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engineering
engineering mechanics statics

Engineering Mechanics Statics 14th edition Russell C. Hibbeler - Solutions

Replace the loading system acting on the post by an equivalent resultant force and couple moment at point B. 650 N 500 N 30° 300 N 1500 N - m 60° A -3 m -5 m- m
Replace the loading system acting on the post by an equivalent resultant force and couple moment at point A. 650 N 500 N 30 300 N 1500 N · m 60° B -3 m 5 m 2 m
Determine the resultant couple moment of the two couples that act on the assembly. Specify its magnitude and coordinate direction angles. 60 Ib 2 in. -2 in. 80 lb 30° 4 in. 80 lb 3 in.. 60 lb
Two couples act on the beam as shown.If F = 150 lb, determine the resultant couple moment. 200 Ib 1.5 ft 200 lb F 4 ft
Determine the magnitude of F so that the resultant couple moment is 12 kN•m, counterclockwise. Where on the beam does the resultant couple moment act? -F F 30 30° 8 kN 0.3 m 1.2 m 0.4 m- 8 kN
If the valve can be opened with a couple moment of 25N•m, determine the required magnitude of each couple force which must be applied to the wheel. -150 mm -150 mm
The man tries to open the valve by applying the couple forces of F = 75 N to the wheel. Determine the couple moment produced. -150 mm -150 mm
Determine the magnitude of the couple force F so that the resultant couple moment on the crank is zero. 150 lb 5 in. 30° 30° 150 lb 5 in. 4n. 30° 4 in. F
If the resultant couple of the three couples acting on the triangular block is to be zero, determine the magnitude of forces F and P. -F F 150 N B 300 mm 500 mm 600 mm 150 N -P -400 mm
A twist of 4N•m is applied to the handle of the screwdriver. Resolve this couple moment into a pair of couple forces F exerted on the handle and P exerted on the blade. 4 N m 30 mm F 5 mm
The force of F = 30 N acts on the bracket as shown. Determine the moment of the force about the a-a axis of the pipe if α = 60°, β = 60°, and γ = 45°. Also, determine the coordinate direction angles of F in order to produce the maximum moment about the a-a axis.What is this moment? F= 30 N
A horizontal force of F = {-50i} N is applied perpendicular to the handle of the pipe wrench. Determine the moment that this force exerts along the axis OA (z axis) of the pipe assembly. Both the wrench and pipe assembly, OABC, lie in the y-z plane. Suggestion: Use a scalar analysis. B 0.8 m
he board is used to hold the end of a four-way lug wrench in position. If a torque of 30 N•m about the x axis is required to tighten the nut, determine the required magnitude of the force F that the man’s foot must apply on the end of the wrench in order to turn it. Force F lies in a vertical
The board is used to hold the end of a four-way lug wrench in the position shown when the man applies a force of F = 100N. Determine the magnitude of the moment produced by this force about the x axis. Force F lies in a vertical plane. 60 -250 mm 250 mm
Strut AB of the 1-m-diameter hatch door exerts a force of 450 N on point B. Determine the moment of this force about point O. 30 0.5 m F = 450 N 0.5 m 30
force F having a magnitude of acts along the diagonal of F = 100N the parallelepiped. Determine the moment of F about point A, using MA = rB × F and MA = rC × F. 200 mm 400 mm B 600 mm
Determine the moment of force F about point O. The force has a magnitude of 800 N and coordinate direction angles of α = 60°, β = 120°, γ = 45°. Express the result as a Cartesian vector. 0.4 m A, -0.5 m- 0.3 m
Determine the coordinate direction angles α, β,γ of force F, so that the moment of F about O is zero. 0.4 m A, -0.5 m- 0.3 m
Determine the moment of the force of F = 600 N about point A. 4 m B 450- 4 m F 6 m 6 m
Determine the moment of the force F about point P. Express the result as a Cartesian vector. 2m 3 m- 3 m 1m A F= (2i + 4j – 6k) kN
Determine the moment of the force F about point P. Express the result as a Cartesian vector. F = (-6i + 4 j+ 8k} kN A 4 m 6 m 3 m y 1 m 2 m
Determine the moment of the force F about point O. Express the result as a Cartesian vector. F = (-6i + 4 j+ 8k} kN A 4 m 6 m 3 m y 1 m 2 m
If the 1500-lb boom AB, the 200-lb cage BCD, and the 175-lb man have centers of gravity located at points G1 , G2 and G3 , respectively, determine the resultant moment produced by all the weights about point A. G3 D 2.5 ft'1.75 ft 20 ft 10 ft 75°
If the 1500-lb boom AB, the 200-lb cage BCD, and the 175-lb man have centers of gravity located at points G1, G2 and G3, respectively, determine the resultant moment produced by each weight about point A. G3 D 2.5 ft'1.75 ft 20 ft 10 ft 75°
