Fuerzas en 3D y Equilibrio de Una Particula en 3D - Estatica de Beer 9Ed

54

PROBLEMS

2.71 Determine (a) the x, y, and z components of the 750-N force, (b) the angles ux, uy, and uz that the force forms with the coordinate axes.

2.72 Determine (a) the x, y, and z components of the 900-N force, (b) the angles ux, uy, and uz that the force forms with the coordinate axes.

2.73 A horizontal circular plate is suspended as shown from three wires that are attached to a support at D and form 30 angles with the vertical. Knowing that the x component of the force exerted by wire AD on the plate is 110.3 N, determine (a) the tension in wire AD, (b) the angles ux, uy, and uz that the force exerted at A forms with the coordinate axes.

2.74 A horizontal circular plate is suspended as shown from three wires that are attached to a support at D and form 30 angles with the vertical. Knowing that the z component of the force exerted by wire BD on the plate is 232.14 N, determine (a) the tension in wire BD, (b) the angles ux, uy, and uz that the force exerted at B forms with the coordinate axes.

2.75 A horizontal circular plate is suspended as shown from three wires that are attached to a support at D and form 30 angles with the vertical. Knowing that the tension in wire CD is 60 lb, determine (a) the components of the force exerted by this wire on the plate, (b) the angles ux, uy, and uz that the force forms with the coordinate axes.

2.76 A horizontal circular plate is suspended as shown from three wires that are attached to a support at D and form 30 angles with the vertical. Knowing that the x component of the force exerted by wire CD on the plate is 220 lb, determine (a) the tension in wire CD, (b) the angles ux, uy, and uz that the force exerted at C forms with the coordinate axes.

2.77 The end of the coaxial cable AE is attached to the pole AB, which is strengthened by the guy wires AC and AD. Knowing that the tension in wire AC is 120 lb, determine (a) the components of the force exerted by this wire on the pole, (b) the angles ux, uy, and uz that the force forms with the coordinate axes.

2.78 The end of the coaxial cable AE is attached to the pole AB, which is strengthened by the guy wires AC and AD. Knowing that the tension in wire AD is 85 lb, determine (a) the components of the force exerted by this wire on the pole, (b) the angles ux, uy, and uz that the force forms with the coordinate axes.

2.79 Determine the magnitude and direction of the force F 5 (320 N)i 1(400 N)j 2 (250 N)k.

Fig. P2.71 and P2.72

y

x

z

900 N

750 N

35

25

20

65

O

Fig. P2.73, P2.74, P2.75, and P2.76

y

xz

6040

50A C

D

B

O


3660

48

20x

y

z

A

BC

E

D

bee29400_ch02_014-071.indd Page 54 11/28/08 9:21:21 PM user-s173bee29400_ch02_014-071.indd Page 54 11/28/08 9:21:21 PM user-s173 /Volumes/204/MHDQ076/work%0/indd%0/Volumes/204/MHDQ076/work%0/indd%0

55Problems 2.80 Determine the magnitude and direction of the force F 5 (240 N)i 2 (270 N)j 1 (680 N)k.

2.81 A force acts at the origin of a coordinate system in a direction defined by the angles ux 5 70.9 and uy 5 144.9. Knowing that the z component of the force is 252 lb, determine (a) the angle uz, (b) the other components and the magnitude of the force.

2.82 A force acts at the origin of a coordinate system in a direction defined by the angles uy 5 55 and uz 5 45. Knowing that the x component of the force is 2500 lb, determine (a) the angle ux, (b) the other components and the magnitude of the force.

2.83 A force F of magnitude 210 N acts at the origin of a coordinate system. Knowing that Fx 5 80 N, uz 5 151.2, and Fy , 0, deter-mine (a) the components Fy and Fz, (b) the angles ux and uy.

2.84 A force F of magnitude 230 N acts at the origin of a coordinate system. Knowing that ux 5 32.5, Fy 5 260 N, and Fz . 0, deter-mine (a) the components Fx and Fz, (b) the angles uy and uz.

2.85 A transmission tower is held by three guy wires anchored by bolts at B, C, and D. If the tension in wire AB is 525 lb, determine the components of the force exerted by the wire on the bolt at B.

