Ejercicios Del Tema 1 y Tema 2 - Estatica Beer Jhonson 9ed

PROBLEMS

25

2.1 Two forces P and Q are applied as shown at point A of a hook support. Knowing that P 5 75 N and Q 5 125 N, determine graphically the magnitude and direction of their resultant using (a) the parallelogram law, (b) the triangle rule.

2.2 Two forces P and Q are applied as shown at point A of a hook support. Knowing that P 5 60 lb and Q 5 25 lb, determine graphically the magnitude and direction of their resultant using (a) the parallelogram law, (b) the triangle rule.

2.3 The cable stays AB and AD help support pole AC. Knowing that the tension is 120 lb in AB and 40 lb in AD, determine graphically the magnitude and direction of the resultant of the forces exerted by the stays at A using (a) the parallelogram law, (b) the triangle rule.

20 35

A

PQ

Fig. P2.1 and P2.2

A

B C D

10 ft

8 ft 6 ft

Fig. P2.3

2.4 Two forces are applied at point B of beam AB. Determine graphi-cally the magnitude and direction of their resultant using (a) the parallelogram law, (b) the triangle rule.

2.5 The 300-lb force is to be resolved into components along lines a-a9and b-b9. (a) Determine the angle a by trigonometry knowing that the component along line a-a9 is to be 240 lb. (b) What is the cor-responding value of the component along b-b9?

2.6 The 300-lb force is to be resolved into components along lines a-a9and b-b9. (a) Determine the angle a by trigonometry knowing that the component along line b-b9 is to be 120 lb. (b) What is the cor-responding value of the component along a-a9?

2.7 Two forces are applied as shown to a hook support. Knowing that the magnitude of P is 35 N, determine by trigonometry (a) the required angle a if the resultant R of the two forces applied to the support is to be horizontal, (b) the corresponding magni-tude of R.

2 kN

3 kN40 60

A

B

Fig. P2.4

300 lb

a a'

b'

b

60a

Fig. P2.5 and P2.6

50 N

25

P

a

Fig. P2.7

Answers to all problems set in straight type (such as 2.1) are given at the end of the book. Answers to problems with a number set in italic type (such as 2.4) are not given.

bee29400_ch02_014-071.indd Page 25 11/28/08 9:20:18 PM user-s173bee29400_ch02_014-071.indd Page 25 11/28/08 9:20:18 PM user-s173 /Volumes/204/MHDQ076/work%0/indd%0/Volumes/204/MHDQ076/work%0/indd%0

2.8 For the hook support of Prob. 2.1, knowing that the magnitude of P is 75 N, determine by trigonometry (a) the required magnitude of the force Q if the resultant R of the two forces applied at A is to be vertical, (b) the corresponding magnitude of R.

2.9 A trolley that moves along a horizontal beam is acted upon by two forces as shown. (a) Knowing that a 5 25, determine by trigo-nometry the magnitude of the force P so that the resultant force exerted on the trolley is vertical. (b) What is the corresponding magnitude of the resultant?

2.10 A trolley that moves along a horizontal beam is acted upon by two forces as shown. Determine by trigonometry the magnitude and direction of the force P so that the resultant is a vertical force of 2500 N.

2.11 A steel tank is to be positioned in an excavation. Knowing that a 5 20, determine by trigonometry (a) the required magnitude of the force P if the resultant R of the two forces applied at A is to be vertical, (b) the corresponding magnitude of R.

26 Statics of Particles

1600 N

P

15

a

A

Fig. P2.9 and P2.10

425 lbA

P

30 a

Fig. P2.11 and P2.12

2.12 A steel tank is to be positioned in an excavation. Knowing that the magnitude of P is 500 lb, determine by trigonometry (a) the required angle a if the resultant R of the two forces applied at A is to be vertical, (b) the corresponding magnitude of R.

2.13 For the hook support of Prob. 2.7, determine by trigonometry (a) the magnitude and direction of the smallest force P for which the resultant R of the two forces applied to the support is hori-zontal, (b) the corresponding magnitude of R.

2.14 For the steel tank of Prob. 2.11, determine by trigonometry (a) the magnitude and direction of the smallest force P for which the resultant R of the two forces applied at A is vertical, (b) the corresponding magnitude of R.

2.15 Solve Prob. 2.2 by trigonometry.




2.18 Two structural members A and B are bolted to a bracket as shown. Knowing that both members are in compression and that the force is 15 kN in member A and 10 kN in member B, determine by trigonometry the magnitude and direction of the resultant of the forces applied to the bracket by members A and B.