The tower crane is used to hoist a 2-Mg load upward at constant velocity. The 1.5-Mg jib BD and 0.5-Mg jib BC have centers of mass at G1 and G2, respectively. Determine the required mass of the counterweight C so that the resultant moment produced by the load and the weight of the tower crane jibs
The tower crane is used to hoist the 2-Mg load upward at constant velocity. The 1.5-Mg jib BD, 0.5-Mg jib BC, and 6-Mg counterweight C have centers of mass at G1 , G2 , and G3 , respectively. Determine the resultant moment produced by the load and the weights of the tower crane jibs about point A
Old clocks were constructed using a fusee B to drive the gears and watch hands. The purpose of the fusee is to increase the leverage developed by the mainspring A as it uncoils and thereby loses some of its tension. The mainspring can develop a torque (moment) Ts = kθ, where k = 0.015 N• m/rad
The torque wrench ABC is used to measure the moment or torque applied to a bolt when the bolt is located at A and a force is applied to the handle at C. The mechanic reads the torque on the scale at B. If an extension AO of length d is used on the wrench, determine the required scale reading if the
The 20-N horizontal force acts on the handle of the socket wrench. Determine the moment of this force about point O. Specify the coordinate direction angles a, b, g of the moment axis. 20 N -200 mm B A T609 10 mm 50 mm y
The 20-N horizontal force acts on the handle of the socket wrench. What is the moment of this force about point B. Specify the coordinate direction angles α, β, γ of the moment axis. 20 N -200 mm- B A T609 10 mm 50 mm y
The towline exerts a force of P = 6 kN at the end of the 8-m-long crane boom. If x = 10 m, determine the position u of the boom so that this force creates a maximum moment about point O. What is this moment? A P = 6 kN 8 m 1 m B.
The towline exerts a force of P = 6 kN at the end of the 8-m-long crane boom. If u = 30°, determine the placement x of the hook at B so that this force creates a maximum moment about point O. What is this moment? A P = 6 kN 8 m 1 m B.
The crowbar is subjected to a vertical force of P = 25 lb at the grip, whereas it takes a force of F = 155 lb at the claw to pull the nail out. Find the moment of each force about point A and determine if P is sufficient to pull out the nail. The crowbar contacts the board at point A. F 60°
Determine the moment about point B of each of the three forces acting on the beam. F = 375 lb F2 = 500 lb 3. B. 0.5 ft tontsa- 8 ft 6 ft -5 ft- 30 F3 = 160 lb
Determine the moment about point A of each of the three forces acting on the beam. F = 375 lb F = 500 lb В. 0.5 ft 8 ft 6 ft 5ft- 5 ft- 30 F3 = 160 lb
The crate has a mass of 130 kg. Determine the tension developed in each cable for equilibrium.
If the maximum force in each rod can not exceed 1500 N, determine the greatest mass of the crate that can be supported. 3 m -2 m- 2 m 3m 1 my 2 m 1 m -3 m
Determine the tension in each cable for equilibrium. 800 N -3 m 5 m 4 ní 2 m 5m- 4 m 4 m - B
Determine the tension developed in the three cables required to support the traffic light, which has a mass of 15 kg. Take h = 4 m. C 6 m D 3 m B 4 m 4 m 4 m 6 m 3 m 3 m
Determine the maximum weight of the crate that can be suspended from cables AB, AC, and AD so that the tension developed in any one of the cables does not exceed 250 lb. 2 ft3 CG 3 ft 4 ft 3 ft
Determine the tension developed in each cable for equilibrium of the 300-lb crate. 2 f3 fr CG 3 ft 6 ft 4 ft 3 ft
Determine the greatest force F that can be applied to the ring if each cable can support a maximum force of 800 lb. F 1 ft 6 ft B
Determine the force in each cable if F = 500 lb. 1 ft 6 ft 2 ft 3 ft
The single elastic cord ABC is used to support the 40-lb load. Determine the position x and the tension in the cord that is required for equilibrium. The cord passes through the smooth ring at B and has an unstretched length of 6 ft and stiffness of k = 50 lb/ft. 5 ft 1 ft [B
Cable ABC has a length of 5 m. Determine the position x and the tension developed in ABC required for equilibrium of the 100-kg sack. Neglect the size of the pulley at B. 3.5 m- — х 0.75 m A
The ring of negligible size is subjected to a vertical force of 200 lb. Determine the required length l of cord AC such that the tension acting in AC is 160 lb. Also, what is the force in cord AB? Use the equilibrium condition to determine the required angle θ for attachment, then determine l
Determine the tension developed in each cord required for equilibrium of the 20-kg lamp. E D 30° B 45° F
The street-lights at A and B are suspended from the two poles as shown. If each light has a weight of 50 lb, determine the tension in each of the three supporting cables and the required height h of the pole DE so that cable AB is horizontal. A E 18 ft 24 ft ft 10 ft