2.86 A transmission tower is held by three guy wires anchored by bolts at B, C, and D. If the tension in wire AD is 315 lb, deter-mine the components of the force exerted by the wire on the bolt at D.

2.87 A frame ABC is supported in part by cable DBE that passes through a frictionless ring at B. Knowing that the tension in the cable is 385 N, determine the components of the force exerted by the cable on the support at D.


y

A

100 ft

25 ftO

B

20 ft

20 ft

60 ftz

D

C

18 ft

74 ft

x

Fig. P2.87

y

xz

A

B

ED

C

O

600 mm

400 mm

480 mm

510 mm

280 mm210 mm


56 Statics of Particles 2.88 For the frame and cable of Prob. 2.87, determine the components of the force exerted by the cable on the support at E.

2.89 Knowing that the tension in cable AB is 1425 N, determine the components of the force exerted on the plate at B.


x

y

z

A

B

D

C

O

600 mm

920 mm

360 mm

900 mm

2.90 Knowing that the tension in cable AC is 2130 N, determine the components of the force exerted on the plate at C.

2.91 Find the magnitude and direction of the resultant of the two forces shown knowing that P 5 300 N and Q 5 400 N.

2.92 Find the magnitude and direction of the resultant of the two forces shown knowing that P 5 400 N and Q 5 300 N.

2.93 Knowing that the tension is 425 lb in cable AB and 510 lb in cable AC, determine the magnitude and direction of the resultant of the forces exerted at A by the two cables.

2.94 Knowing that the tension is 510 lb in cable AB and 425 lb in cable AC, determine the magnitude and direction of the resultant of the forces exerted at A by the two cables.

2.95 For the frame of Prob. 2.87, determine the magnitude and direc-tion of the resultant of the forces exerted by the cable at B knowing that the tension in the cable is 385 N.

2.96 For the cables of Prob. 2.89, knowing that the tension is 1425 N in cable AB and 2130 N in cable AC, determine the magnitude and direction of the resultant of the forces exerted at A by the two cables.


z

x

y

30

20

15

50P

Q


y

xz

A

B

C

D

O

40 in.

60 in.

60 in.45 in.


2.97 The end of the coaxial cable AE is attached to the pole AB, which is strengthened by the guy wires AC and AD. Knowing that the tension in AC is 150 lb and that the resultant of the forces exerted at A by wires AC and AD must be contained in the xy plane, determine (a) the tension in AD, (b) the magnitude and direction of the resultant of the two forces.

2.98 The end of the coaxial cable AE is attached to the pole AB, which is strengthened by the guy wires AC and AD. Knowing that the tension in AD is 125 lb and that the resultant of the forces exerted at A by wires AC and AD must be contained in the xy plane, determine (a) the tension in AC, (b) the magnitude and direction of the resultant of the two forces.

2.15 EQUILIBRIUM OF A PARTICLE IN SPACE According to the definition given in Sec. 2.9, a particle A is in equi-librium if the resultant of all the forces acting on A is zero. The com-ponents R x , R y , R z of the resultant are given by the relations (2.31); expressing that the components of the resultant are zero, we write

oFx 5 0 oFy 5 0 oFz 5 0 (2.34)

Equations (2.34) represent the necessary and sufficient conditions for the equilibrium of a particle in space. They can be used to solve problems dealing with the equilibrium of a particle involving no more than three unknowns. To solve such problems, you first should draw a free-body dia-gram showing the particle in equilibrium and all the forces acting on it. You can then write the equations of equilibrium (2.34) and solve them for three unknowns. In the more common types of problems, these unknowns will represent (1) the three components of a single force or (2) the magnitude of three forces, each of known direction.


3660

48

20x

y

z

A

BC

E

D

572.15 Equilibrium of a Particle in Space

Photo 2.2 While the tension in the four cables supporting the car cannot be found using the three equations of (2.34), a relation between the tensions can be obtained by considering the equilibrium of the hook.


60

2.99 Three cables are used to tether a balloon as shown. Determine the vertical force P exerted by the balloon at A knowing that the ten-sion in cable AB is 259 N.

2.100 Three cables are used to tether a balloon as shown. Determine the vertical force P exerted by the balloon at A knowing that the ten-sion in cable AC is 444 N.

2.101 Three cables are used to tether a balloon as shown. Determine the vertical force P exerted by the balloon at A knowing that the ten-sion in cable AD is 481 N.