2.19 Two structural members A and B are bolted to a bracket as shown. Knowing that both members are in compression and that the force is 10 kN in member A and 15 kN in member B, determine by trigonometry the magnitude and direction of the resultant of the forces applied to the bracket by members A and B.

2.20 For the hook support of Prob. 2.7, knowing that P 5 75 N and a 5 50, determine by trigonometry the magnitude and direction of the resultant of the two forces applied to the support.

The properties established in Secs. 2.7 and 2.8 may be readily extended to the rectangular components of any vector quantity.

A B

40 20


2.7 RECTANGULAR COMPONENTS OF A FORCE. UNIT VECTORS

In many problems it will be found desirable to resolve a force into two components which are perpendicular to each other. In Fig. 2.18 , the force F has been resolved into a component F x along the x axis and a component F y along the y axis. The parallelogram drawn to obtain the two components is a rectangle , and F x and F y are called rectangular components.

O

FFy

Fx x

y

Fig. 2.18

FyFx

Fx

y

O

Fig. 2.19

The x and y axes are usually chosen horizontal and vertical, respectively, as in Fig. 2.18 ; they may, however, be chosen in any two perpendicular directions, as shown in Fig. 2.19 . In determining the rectangular components of a force, the student should think of the construction lines shown in Figs. 2.18 and 2.19 as being parallel to the x and y axes, rather than perpendicular to these axes. This practice will help avoid mistakes in determining oblique compo-nents as in Sec. 2.6.

272.7 Rectangular Components of a Force. Unit Vectors


2.21 and 2.22 Determine the x and y components of each of the forces shown.

33

PROBLEMS

O

Dimensionsin mm

424 N 408 N

800 N

x

y

900

800

600

560 480

Fig. P2.21

29 lb

51 lbOx

y

90 in.

96 in.

28 in.84 in.

80 in.

48 in.

50 lb

Fig. P2.22

2.23 and 2.24 Determine the x and y components of each of the forces shown.

Fig. P2.23

60 lb

50 lb40 lb

25

y

x

60

50

80 N

120 N

150 N 30

35 40

y

x

Fig. P2.24 2.25 Member BD exerts on member ABC a force P directed along

line BD. Knowing that P must have a 300-lb horizontal compo-nent, determine (a) the magnitude of the force P, (b) its vertical component.

Fig. P2.25

A

B

C D

35

Q


2.26 The hydraulic cylinder BD exerts on member ABC a force P directed along line BD. Knowing that P must have a 750-N com-ponent perpendicular to member ABC, determine (a) the magni-tude of the force P, (b) its component parallel to ABC.

2.27 The guy wire BD exerts on the telephone pole AC a force P directed along BD. Knowing that P must have a 120-N component perpendicular to the pole AC, determine (a) the magnitude of the force P, (b) its component along line AC.

2.28 The guy wire BD exerts on the telephone pole AC a force P directed along BD. Knowing that P has a 180-N component along line AC, determine (a) the magnitude of the force P, (b) its component in a direction perpendicular to AC.

2.29 Member CB of the vise shown exerts on block B a force P directed along line CB. Knowing that P must have a 1200-N horizontal component, determine (a) the magnitude of the force P, (b) its verti-cal component.

2.30 Cable AC exerts on beam AB a force P directed along line AC. Knowing that P must have a 350-lb vertical component, determine (a) the magnitude of the force P, (b) its horizontal component.

34 Statics of Particles

Fig. P2.26

60

50

B

C

D

A

Q

A

B

38

C D


55 55

Q

B

C

A

l l

Fig. P2.29

A

B

C

55

Q

Fig. P2.30

200 N

150 N

100 N30

aa

Fig. P2.35

2.31 Determine the resultant of the three forces of Prob. 2.22.




2.35 Knowing that a 5 35, determine the resultant of the three forces shown.


2.36 Knowing that the tension in cable BC is 725 N, determine the resultant of the three forces exerted at point B of beam AB.

35

840 mm

800 mm

500 N

780 N345 12

135A

B

C

L = 1160 mm

Fig. P2.36

120 lb

80 lb

60 lb

a

a'

20


75 lb50 lb

25

65

35

A

B

C

Fig. P2.41

A

100 lb

100 lb

Fig. 2.26

2.9 Equilibrium of a Particle



2.39 For the collar of Prob. 2.35, determine (a) the required value of a if the resultant of the three forces shown is to be vertical, (b) the corresponding magnitude of the resultant.

