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

A steel rod is bent to form a mounting bracket. For each of the mounting brackets and loadings 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 loadings shown, determine the reactions at A and B.
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 50 lb and 30 lb, respectively, and that 1.3 d = ft, 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 30 lb and 20 lb, respectively, and that 1.54 d = ft, determine(a) The tension in cable BC,(b) The reaction at A.
For the frame and loading shown, determine the reactions at A and E when(a) α = 30o,(b) α = 45o.
A lever AB is hinged at C and is attached to a control cable at A. If the lever is subjected to a 300-N vertical force at B, determine(a) The tension in the cable,(b) The reaction at C.
Neglecting friction and the radius of the pulley, determine the tension in cable BCD and the reaction at support A when 80 d = mm.
Neglecting friction and the radius of the pulley, determine the tension in cable BCD and the reaction at support A when 144 d = mm.
Neglecting friction, determine the tension in cable ABD and the reaction at support C.
Rod ABC is bent in the shape of a circular arc of radius R. Knowing that θ = 35o, determine the reaction(a) At B,(b) At C.
Rod ABC is bent in the shape of a circular arc of radius R. Knowing that θ = 50o, determine the reaction(a) At B,(b) At C.
Neglecting friction and the radius of the pulley, determine(a) The tension in cable ABD,(b) The reaction at C.
Neglecting friction, determine the tension in cable ABD and the reaction at C when θ = 60o.
Neglecting friction, determine the tension in cable ABD and the reaction at C when θ = 30o.
Determine the tension in each cable and the reaction at D.
Rod ABCD is bent in the shape of a circular arc of radius 80 mm and rests against frictionless surfaces at A and D. Knowing that the collar at B can move freely on the rod and that θ = 45o. 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 80 mm 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
Bar AC supports two 100-lb loads as shown. Rollers A and C rest against frictionless surfaces and a cable BD is attached at B. Determine(a) The tension in cable BD,(b) The reaction at A,(c) The reaction at C.
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 2/100y = x, where x and y are expressed in mm. Knowing that the input force P = 4 N, 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 y = x2/100, where x and y are expressed in mm. Knowing that the maximum allowable force exerted on the roller at D is 8.5 N, determine(a)
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 = 20o.
Solve Problem 4.43 when α = 30o. P4.43 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 = 20o.
A 20-lb weight can be supported in the three different ways shown. Knowing that the pulleys have a 4-in. radius, determine the reaction at A in each case
A belt passes over two 50-mm-diameter pulleys which are mounted on a bracket as shown. Knowing that M = 0 and Ti = TO = 24 N, determine the reaction at C.
A belt passes over two 50-mm-diameter pulleys which are mounted on a bracket as shown. Knowing that 0.40 M = N ⋅ mm and that Ti and TO are equal to 32 N and 16 N, respectively, determine the reaction at C.
A 350-lb utility pole is used to support at C the end of an electric wire. The tension in the wire is 120 lb, 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 may not exceed
In a laboratory experiment, students hang the masses shown from a beam of negligible mass.(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 masses shown from a beam of negligible mass. 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 2.5 N ⋅ m.
Knowing that the tension in wire BD is 300 lb, determine the reaction at fixed support C for the frame shown.
Determine the range of allowable values of the tension in wire BD if the magnitude of the couple at the fixed support C is not to exceed 75 lb ⋅ ft.
Uniform rod AB of length l and weight W 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, W, 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 blocks are connected by an elastic cord which passes over a pulley at C.(a) Express the tension in the cord in terms of W and θ.(b) Determine the value of θ for which the tension in the cord
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
Rod AB is acted upon by a couple M and two forces, each of magnitude P.(a) Derive an equation in θ , P, M, and l which must be satisfied when the rod is in equilibrium.(b) Determine the value of θ corresponding to equilibrium when 150 lb M = ⋅ in., P = 20lb, and l = 6 in.
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 correspondin to equilibrium
Solve Sample Problem 4.5 assuming that the spring is unstretched when θ = 90o.
A collar B of weight W can move freely along the vertical rod shown. The constant of the spring is k, and the spring is unstretched when θ = 0.(a) Derive an equation in θ, W, k, and l which must be satisfied when the collar is in equilibrium.(b) Knowing that W = 3 lb, l = 6 in., and k = 8 lb/ft,
A slender rod AB, of mass m, 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 when θ = 0.(a) Neglecting the mass of the blocks, derive an equation in m, g, k, l, and θ which must be satisfied when the rod is in
The bracket ABC can be supported in the eight different ways shown. All connections consist of smooth 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 indeterminate,(c) The
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 in Problem 4.61, and, wherever possible, compute the reactions. P6.1 The
Horizontal and vertical links are hinged to a wheel, and forces are applied to the links as shown. Knowing that a = 3.0 in., 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 42 lb.