2.102 Three cables are used to tether a balloon as shown. Knowing that the balloon exerts an 800-N vertical force at A, determine the ten-sion in each cable.

2.103 A crate is supported by three cables as shown. Determine the weight of the crate knowing that the tension in cable AB is 750 lb.

2.104 A crate is supported by three cables as shown. Determine the weight of the crate knowing that the tension in cable AD is 616 lb.

PROBLEMS

A

B

C

D

O4.20 m

4.20 m

3.30 m

5.60 m

2.40 mx

y

z

Fig. P2.99, P2.100, P2.101, and P2.102

x

y

z

A

B

C

DO

36 in.

27 in.

60 in.

32 in.

40 in.

Fig. P2.103, P2.104, P2.105, and P2.106

2.105 A crate is supported by three cables as shown. Determine the weight of the crate knowing that the tension in cable AC is 544 lb.

2.106 A 1600-lb crate is supported by three cables as shown. Determine the tension in each cable.


61Problems 2.107 Three cables are connected at A, where the forces P and Q are applied as shown. Knowing that Q 5 0, find the value of P for which the tension in cable AD is 305 N.

2.108 Three cables are connected at A, where the forces P and Q are applied as shown. Knowing that P 5 1200 N, determine the values of Q for which cable AD is taut.

2.109 A transmission tower is held by three guy wires attached to a pin at A and anchored by bolts at B, C, and D. If the tension in wire AB is 630 lb, determine the vertical force P exerted by the tower on the pin at A.

y

x

z

220 mm

240 mm

960 mm

Q

P

AB

C

D

O

380 mm

320 mm

960 mm

Fig. P2.107 and P2.108

2.110 A transmission tower is held by three guy wires attached to a pin at A and anchored by bolts at B, C, and D. If the tension in wire AC is 920 lb, determine the vertical force P exerted by the tower on the pin at A.

2.111 A rectangular plate is supported by three cables as shown. Knowing that the tension in cable AC is 60 N, determine the weight of the plate.

Fig. P2.109, and P2.110

y

A90 ft

30 ft

OB

30 ft

20 ft

45 ft

z

D

C

60 ft

65 ftx

x

y

z

A

B

C

DO

250

130360

360

320450

480

Dimensions in mm

Fig. P2.111 and P2.112

2.112 A rectangular plate is supported by three cables as shown. Knowing that the tension in cable AD is 520 N, determine the weight of the plate.


62 Statics of Particles 2.113 For the transmission tower of Probs. 2.109 and 2.110, determine the tension in each guy wire knowing that the tower exerts on the pin at A an upward vertical force of 2100 lb.

2.114 A horizontal circular plate weighing 60 lb is suspended as shown from three wires that are attached to a support at D and form 30 angles with the vertical. Determine the tension in each wire.

2.115 For the rectangular plate of Probs. 2.111 and 2.112, determine the tension in each of the three cables knowing that the weight of the plate is 792 N.

2.116 For the cable system of Probs. 2.107 and 2.108, determine the tension in each cable knowing that P 5 2880 N and Q 5 0.

2.117 For the cable system of Probs. 2.107 and 2.108, determine the tension in each cable knowing that P 5 2880 N and Q 5 576 N.

2.118 For the cable system of Probs. 2.107 and 2.108, determine the tension in each cable knowing that P 5 2880 N and Q 5 2576 N (Q is directed downward).

2.119 Using two ropes and a roller chute, two workers are unloading a 200-lb cast-iron counterweight from a truck. Knowing that at the instant shown the counterweight is kept from moving and that the positions of points A, B, and C are, respectively, A(0, 220 in., 40 in.), B(240 in., 50 in., 0), and C(45 in., 40 in., 0), and assuming that no friction exists between the counterweight and the chute, deter-mine the tension in each rope. (Hint: Since there is no friction, the force exerted by the chute on the counterweight must be perpen-dicular to the chute.)

2.120 Solve Prob. 2.119 assuming that a third worker is exerting a force P 5 2(40 lb)i on the counterweight.

2.121 A container of weight W is suspended from ring A. Cable BAC passes through the ring and is attached to fixed supports at B and C. Two forces P 5 Pi and Q 5 Qk are applied to the ring to maintain the container in the position shown. Knowing that W 5 376 N, determine P and Q. (Hint: The tension is the same in both portions of cable BAC.)

x

O

A

CB

y

z80 in.