2.40 For the beam of Prob. 2.36, determine (a) the required tension in cable BC if the resultant of the three forces exerted at point B is to be vertical, (b) the corresponding magnitude of the resultant.

2.41 Determine (a) the required tension in cable AC, knowing that the resultant of the three forces exerted at point C of boom BC must be directed along BC, (b) the corresponding magnitude of the resultant.

2.42 For the block of Probs. 2.37 and 2.38, determine (a) the required value of a if the resultant of the three forces shown is to be parallel to the incline, (b) the corresponding magnitude of the resultant.

2.9 EQUILIBRIUM OF A PARTICLE In the preceding sections, we discussed the methods for determining the resultant of several forces acting on a particle. Although it has not occurred in any of the problems considered so far, it is quite possible for the resultant to be zero. In such a case, the net effect of the given forces is zero, and the particle is said to be in equilibrium. We thus have the following definition: When the resultant of all the forces acting on a particle is zero, the particle is in equilibrium. A particle which is acted upon by two forces will be in equi-librium if the two forces have the same magnitude and the same line of action but opposite sense. The resultant of the two forces is then zero. Such a case is shown in Fig. 2.26 .


41

PROBLEMS

2.43 Two cables are tied together at C and are loaded as shown. Know-ing that a 5 20, determine the tension (a) in cable AC, (b) in cable BC.

2.44 Two cables are tied together at C and are loaded as shown. Deter-mine the tension (a) in cable AC, (b) in cable BC.

Fig. P2.43

40A B

C

200 kg

a

Fig. P2.44

A

B

C500 N50

30

45

A B

C

P

25

a

Fig. P2.45

75

75

200 kg

C

A

B

Fig. P2.46

2.45 Two cables are tied together at C and are loaded as shown. Know-ing that P 5 500 N and a 5 60, determine the tension in (a) in cable AC, (b) in cable BC.

2.46 Two cables are tied together at C and are loaded as shown. Deter-mine the tension (a) in cable AC, (b) in cable BC.


42 Statics of Particles 2.47 Knowing that a 5 20, determine the tension (a) in cable AC, (b) in rope BC.

Fig. P2.47

5

A

C

B

1200 lb

30 20

300 lb

A

B

C

Fig. P2.48

50

40

A

B

P

Q

FA

FB


FD

FC

FA

FBB

A

D

C

34


2.48 Knowing that a 5 55 and that boom AC exerts on pin C a force directed along line AC, determine (a) the magnitude of that force, (b) the tension in cable BC.

2.49 Two forces P and Q are applied as shown to an aircraft connection. Knowing that the connection is in equilibrium and that P 5 500 lb and Q 5 650 lb, determine the magnitudes of the forces exerted on the rods A and B.

2.50 Two forces P and Q are applied as shown to an aircraft connection. Knowing that the connection is in equilibrium and that the mag-nitudes of the forces exerted on rods A and B are FA 5 750 lb and FB 5 400 lb, determine the magnitudes of P and Q.

2.51 A welded connection is in equilibrium under the action of the four forces shown. Knowing that FA 5 8 kN and FB 5 16 kN, determine the magnitudes of the other two forces.

2.52 A welded connection is in equilibrium under the action of the four forces shown. Knowing that FA 5 5 kN and FD 5 6 kN, determine the magnitudes of the other two forces.


43Problems 2.53 Two cables tied together at C are loaded as shown. Knowing that Q 5 60 lb, determine the tension (a) in cable AC, (b) in cable BC.

2.54 Two cables tied together at C are loaded as shown. Determine the range of values of Q for which the tension will not exceed 60 lb in either cable.

2.55 A sailor is being rescued using a boatswains chair that is suspended from a pulley that can roll freely on the support cable ACB and is pulled at a constant speed by cable CD. Knowing that a 5 30 and b 5 10 and that the combined weight of the boatswains chair and the sailor is 900 N, determine the tension (a) in the support cable ACB, (b) in the traction cable CD.


A

B

C

P = 75 lb

30

30

60

Q

AB

C

D


A B

C

1200 N

2.1 m 2.1 m

Fig. P2.60

2.56 A sailor is being rescued using a boatswains chair that is suspended from a pulley that can roll freely on the support cable ACB and is pulled at a constant speed by cable CD. Knowing that a 5 25 and b 5 15 and that the tension in cable CD is 80 N, determine (a) the combined weight of the boatswains chair and the sailor, (b) the tension in the support cable ACB.

