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engineering
mechanical engineering

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

Cable ABCDE supports three loads as shown. Knowing that dC = 3.6 ft, determine(a) The reaction at E,(b) The distances dB and dD.
Cable ABCDE supports three loads as shown. Determine(a) The distance dC for which portion CD of the cable is horizontal,(b) The corresponding reactions at the supports.
An oil pipeline is supported at 6-m intervals by vertical hangers attached to the cable shown. Due to the combined weight of the pipe and its contents, the tension in each hanger is 4kN. Knowing that dC = 12 m, determine(a) The maximum tension in the cable,(b) The distance dD.
Solve Prob. 7.94 assuming that dC = 9 m.
Cable ABC supports two boxes as shown. Knowing that b = 3.6 m, determine(a) The required magnitude of the horizontal force P,(b) The corresponding distance a.
Cable ABC supports two boxes as shown. Determine the distances a and b when a horizontal force P of magnitude 100 N is applied at C.
Knowing that WB = 150 lb and WC = 50 lb, determine the magnitude of the force P required to maintain equilibrium.
Knowing that WB = 40 lb and WC = 22 lb, determine the magnitude of the force P required to maintain equilibrium.
If a = 4.5m, determine the magnitudes of P and Q required to maintain the cable in the shape shown.
If a = 6 m, determine the magnitudes of P and Q required to maintain the cable in the shape shown.
A transmission cable having a mass per unit length of 1 kg/m is strung between two insulators at the same elevation that are 60 m apart. Knowing that the sag of the cable is 1.2 m, determine(a) The maximum tension in the cable,(b) The length of the cable.
Two cables of the same gauge are attached to a transmission tower at B. Since the tower is slender, the horizontal component of the resultant of the forces exerted by the cables at B is to be zero. Knowing that the mass per unit length of the cables is 0.4 kg/m, determine(a) The required sag h,(b)
The center span of the George Washington Bridge, as originally constructed, consisted of a uniform roadway suspended from four cables. The uniform load supported by each cable was w = 9.75 kips/ft along the horizontal. Knowing that the span L is 3500 ft and that the sag h is 316 ft, determine for
Each cable of the Golden Gate Bridge supports a load w = 11.1 kips/ft along the horizontal. Knowing that the span L is 4150 ft and that the sag h is 464 ft, determine(a) The maximum tension in each cable,(b) The length of each cable.
To mark the positions of the rails on the posts of a fence, a homeowner ties a cord to the post at A, passes the cord over a short piece of pipe attached to the post at B, and ties the free end of the cord to a bucket filled with bricks having a total mass of 20 kg. Knowing that the mass per unit
A small ship is tied to a pier with a 5-m length of rope as shown. Knowing that the current exerts on the hull of the ship a 300-N force directed from the bow to the stern and that the mass per unit length of the rope is 2.2 kg/m, determine(a) The maximum tension in the rope,(b) The sag h.
The center span of the Verrazano-Narrows Bridge consists of two uniform roadways suspended from four cables. The design of the bridge allowed for the effect of extreme temperature changes which cause the sag of the center span to vary from hw = 386 ft in winter to hs = 394 ft in summer. Knowing
A cable of length L + Δ is suspended between two points which are at the same elevation and a distance L apart.(a) Assuming that Δ is small compared to L and that the cable is parabolic, determine the approximate sag in terms of L and Δ .(b) If L = 30 m and Δ = 1.2 m, determine the approximate
Each cable of the side spans of the Golden Gate Bridge supports a load w = 10.2 kips/ft along the horizontal. Knowing that for the side spans the maximum vertical distance h from each cable to the chord AB is 30 ft and occurs at mid span, determine(a) The maximum tension in each cable,(b) The slope
A steam pipe weighting 50 lb/ft that passes between two buildings 60 ft apart is supported by a system of cables as shown. Assuming that the weight of the cable is equivalent to a uniformly distributed loading of 7.5 lb/ft, determine(a) The location of the lowest point C of the cable,(b) The
Chain AB supports a horizontal, uniform steel beam having a mass per unit length of 85 kg/m. If the maximum tension in the cable is not to exceed 8kN, determine(a) The horizontal distance a from A to the lowest point C of the chain,(b) The approximate length of the chain.
Chain AB of length 6.4 m supports a horizontal, uniform steel beam having a mass per unit length of 85 kg/m. Determine(a) The horizontal distance a from A to the lowest point C of the chain,(b) The maximum tension in the chain.