40 in.

Fig. P2.1 19

Fig. P2.121

QP

O

A

C

B

y

xz

W

160 mm

400 mm

130 mm

150 mm

240 mm

y

xz

6040

50A C

D

B

O

Fig. P2.114


63Problems 2.122 For the system of Prob. 2.121, determine W and Q knowing that P 5 164 N.

2.123 A container of weight W is suspended from ring A, to which cables AC and AE are attached. A force P is applied to the end F of a third cable that passes over a pulley at B and through ring A and that is attached to a support at D. Knowing that W 5 1000 N, deter-mine the magnitude of P. (Hint: The tension is the same in all portions of cable FBAD.)

2.124 Knowing that the tension in cable AC of the system described in Prob. 2.123 is 150 N, determine (a) the magnitude of the force P, (b) the weight W of the container.

2.125 Collars A and B are connected by a 25-in.-long wire and can slide freely on frictionless rods. If a 60-lb force Q is applied to collar B as shown, determine (a) the tension in the wire when x 5 9 in., (b) the corresponding magnitude of the force P required to main-tain the equilibrium of the system.

y

xz

0.78 m

0.40 m

0.40 mP

O

B

F

E

C

W

A

D

1.60 m

0.86 m

1.20 m

1.30 m

Fig. P2.123

20 in.

x

x

y

z

z

BQ

P

A

O

Fig. P2.125 and P2.126

2.126 Collars A and B are connected by a 25-in.-long wire and can slide freely on frictionless rods. Determine the distances x and z for which the equilibrium of the system is maintained when P 5 120 lb and Q 5 60 lb.


67

REVIEW PROBLEMS

2.127 The direction of the 75-lb forces may vary, but the angle between the forces is always 50. Determine the value of a for which the resultant of the forces acting at A is directed horizontally to the left.

2.128 A stake is being pulled out of the ground by means of two ropes as shown. Knowing the magnitude and direction of the force exerted on one rope, determine the magnitude and direction of the force P that should be exerted on the other rope if the resul-tant of these two forces is to be a 40-lb vertical force.

2.129 Member BD exerts on member ABC a force P directed along line BD. Knowing that P must have a 240-lb vertical component, determine (a) the magnitude of the force P, (b) its horizontal component.

2.130 Two cables are tied together at C and loaded as shown. Determine the tension (a) in cable AC, (b) in cable BC.

Fig. P2.127

240 lb

75 lb

75 lb

50

30A

Fig. P2.128

30 lb P

25

40Q

D

A B C

Fig. P2.129

8.5 ft5 ft

12 ft 7.5 ft

396 lb

A B

C 9 ft

Fig. P2.130

2.131 Two cables are tied together at C and loaded as shown. Knowing that P 5 360 N, determine the tension (a) in cable AC, (b) in cable BC.

2.132 Two cables are tied together at C and loaded as shown. Determine the range of values of P for which both cables remain taut. Fig. P2.131 and P2.132

A B

P

Q = 480 N

C

34

600 mm

250 mm


68 Statics of Particles 2.133 A force acts at the origin of a coordinate system in a direction defined by the angles ux 5 69.3 and uz 5 57.9. Knowing that the y component of the force is 2174 lb, determine (a) the angle uy, (b) the other components and the magnitude of the force.

2.134 Cable AB is 65 ft long, and the tension in that cable is 3900 lb. Determine (a) the x, y, and z components of the force exerted by the cable on the anchor B, (b) the angles ux, uy, and uz defining the direction of that force.

2.135 In order to move a wrecked truck, two cables are attached at A and pulled by winches B and C as shown. Knowing that the ten-sion is 10 kN in cable AB and 7.5 kN in cable AC, determine the magnitude and direction of the resultant of the forces exerted at A by the two cables.