Using the method of Section 4.7, solve Problem 4.21. P4.21 The required tension in cable AB is 800 N. Determine(a) The vertical force P which must be applied to the pedal,(b) The corresponding reaction at C.
Using the method of Section 4.7, solve Problem 4.22. P4.22 Determine the maximum tension which can be developed in cable AB if the maximum allowable value of the reaction at C is 1000 N.
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 = 3.5 in. and P = 30 lb, 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 600 lb and that the horizontal force P is not to exceed 65 lb, determine the largest acceptable value of distance l.
For the frame and loading shown, determine the reactions at C and D.
For the frame and loading shown, determine the reactions at A and C.
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 100-N 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 60-N force is applied as indicated to the handle
A 200-lb crate is attached to the trolley-beam system shown. Knowing that a = 1.5 ft, determine(a) The tension in cable CD,(b) The reaction at B.
Solve Problem 4.73 assuming that 3 a = ft. P4.73 A 200-lb crate is attached to the trolley-beam system shown. Knowing that a = 1.5 ft, determine(a) The tension in cable CD,(b) The reaction at B.
A 20-kg roller, of diameter 200 mm, which is to be used on a tile floor, is resting directly on the subflooring 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 subflooring 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.
A small hoist is mounted on the back of a pickup truck and is used to lift a 120-kg crate. Determine(a) The force exerted on the hoist by the hydraulic cylinder BC,(b) The reaction at A.
The clamp shown is used to hold the rough work piece C Knowing that the maximum allowable compressive force on the work piece is 200 N and neglecting the effect of friction at A, determine the corresponding(a) Reaction at B,(b) Reaction at A,(c) Tension in the bolt.
A modified peavey is used to lift a 0.2-m-diameter log of mass 36 kg. 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 a 0.2-m-diameter log of mass 36 kg. 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.
Member ABC is supported by a pin and bracket at B and by an inextensible cord at A and C and passing over a frictionless pulley at D. The tension may be assumed to be the same in portion AD and CD of the cord. For the loading shown and neglecting the size of the pulley, determine the tension in the
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.
Using the method of Section 4.7, solve Problem 4.18. P4.18 Determine the reactions at A and B when(a) h = 0,(b) h = 8 in.
Using the method of Section 4.7, solve Problem 4.28. P4.28 A lever is hinged at C and is attached to a control cable at A. If the lever is subjected to a 300-N vertical force at B, determine(a) The tension in the cable,(b) The reaction at C.
Knowing that θ = 35o, determine the reaction(a) At B,(b) At C.
Knowing that θ = 50o, determine the reaction(a) At B,(b) At C.
A slender rod of length L and weight W is held in equilibrium as shown, with one end against a frictionless wall and the other end attached to a cord of length S. Derive an expression for the distance h in terms of L and S. Show that this position of equilibrium does not exist if S > 2L.
A slender rod of length L = 200 mm is held in equilibrium as shown, with one end against a frictionless wall and the other end attached to a cord of length S = 300 mm. Knowing that the mass of the rod is 1.5 kg, determine(a) The distance h,(b) The tension in the cord,(c) The reaction at B.
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 β =25°, determine(a) The angle θ that the rod forms with the vertical,(b) The reactions at A and B.
A uniform slender rod of mass 5 g and length 250 mm is balanced on a glass of inner diameter 70 mm. Neglecting friction determine the angle θ corresponding to equilibrium.
Rod AB is bent into the shape of a circular arc and is lodged between two pegs D and E. It supports a load P at end B. Neglecting friction and the weight of the rod determine the distance c corresponding to equilibrium when a = 1 in. and R = 5 in.
A uniform rod AB of weight W and length 2R rests inside a hemispherical bowl of radius R as shown. Neglecting friction determine the angle θ corresponding to equilibrium.
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.
A uniform slender rod of length 2L and mass m rests against a roller at D and is held in the equilibrium position shown by a cord of length a. Knowing that L = 200 mm, determine(a) The angle θ,(b) The length a.