A cable AB of span L and a simple beam A′ B′ of the same span are subjected to identical vertical loadings as shown. Show that the magnitude of the bending moment at a point C′ in the beam is equal to the product, T0h where T0 is the magnitude of the horizontal component of the tension force
Making use of the property established in Prob. 7.114, solve the problem indicated by first solving the corresponding beam problem. Prob. 7.89a
Making use of the property established in Prob. 7.114, solve the problem indicated by first solving the corresponding beam problem. Prob. 7.92b
Making use of the property established in Prob. 7.114, solve the problem indicated by first solving the corresponding beam problem. Prob. 7.94b
Making use of the property established in Prob. 7.114, solve the problem indicated by first solving the corresponding beam problem. Prob. 7.95b
Show that the curve assumed by a cable that carries a distributed load w(x) is defined by the differential equation d2y/dx2 = w(x)/T0, where T0 is the tension at the lowest point.
Using the property indicated in Prob. 7.119, determine the curve assumed by a cable of span L and sag h carrying a distributed load w = w0 cos(πx/L), where x is measured from mid-span. Also determine the maximum and minimum values of the tension in the cable.
If the weight per unit length of the cable AB is w0 cos2 θ, prove that the curve formed by the cable is a circular arc.
Two hikers are standing 30-ft apart and are holding the ends of a 35-ft length of rope as shown. Knowing that the weight per unit length of the rope is 0.05 lb/ft, determine(a) The sag h,(b) The magnitude of the force exerted on the hand of a hiker.
A 60-ft chain weighing 120 lb is suspended between two points at the same elevation. Knowing that the sag is 24 ft, determine(a) The distance between the supports,(b) The maximum tension in the chain.
A 200-ft steel surveying tape weighs 4 lb. If the tape is stretched between two points at the same elevation and pulled until the tension at each end is 16 lb, determine the horizontal distance between the ends of the tape. Neglect the elongation of the tape due to the tension.
An electric transmission cable of length 130 m and mass per unit length of 3.4 kg/m is suspended between two points at the same elevation. Knowing that the sag is 30 m, determine the horizontal distance between the supports and the maximum tension.
A 30-m length of wire having a mass per unit length of 0.3 kg/m is attached to a fixed support at A and to a collar at B. Neglecting the effect of friction, determine(a) The force P for which h = 12 m,(b) The corresponding span L.
A 30-m length of wire having a mass per unit length of 0.3 kg/m is attached to a fixed support at A and to a collar at B. Neglecting the effect of friction, determine(a) The force P for which h = 12 m,(b) The corresponding span L.
A 30-m length of wire having a mass per unit length of 0.3 kg/m is attached to a fixed support at A and to a collar at B. Neglecting the effect of friction, determine(a) The sag h for which L = 22.5 m,(b) The corresponding force P.
A 30-ft wire is suspended from two points at the same elevation that are 20 ft apart. Knowing that the maximum tension is 80 lb, determine(a) The sag of the wire,(b) The total weight of the wire.
Determine the sag of a 45-ft chain which is attached to two points at the same elevation that are 20 ft apart. Discuss.
A 10-m rope is attached to two supports A and B as shown. Determine(a) The span of the rope for which the span is equal to the sag,(b) The corresponding angle θB.
A cable having a mass per unit length of 3 kg/m is suspended between two points at the same elevation that are 48 m apart. Determine the smallest allowable sag of the cable if the maximum tension is not to exceed 1800 N. Discuss.
An 8-m length of chain having a mass per unit length of 3.72 kg/m is attached to a beam at A and passes over a small pulley at B as shown. Neglecting the effect of friction, determine the values of distance a for which the chain is in equilibrium.
A motor M is used to slowly reel in the cable shown. Knowing that the weight per unit length of the cable is 0.5 lb/ft, determine the maximum tension in the cable when h = 15 ft.
A motor M is used to slowly reel in the cable shown. Knowing that the weight per unit length of the cable is 0.5 lb/ft, determine the maximum tension in the cable when h = 9 ft.
To the left of point B the long cable ABDE rests on the rough horizontal surface shown. Knowing that the weight per unit length of the cable is 1.5 lb/ft, determine the force F when a = 10.8 ft.
To the left of point B the long cable ABDE rests on the rough horizontal surface shown. Knowing that the weight per unit length of the cable is 1.5 lb/ft, determine the force F when a = 18 ft.
A uniform cable has a mass per unit length of 4 kg/m and is held in the position shown by a horizontal force P applied at B. Knowing that P = 800 N and θA = 60°, determine(a) The location of point B,(b) The length of the cable.
A uniform cable having a mass per unit length of 4 kg/m is held in the position shown by a horizontal force P applied at B. Knowing that P = 600 N and θA = 60°, determine(a) The location of point B,(b) The length of the cable.