Fig. P2.134 12 m

9.60 m

6 m

15 m

18 m

30

A

B

C

Fig. P2.135

x

y

zC

BO

D

A

50

56 ft

20

Fig. P2.136

x

y

z

A

B

D

C

O

600 mm

320 mm

360 mm

500 mm

450 mm

2.136 A container of weight W 5 1165 N is supported by three cables as shown. Determine the tension in each cable.


69Review Problems

Fig. P2.137

200 mm

x

y

y

z zB

Q

P

A

O

2.137 Collars A and B are connected by a 525-mm-long wire and can slide freely on frictionless rods. If a force P 5 (341 N)j is applied to collar A, determine (a) the tension in the wire when y 5 155 mm, (b) the magnitude of the force Q required to maintain the equi-librium of the system.

2.138 Solve Prob. 2.137 assuming that y 5 275 mm.


Cover PageTitle PageCopyright PageAbout the AuthorsPrefaceList of SymbolsContents1 Introduction1.1 What Is Mechanics?1.2 Fundamental Concepts and Principles1.3 Systems of Units1.4 Conversion from One System of Units to Another1.5 Method of Problem Solution1.6 Numerical Accuracy

2 Statics of Particles2.1 IntroductionForces in a Plane2.2 Force on a Particle. Resultant of Two Forces2.3 Vectors2.4 Addition of Vectors2.5 Resultant of Several Concurrent Forces2.6 Resolution of a Force into Components2.7 Rectangular Components of a Force. Unit Vectors2.8 Addition of Forces by Summing x and y Components2.9 Equilibrium of a Particle2.10 Newtons First Law of Motion2.11 Problems Involving the Equilibrium of a Particle. Free-Body DiagramsForces in Space2.12 Rectangular Components of a Force in Space2.13 Force Defined by Its Magnitude and Two Points on Its Line of Action2.14 Addition of Concurrent Forces in Space2.15 Equilibrium of a Particle in SpaceReview and SummaryReview ProblemsComputer Problems

3 Rigid Bodies: Equivalent Systems of Forces3.1 Introduction3.2 External and Internal Forces3.3 Principle of Transmissibility. Equivalent Forces3.4 Vector Product of Two Vectors3.5 Vector Products Expressed in Terms of Rectangular Components3.6 Moment of a Force about a Point3.7 Varignons Theorem3.8 Rectangular Components of the Moment of a Force3.9 Scalar Product of Two Vectors3.10 Mixed Triple Product of Three Vectors3.11 Moment of a Force about a Given Axis3.12 Moment of a Couple3.13 Equivalent Couples3.14 Addition of Couples3.15 Couples Can Be Represented by Vectors3.16 Resolution of a Given Force into a Force at O and a Couple3.17 Reduction of a System of Forces to One Force and One Couple3.18 Equivalent Systems of Forces3.19 Equipollent Systems of Vectors3.20 Further Reduction of a System of Forces*3.21 Reduction of a System of Forces to a WrenchReview and SummaryReview ProblemsComputer Problems

4 Equilibrium of Rigid Bodies4.1 Introduction4.2 Free-Body DiagramEquilibrium in Two Dimensions4.3 Reactions at Supports and Connections for a Two-Dimensional Structure4.4 Equilibrium of a Rigid Body in Two Dimensions4.5 Statically Indeterminate Reactions. Partial Constraints4.6 Equilibrium of a Two-Force Body4.7 Equilibrium of a Three-Force BodyEquilibrium in Three Dimensions4.8 Equilibrium of a Rigid Body in Three Dimensions4.9 Reactions at Supports and Connections for a Three-Dimensional StructureReview and SummaryReview ProblemsComputer Problems

5 Distributed Forces: Centroids and Centers of Gravity5.1 IntroductionAreas and Lines5.2 Center of Gravity of a Two-Dimensional Body5.3 Centroids of Areas and Lines5.4 First Moments of Areas and Lines5.5 Composite Plates and Wires5.6 Determination of Centroids by Integration5.7 Theorems of Pappus-Guldinus*5.8 Distributed Loads on Beams*5.9 Forces on Submerged SurfacesVolumes5.10 Center of Gravity of a Three-Dimensional Body. Centroid of a Volume5.11 Composite Bodies5.12 Determination of Centroids of Volumes by IntegrationReview and SummaryReview ProblemsComputer Problems

6 Analysis of Structures6.1 IntroductionTrusses6.2 Definition of a Truss6.3 Simple Trusses6.4 Analysis of Trusses by the Method of Joints*6.5 Joints under Special Loading Conditions*6.6 Space Trusses6.7 Analysis of Trusses by the Method of Sections*6.8 Trusses Made of Several Simple TrussesFrames and Machines6.9 Structures Containing Multiforce Members6.10 Analysis of a Frame6.11 Frames Which Cease to Be Rigid When Detached from Their Supports6.12 MachinesReview and SummaryReview ProblemsComputer Problems

