2720-lb piece of machinery hangs from a cable which passes over a pulley at E and is attached to a support at D. The boom AE is supported by a ball-and-socket joint at A and by two cables BF and CF. Determine(a) The tensions in cables 5BF and CF,(b) The reaction at A.
Cable CD is attached to the 10-m mast ABC as shown. The base A of the mast is supported by a ball-and-socket joint, and the mast is guyed by cables BE and BF. Knowing that θ =30° and φ =10° and that the tension in cable CD is 600 N, determine(a) The tensions in cables BE and
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