The cable ACB weighs 0.3 lb/ft. Knowing that the lowest point of the cable is located at a distance a = 1.8 ft below the support A, determine(a) The location of the lowest point C,(b) The maximum tension in the cable.
The cable ACB weighs 0.3 lb/ft. Knowing that the lowest point of the cable is located at a distance a = 6 ft below the support A, determine(a) The location of the lowest point C,(b) The maximum tension in the cable.
Denoting by θ the angle formed by a uniform cable and the horizontal, show that at any point(a) s = c tan θ,(b) y = c sec θ
(a) Determine the maximum allowable horizontal span for a uniform cable of mass per unit length m′ if the tension in the cable is not to exceed a given value Tm.(b) Using the result of part a, determine the maximum span of a steel wire for which h m′ = 0.34 kg/m and Tm = 32kN.
A cable has a weight per unit length of 2 lb/ft and is supported as shown. Knowing that the span L is 18 ft, determine the two values of the sag h for which the maximum tension is 80 lb.
Determine the sag-to-span ratio for which the maximum tension in the cable is equal to the total weight of the entire cable AB.
A cable of weight w per unit length is suspended between two points at the same elevation that are a distance L apart. Determine (a) The sag-to-span ratio for which the maximum tension is as small as possible,(b) The corresponding values of θB and Tm.
For the beam and loading shown,(a) Draw the shear and bending moment diagrams,(b) Determine the maximum absolute values of the shear and bending moment.
For the beam and loading shown,(a) Draw the shear and bending moment diagrams,(b) Determine the maximum absolute values of the shear and bending moment.
Two loads are suspended as shown from the cable ABCD. Knowing that hB = 1.8 m, determine(a) The distance hC,(b) The components of the reaction at D,(c) The maximum tension in the cable.
Knowing that the maximum tension in cable ABCD is 15kN, determine(a) The distance hB,(b) The distance hC.
A semicircular rod of weight W and uniform cross section is supported as shown. Determine the bending moment at point J when θ = 60°.
A semicircular rod of weight W and uniform cross section is supported as shown. Determine the bending moment at point J when θ = 150°.
Determine the internal forces at point J of the structure shown.
Determine the internal forces at point K of the structure shown.
Two small channel sections DF and EH have been welded to the uniform beam AB of weight W = 3kN to form the rigid structural member shown. This member is being lifted by two cables attached at D and E. Knowing the θ = 30° and neglecting the weight of the channel sections,(a) Draw the shear and
Cable ABC supports two loads as shown. Knowing that b = 4 ft, determine(a) The required magnitude of the horizontal force P,(b) The corresponding distance a.
Determine whether the block shown is in equilibrium, and find the magnitude and direction of the friction force when θ = 30o and P = 200 N.
Determine whether the block shown is in equilibrium, and find the magnitude and direction of the friction force when θ = 35o and P = 400 N.
Determine whether the 20-lb block shown is in equilibrium, and find the magnitude and direction of the friction force when P = 8 lb and θ = 20°.
Determine whether the 20-lb block shown is in equilibrium, and find the magnitude and direction of the friction force when P = 12.5 lb and θ = 15°.
Knowing that θ = 25°, determine the range of values of P for which equilibrium is maintained.
Knowing that the coefficient of friction between the 60-lb block and the incline is 0.25, sμ = determine(a) The smallest value of P for which motion of the block up the incline is impending,(b) The corresponding value of β.
Considering only values of θ less than 90°, determine the smallest value of θ for which motion of the block to the right is impending when(a) 30 m = kg,(b) m =40 kg.
Knowing that the coefficient of friction between the 30-lb block and the incline is μ = 0.25, determine(a) The smallest value of P required to maintain the block in equilibrium,(b) The corresponding value of β
A 6-kg block is at rest as shown. Determine the positive range of values of θ for which the block is in equilibrium if (a) θ is less than 90°,(b) θ is between 90° and 180°.
Knowing that 25 P = lb, determine the range of values of θ for which equilibrium of the 18-lb block is maintained.
The coefficients of friction are μs = 0.40 and μk = 0.30 between all surfaces of contact. Determine the force P for which motion of the 60-lb block is impending if cable AB(a) Is attached as shown,(b) Is removed.
The coefficients of friction are μs = 0.40 and μk = 0.30 between all surfaces of contact. Determine the force P for which motion of the 60-lb block is impending if cable AB(a) Is attached as shown,(b) Is removed.
The 8-kg block A is attached to link AC and rests on the 12-kg block B. Knowing that the coefficient of static friction is 0.20 between all surfaces of contact and neglecting the mass of the link, determine the value of θ for which motion of block B is impending.
The 8-kg block A and the 16-kg block B are at rest on an incline as shown. Knowing that the coefficient of static friction is 0.25 between all surfaces of contact, determine the value of θ for which motion is impending.