7 Forces in Beams and Cables*7.1 Introduction*7.2 Internal Forces in MembersBeams*7.3 Various Types of Loading and Support*7.4 Shear and Bending Moment in a Beam*7.5 Shear and Bending-Moment Diagrams*7.6 Relations among Load, Shear, and Bending MomentCables*7.7 Cables with Concentrated Loads*7.8 Cables with Distributed Loads*7.9 Parabolic Cable*7.10 CatenaryReview and SummaryReview ProblemsComputer Problems

8 Friction8.1 Introduction8.2 The Laws of Dry Friction. Coefficients of Friction8.3 Angles of Friction8.4 Problems Involving Dry Friction8.5 Wedges8.6 Square-Threaded Screws*8.7 Journal Bearings. Axle Friction*8.8 Thrust Bearings. Disk Friction*8.9 Wheel Friction. Rolling Resistance*8.10 Belt FrictionReview and SummaryReview ProblemsComputer Problems

9 Distributed Forces: ixMoments of Inertia9.1 IntroductionMoments of Inertia of Areas9.2 Second Moment, or Moment of Inertia, of an Area9.3 Determination of the Moment of Inertia of an Area by Integration9.4 Polar Moment of Inertia9.5 Radius of Gyration of an Area9.6 Parallel-Axis Theorem9.7 Moments of Inertia of Composite Areas*9.8 Product of Inertia*9.9 Principal Axes and Principal Moments of Inertia*9.10 Mohrs Circle for Moments and Products of InertiaMoments of Inertia of a Mass9.11 Moment of Inertia of a Mass9.12 Parallel-Axis Theorem9.13 Moments of Inertia of Thin Plates9.14 Determination of the Moment of Inertia of a Three-Dimensional Body by Integration9.15 Moments of Inertia of Composite Bodies*9.16 Moment of Inertia of a Body with Respect to an Arbitrary Axis through O . Mass Products of Inertia*9.17 Ellipsoid of Inertia. Principal Axes of Inertia*9.18 Determination of the Principal Axes and Principal Moments of Inertia of a Body of Arbitrary ShapeReview and SummaryReview ProblemsComputer Problems

10 Method of Virtual Work*10.1 Introduction*10.2 Work of a Force*10.3 Principle of Virtual Work*10.4 Applications of the Principle of Virtual Work*10.5 Real Machines. Mechanical Efficiency*10.6 Work of a Force during a Finite Displacement*10.7 Potential Energy*10.8 Potential Energy and Equilibrium*10.9 Stability of EquilibriumReview and SummaryReview ProblemsComputer Problems

11 Kinematics of Particles11.1 Introduction to DynamicsRectilinear Motion of Particles11.2 Position, Velocity, and Acceleration11.3 Determination of the Motion of a Particle11.4 Uniform Rectilinear Motion11.5 Uniformly Accelerated Rectilinear Motion11.6 Motion of Several Particles*11.7 Graphical Solution of Rectilinear-Motion Problems*11.8 Other Graphical MethodsCurvilinear Motion of Particles11.9 Position Vector, Velocity, and Acceleration11.10 Derivatives of Vector Functions11.11 Rectangular Components of Velocity and Acceleration11.12 Motion Relative to a Frame in Translation11.13 Tangential and Normal Components11.14 Radial and Transverse ComponentsReview and SummaryReview ProblemsComputer Problems

12 Kinetics of Particles: Newtons Second Law12.1 Introduction12.2 Newtons Second Law of Motion12.3 Linear Momentum of a Particle. Rate of Change of Linear Momentum12.4 Systems of Units12.5 Equations of Motion12.6 Dynamic Equilibrium12.7 Angular Momentum of a Particle. Rate of Change of Angular Momentum12.8 Equations of Motion in Terms of Radial and Transverse Components12.9 Motion under a Central Force. Conservation of Angular Momentum12.10 Newtons Law of Gravitation*12.11 Trajectory of a Particle under a Central Force*12.12 Application to Space Mechanics*12.13 Keplers Laws of Planetary MotionReview and SummaryReview ProblemsComputer Problems