Gears A and B are attached to a shaft supported by bearings at C and D. The diameters of gears A and B are 150 mm and 75 mm, 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 Problem 4.96 assuming that for gear A the tangential and radial forces are acting at E, so that FA = (1325 N)j + (482 N)k. P4.96 Gears A and B are attached to a shaft supported by bearings at C and D. The diameters of gears A and B are 150 mm and 75 mm, respectively, and the tangential and
Two transmission belts pass over sheaves welded to an axle supported by bearings at B and D. The sheave at A has a radius of 50 mm, and the sheave at C has a radius of 40mm, Knowing that the system rotates with a constant rate, determine(a) The tension T,(b) The reactions at B and D. Assume that
For the portion of a machine shown, the 4-in.-diameter pulley A and wheel B are fixed to a shaft supported by bearings at C and D. The spring of constant 2 lb/in. is unstretched when θ = 0, and the bearing at C does not exert any axial force. Knowing that θ = 180° and that the machine is at rest
Solve Problem 4.99 for θ = 90°. P4.99 For the portion of a machine shown, the 4-in.-diameter pulley A and wheel B are fixed to a shaft supported by bearings at C and D. The spring of constant 2 lb/in. is unstretched when θ = 0, and the bearing at C does not exert any axial force. Knowing that θ
A 1.2×2.4- m sheet of plywood having a mass of 17 kg has been temporarily placed among three pipe supports. The lower edge of the sheet rests on small collars A and B and its upper edge leans against pipe C. Neglecting friction at all surfaces, determine the reactions at A, B, and C.
The 200× 200-mmsquare plate shown has a mass of 25 kg and is supported by three vertical wires. Determine the tension in each wire.
The 200 × 200-mmsquare plate shown has a mass of 25 kg and is supported by three vertical wires. Determine the mass and location of the lightest block which should be placed on the plate if the tensions in the three cables are to be equal.
A camera of mass 240 g is mounted on a small tripod of mass 200g, assuming that the mass 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 = 0,(b) The maximum
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 a = 1. 25 ft, determine the tension in each wire.
For the pile assembly of Problem 4.105, determine(a) The largest permissible value of a if the assembly is not to tip,(b) The corresponding tension in each wire. P4.105 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
A uniform aluminum rod of weight W is bent into a circular ring of radius R and is supported by three wires as shown. Determine the tension in each wire.
A uniform aluminum rod of weight W is bent into a circular ring of radius R and is supported by three wires as shown. A small collar of weight W′ is then placed on the ring and positioned so that the tensions in the three wires are equal. Determine(a) The position of the collar,(b) The value of
An opening in a floor is covered by a 3 4-× ft sheet of plywood weighing 12 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 Problem 4.109 assuming that the small block C is moved and placed under edge DE at a point 0.5 ft from corner E.
The 10-kg square plate shown is supported by three vertical wires. Determine(a) The tension in each wire when a = 100 mm,(b) The value of a for which tensions in the three wires are equal.
The 3-m flagpole AC forms an angle of 30o 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 0.9 m, determine the tension in each brace and the reaction at C.
A 3-m boom is acted upon by the 4-kN force shown. Determine the tension in each cable and the reaction at the ball-and-socket joint at A.
An 8-ft-long boom is held by a ball-and-socket joint at C and by two cables AD and BE. Determine the tension in each cable and the reaction at C.
Solve Problem 4.114 assuming that the given 198-lb load is replaced with two 99-lb loads applied at A and B.P4.114 An 8-ft-long boom is held by a ball-and-socket joint at C and by two cables AD and BE. Determine the tension in each cable and the reaction at C.
The 18-ft pole ABC is acted upon by a 210-lb force as shown. The pole is held by a ball-and-socket joint at A and by two cables BD and BE. For a = 9 ft, determine the tension in each cable and the reaction at A.
Solve Problem 4.116 for a = 4.5 ft. P4.116 The 18-ft pole ABC is acted upon by a 210-lb force as shown. The pole is held by a ball-and-socket joint at A and by two cables BD and BE. For a = 9 ft, determine the tension in each cable and the reaction at A.
Two steel pipes ABCD and EBF are welded together at B to form the boom shown. The boom is held by a ball-and-socket joint at D and by two cables EG and ICFH; cable ICFH passes around frictionless pulleys at C and F. For the loading shown, determine the tension in each cable and the reaction at D.
Solve Problem 4.118 assuming that the 560-N load is applied at B. P4.118 Two steel pipes ABCD and EBF are welded together at B to form the boom shown. The boom is held by a ball-and-socket joint at D and by two cables EG and ICFH; cable ICFH passes around frictionless pulleys at C and F. For the
The lever AB is welded to the bent rod BCD which is supported by bearings at E and F and by cable DG. Knowing that the bearing at E does not exert any axial thrust, determine(a) The tension in cable DG,(b) The reactions at E and F.
A 30-kg cover for a roof opening is hinged at corners A and B. The roof forms s an angle of 30o with the horizontal, and the cover is maintained in a horizontal position by the brace CE. Determine(a) The magnitude of the force exerted by the brace,(b) The reactions at the hinges. Assume that the
The rectangular plate shown has a mass of 15 kg and is held in the position shown by hinges A and B and cable EF. Assuming that the hinge at B does not exert any axial thrust, determine(a) The tension in the cable,(b) The reactions at A and B.

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