A 48-kg cabinet is mounted on casters which can be locked to prevent their rotation. The coefficient of static friction between the floor and each caster is 0.30. Assuming that the casters at A and B are locked, determine(a) The force P required for impending motion of the cabinet to the right,(b)
A 48-kg cabinet is mounted on casters which can be locked to prevent their rotation. The coefficient of static friction between the floor and each caster is 0.30. Knowing that 640 h = mm, determine the magnitude of the force P required for impending motion of the cabinet to the right(a) If all
The cylinder shown is of weight W and radius r, and the coefficient of static friction μs is the same at A and B. Determine the magnitude of the largest couple M which can be applied to the cylinder if it is not to rotate.
The cylinder shown is of weight W and radius r. Express in terms of W and r the magnitude of the largest couple M which can be applied to the cylinder if it is not to rotate assuming that the coefficient of static friction is(a) Zero at A and 0.36 at B,(b) 0.30 at A and 0.36 at B.
The hydraulic cylinder shown exerts a force of 680 lb directed to the right on point B and to the left on point E. Determine the magnitude of the couple M required to rotate the drum clockwise at a constant speed.
A couple M of magnitude 70 lb ⋅ft is applied to the drum as shown. Determine the smallest force which must be exerted by the hydraulic cylinder on joints B and E if the drum is not to rotate.
A 19.5-ft ladder AB leans against a wall as shown. Assuming that the coefficient of static friction μs is the same at A and B, determine the smallest value of μs for which equilibrium is maintained.
A 19.5-ft ladder AB leans against a wall as shown. Assuming that the coefficient of static friction μs is the same at A and B, determine the smallest value of μs for which equilibrium is maintained.
End A of a slender, uniform rod of weight W and length L bears on a horizontal surface as shown, while end B is supported by a cord BC of length L. Knowing that the coefficient of static friction is 0.40, determine(a) The value of θ for which motion is impending,(b) The corresponding value of the
A slender rod of length L is lodged between peg C and the vertical wall and supports a load P at end A. Knowing that the coefficient of static friction between the peg and the rod is 0.25 and neglecting friction at the roller, determine the range of values of the ratio L/a for which equilibrium is
The basic components of a clamping device are bar AB, locking plate CD, and lever EFG; the dimensions of the slot in CD are slightly larger than those of the cross section of AB. To engage the clamp, AB is pushed against the work piece, and then force P is applied. Knowing that 160 P = N and
A window sash having a mass of 4 kg is normally supported by two 2-kg sash weights. Knowing that the window remains open after one sash cord has broken, determine the smallest possible value of the coefficient of static friction (Assume that the sash is slightly smaller that the frame and will bind
The steel-plate clamp shown is used to lift a steel plate H of mass 250 kg. Knowing that the normal force exerted on steel cam EG by pin D forms an angle of 40° with the horizontal and neglecting the friction force between the cam and the pin, determine the smallest allowable value of the
The 5-in.-radius cam shown is used to control the motion of the plate CD. Knowing that the coefficient of static friction between the cam and the plate is 0.45 and neglecting friction at the roller supports, determine(a) The force P for which motion of the plate is impending knowing that the plate
A child having a mass of 18 kg is seated halfway between the ends of a small, 16-kg table as shown. The coefficient of static friction is 0.20 between the ends of the table and the floor. If a second child pushes on edge B of the table top at a point directly opposite to the first child with a
A pipe of diameter 3 in. is gripped by the still son wrench shown. Portions AB and DE of the wrench are rigidly attached to each other and portion CF is connected by a pin at D. If the wrench is to grip the pipe and be self-locking, determine the required minimum coefficients of friction at A and C.
Solve Problem 8.30 assuming that the diameter of the pipe is 1.5 in.
The 25-kg plate ABCD is attached at A and D to collars which can slide on the vertical rod. Knowing that the coefficient of static friction is 0.40 between both collars and the rod, determine whether the plate is in equilibrium in the position shown when the magnitude of the vertical force applied
In Problem 8.32, determine the range of values of the magnitude P of the vertical force applied at E for which the plate will move downward.
A collar B of weight W is attached to the spring AB and can move along the rod shown. The constant of the spring is 1.5kN/m and the spring is unstretched when en θ = 0. Knowing that the coefficient of static friction between the collar and the rod is 0.40, determine the range of values of W for
A collar B of weight W is attached to the spring AB and can move along the rod shown. The constant of the spring is 1.5 kN/m and the spring is unstretched when en θ = 0. Knowing that the coefficient of static friction between the collar and the rod is 0.40, determine the range of values of W for

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