Determine the magnitude of F1 and the distance y if x = 1.5 m and F2 = 1000 N. D B 2 m
Determine the distances x and y for equilibrium if F1 = 800 N and F2 = 1000 N. D B 2 m
Determine the unstretched length of DB to hold the 40-kg crate in the position shown. Take k = 180 N/m. -2 m- -3 m- B 2 m ww D
If the spring DB has an unstretched length of 2 m, determine the stiffness of the spring to hold the 40-kg crate in the position shown. -2 m- -3 m- B 2 m ww D
Determine the stiffness kT of the single spring such that the force F will stretch it by the same amount s as the force F stretches the two springs. Express kT in terms of stiffness k1 and k2 of the two springs. Unstretched position kT ww F ki k2
A nuclear-reactor vessel has a weight of 500(103) lb. Determine the horizontal compressive force that the spreader bar AB exerts on point A and the force that each cable segment CA and AD exert on this point while the vessel is hoisted upward at constant velocity. 30 30 A B D E
The lift sling is used to hoist a container having a mass of 500 kg. Determine the force in each of the cables AB and AC as a function of θ. If the maximum tension allowed in each cable is 5 kN, determine the shortest lengths of cables AB and AC that can be used for the lift. The center of
The cords ABC and BD can each support a maximum load of 100 lb. Determine the maximum weight of the crate, and the angle θ for equilibrium. 1213
The man attempts to pull down the tree using the cable and small pulley arrangement shown. If the tension in AB is 60 lb, determine the tension in cable CAD and the angle θ which the cable makes at the pulley. 20° 30°
The members of a truss are connected to the gusset plate. If the forces are concurrent at point O, determine the magnitudes of F and T for equilibrium.Take θ = 90°. 9 kN F S03 r000 1006
The bearing consists of rollers, symmetrically confined within the housing. The bottom one is subjected to a 125-N force at its contact A due to the load on the shaft. Determine the normal reactions NB and NC on the bearing at its contact points B and C for equilibrium. 40 B 125 N
Determine the magnitudes of the components of force F = 90 lb acting parallel and perpendicular to diagonal AB of the crate. F= 90 Ib 60° B. 45° 1 ft 3 ft 1.5 ft
If the force F = 100 N lies in the plane DBEC, which is parallel to the x–z plane, and makes an angle of 10° with the extended line DB as shown, determine the angle that F makes with the diagonal AB of the crate.
Determine the angle u between the pipe segments BA and BC. 3 ft' 4 ft 2 ft F = (30i – 45j + 50k) Ib 4 ft
Determine the magnitude of the projected component of along AC. Express this component as a Cartesian vector. 3 ft' 4 ft 2 ft F = (30i – 45j + 50k) Ib 4 ft
Determine the magnitudes of the components of acting along and perpendicular to segment BC of the pipe assembly 3 ft' 4 ft 4 ft F = (30i – 45j + 50k} lb 4 ft
Determine the magnitude of the projection of force F = 600 N along the u axis. F= 600 N. 4 m -4 m- 2m y 30°
Determine the angle between the y axis of the pole and the wire AB. -3 ft. 2 f -2f- 2 ft
Determine the magnitude of the projection of the force F1 along cable AC. F = 40 N 4 m F, = 70 N |A 2 m 3 m 2 m -3 m 3 m
Determine the angle θ between the two cables. F = 40 N 4 m * F,= 70 N 2 m 3 m 3 m 2 m 3 m
Express force F in Cartesian vector form if point B is located 3 m along the rod end C. B 4 m 4 m F = 600 N 3 m 6 m 4 m
Express the force F in Cartesian vector form if it acts at the midpoint B of the rod. A 4 m B 4 m F = 600 N 3 m 6 m D
Determine the magnitude and coordinates on angles of the resultant force. A 40 lb 20 lb 4 ft C 2 ft 20 y -2 ft 1.5 ft B -3 ft
The 8-m-long cable is anchored to the ground at A. If z = 5 m, determine the location + x, + y of point A. Choose a value such that x = y. В y
The 8-m-long cable is anchored to the ground at A. If x = 4 m and y = 2 m, determine the coordinate z to the highest point of attachment along the column. B y
Express force F as a Cartesian vector; then determine its coordinate direction angles. F = 135 lb 10 ft 5 ft 70° 30
Determine the magnitude and coordinate direction angles of the resultant force, and sketch this vector on the coordinate system. F = 200 N F = 150 N F, = 90 N 60° y 45° 0000
Express each force in Cartesian vector form. F = 200 N F, = 150 N F, = 90 N 60° 45°
Specify the magnitude and coordinate direction angles α1, β1, γ1 of F1 so that the resultant of the three forces acting on the bracket FR = {-350k}lb is Note that F3 lies in the x–y plane.