13 Kinetics of Particles: Energy and Momentum Methods13.1 Introduction13.2 Work of a Force13.3 Kinetic Energy of a Particle. Principle of Work and Energy13.4 Applications of the Principle of Work and Energy13.5 Power and Efficiency13.6 Potential Energy*13.7 Conservative Forces13.8 Conservation of Energy13.9 Motion under a Conservative Central Force. Application to Space Mechanics13.10 Principle of Impulse and Momentum13.11 Impulsive Motion13.12 Impact13.13 Direct Central Impact13.14 Oblique Central Impact13.15 Problems Involving Energy and MomentumReview and SummaryReview ProblemsComputer Problems

14 Systems of Particles14.1 Introduction14.2 Application of Newtons Laws to the Motion of a System of Particles. Effective Forces14.3 Linear and Angular Momentum of a System of Particles14.4 Motion of the Mass Center of a System of Particles14.5 Angular Momentum of a System of Particles about Its Mass Center14.6 Conservation of Momentum for a System of Particles14.7 Kinetic Energy of a System of Particles14.8 Work-Energy Principle. Conservation of Energy for a System of Particles14.9 Principle of Impulse and Momentum for a System of Particles*14.10 Variable Systems of Particles*14.11 Steady Stream of Particles*14.12 Systems Gaining or Losing MassReview and SummaryReview ProblemsComputer Problems

16 Plane Motion of Rigid Bodies: Forces and Accelerations16.1 Introduction16.2 Equations of Motion for a Rigid Body16.3 Angular Momentum of a Rigid Body in Plane Motion16.4 Plane Motion of a Rigid Body. DAlemberts Principle*16.5 A Remark on the Axioms of the Mechanics of Rigid Bodies16.6 Solution of Problems Involving the Motion of a Rigid Body16.7 Systems of Rigid Bodies16.8 Constrained Plane MotionReview and SummaryReview ProblemsComputer Problems

1 7 Plane Motion of Rigid Bodies: Energy and Momentum Methods17.1 Introduction17.2 Principle of Work and Energy for a Rigid Body17.3 Work of Forces Acting on a Rigid Body17.4 Kinetic Energy of a Rigid Body in Plane Motion17.5 Systems of Rigid Bodies17.6 Conservation of Energy17.7 Power17.8 Principle of Impulse and Momentum for the Plane Motion of a Rigid Body17.9 Systems of Rigid Bodies17.10 Conservation of Angular Momentum17.11 Impulsive Motion17.12 Eccentric ImpactReview and SummaryReview ProblemsComputer Problems

18 Kinetics of Rigid Bodies in Three Dimensions*18.1 Introduction*18.2 Angular Momentum of a Rigid Body in Three Dimensions*18.3 Application of the Principle of Impulse and Momentum to the Three-Dimensional Motion of a Rigid Body*18.4 Kinetic Energy of a Rigid Body in Three Dimensions*18.5 Motion of a Rigid Body in Three Dimensions*18.6 Eulers Equations of Motion. Extension of DAlemberts Principle to the Motion of a Rigid Body in Three Dimensions*18.7 Motion of a Rigid Body about a Fixed Point*18.8 Rotation of a Rigid Body about a Fixed Axis*18.9 Motion of a Gyroscope. Eulerian Angles*18.10 Steady Precession of a Gyroscope*18.11 Motion of an Axisymmetrical Body under No ForceReview and SummaryReview ProblemsComputer Problems

19 Mechanical Vibrations19.1 IntroductionVibrations without Damping19.2 Free Vibrations of Particles. Simple Harmonic Motion19.3 Simple Pendulum (Approximate Solution)*19.4 Simple Pendulum (Exact Solution19.5 Free Vibrations of Rigid Bodies19.6 Application of the Principle of Conservation of Energy19.7 Forced VibrationsDamped Vibrations*19.8 Damped Free Vibrations*19.9 Damped Forced Vibrations*19.10 Electrical AnaloguesReview and SummaryReview ProblemsComputer Problems

Appendix Fundamentals of Engineering ExaminationPhoto CreditsIndexAnswers to Problems

Fuerzas en 3D y Equilibrio de Una Particula en 3D - Estatica de Beer 9Ed

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