Determine the magnitude and coordinate direction angles of the resultant force, and sketch this vector on the coordinate system. F2 = 525 N 120 45° F = 450 N
Determine the magnitude and coordinate direction angles of the resultant force, and sketch this vector on the coordinate system. F, = 125 N 20 60° 45° 60° F = 400 N %3D
Determine the coordinate direction angles of F1. F = 300 N 60° 120 45° 45° 60°- F2= 500 N
The screw eye is subjected to the two forces shown. Express each force in Cartesian vector form and then determine the resultant force. Find the magnitude and coordinate direction angles of the resultant force. F = 300 N 60 120° 45° 45° 60°- F2 = 500 N
Determine the magnitude and coordinate direction angles of the resultant force and sketch this vector on the coordinate system. F = 80 lb 30 40° F= 130 lb
Determine the magnitude and coordinate direction angles of the force F acting on the support. The component of F in the x-y plane is 7 kN. F 30 40° 7 kN
If F = 5 kN and θ = 30°, determine the magnitude of the resultant force and its direction, measured counterclockwise from the positive x axis. 4 kN 15° 30° 6 kN
Three forces act on the bracket. Determine the magnitude and direction θ of F so that the resultant force is directed along the positive x′ axis and has a magnitude of 8 kN. 4 kN F 15° 30 6 kN
Determine the magnitude of the resultant force and its direction measured counterclockwise from the positive x axis. F2 = 26 kN 1213 5 30 F, = 30 kN
Determine the x and y components of each force acting on the gusset plate of a bridge truss. Show that the resultant force is zero. F = 6 kN F = 8 kN 888 F = 4 kN F, = 6 kN 888 888
Determine the magnitude of the resultant force and its orientation measured counterclockwise from the positive x axis. F = 15 kN 40° F = 26 kN 13 12 30° F3 = 36 kN
Determine the magnitude of the resultant force and its direction, measured clockwise from the positive x axis. 40 lb 3. 30 lb 13 V12 91 lb
Determine the magnitude of the resultant force and its direction measured counterclockwise from the positive x axis. F = 750 N 45° 30° F = 850 N F2 = 625 N
Express F1, F2, and F3 as Cartesian vectors F3= 750 N 45° F = 850 N 30° F= 625 N
Determine the magnitude of the resultant force and its direction, measured counterclockwise from the positive x axis. F = 8 kN F2 = 5 kN 60° 45° F = 4 kN
Express each of the three forces acting on the support in Cartesian vector form and determine the magnitude of the resultant force and its direction, measured clockwise from positive x axis. F, = 50 N 3 F = 30 N 15° F = 80 N
Resolve each force acting on the gusset plate into its x and y components, and express each force as a Cartesian vector. F3 = 650 N F2 = 750 N 45° F, = 900 N
Determine the magnitude of the resultant force and its direction measured counterclockwise from the positive x axis. y 60° 30 F = 400 N 45° F= 250 N
Resolve F1 and F2 into their x and y components. 60° 30 F = 400 N 45° F2 = 250 N
Determine the magnitude of the resultant force and its direction, measured counterclockwise from the positive x axis. y F1 = 200 N 45° 30° F = 150 N
If the resultant force of the two tugboats is required to be directed towards the positive x-axis, and FR is to be a minimum, determine the magnitude of FR and FB and the angle θ. FA= 2 kN 30 B
If FB = 3kN and θ = 45°, determine the magnitude of the resultant force of the two tugboats and its direction measured clockwise from the positive x axis. F= 2 kN 30 FB B.
If the resultant force of the two tugboats is 3kN, directed along the positive axis, determine the required magnitude of force FB and its direction θ. FA= 2 kN 30° FB

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