2.57 For the cables of Prob. 2.45, it is known that the maximum allow-able tension is 600 N in cable AC and 750 N in cable BC. Determine (a) the maximum force P that can be applied at C, (b) the corre-sponding value of a.

2.58 For the situation described in Fig. P2.47, determine (a) the value of a for which the tension in rope BC is as small as possible, (b) the corresponding value of the tension.

2.59 For the structure and loading of Prob. 2.48, determine (a) the value of a for which the tension in cable BC is as small as possible, (b) the corresponding value of the tension.

2.60 Knowing that portions AC and BC of cable ACB must be equal, determine the shortest length of cable that can be used to support the load shown if the tension in the cable is not to exceed 870 N.


44 Statics of Particles 2.61 Two cables tied together at C are loaded as shown. Knowing that the maximum allowable tension in each cable is 800 N, deter-mine (a) the magnitude of the largest force P that can be applied at C, (b) the corresponding value of a.


35A B

C

P

50

a

50 lb

x

C

B

A

P

20 in.


A

P

B

160 kg


T

TT T T

(a) (b) (c) (d) (e)

Fig. P2.67

2.62 Two cables tied together at C are loaded as shown. Knowing that the maximum allowable tension is 1200 N in cable AC and 600 N in cable BC, determine (a) the magnitude of the largest force P that can be applied at C, (b) the corresponding value of a.

2.63 Collar A is connected as shown to a 50-lb load and can slide on a frictionless horizontal rod. Determine the magnitude of the force P required to maintain the equilibrium of the collar when (a) x 5 4.5 in., (b) x 5 15 in.

2.64 Collar A is connected as shown to a 50-lb load and can slide on a frictionless horizontal rod. Determine the distance x for which the collar is in equilibrium when P 5 48 lb.

2.65 A 160-kg load is supported by the rope-and-pulley arrangement shown. Knowing that b 5 20, determine the magnitude and direc-tion of the force P that must be exerted on the free end of the rope to maintain equilibrium. (Hint: The tension in the rope is the same on each side of a simple pulley. This can be proved by the methods of Chap. 4.)

2.66 A 160-kg load is supported by the rope-and-pulley arrangement shown. Knowing that a 5 40, determine (a) the angle b, (b) the magnitude of the force P that must be exerted on the free end of the rope to maintain equilibrium. (See the hint for Prob. 2.65.)

2.67 A 600-lb crate is supported by several rope-and-pulley arrange-ments as shown. Determine for each arrangement the tension in the rope. (See the hint for Prob. 2.65.)


AD

B

C

P

25

55

Q


2.68 Solve parts b and d of Prob. 2.67, assuming that the free end of the rope is attached to the crate.

2.69 A load Q is applied to the pulley C, which can roll on the cable ACB. The pulley is held in the position shown by a second cable CAD, which passes over the pulley A and supports a load P. Knowing that P 5 750 N, determine (a) the tension in cable ACB, (b) the magnitude of load Q.

2.70 An 1800-N load Q is applied to the pulley C, which can roll on the cable ACB. The pulley is held in the position shown by a second cable CAD, which passes over the pulley A and supports a load P. Determine (a) the tension in cable ACB, (b) the magnitude of load P.

FORCES IN SPACE

2.12 RECTANGULAR COMPONENTS OF A FORCE IN SPACE

The problems considered in the first part of this chapter involved only two dimensions; they could be formulated and solved in a single plane. In this section and in the remaining sections of the chapter, we will discuss problems involving the three dimensions of space. Consider a force F acting at the origin O of the system of rectangular coordinates x, y, z. To define the direction of F , we draw the vertical plane OBAC containing F ( Fig. 2.30 a ). This plane passes through the vertical y axis; its orientation is defined by the angle f it forms with the xy plane. The direction of F within the plane is defined by the angle u y that F forms with the y axis. The force F may be resolved into a vertical component F y and a horizontal com-ponent F h ; this operation, shown in Fig. 2.30 b , is carried out in plane OBAC according to the rules developed in the first part of the chap-ter. The corresponding scalar components are Fy 5 F cos uy Fh 5 F sin uy (2.16) But F h may be resolved into two rectangular components F x and F z along the x and z axes, respectively. This operation, shown in Fig. 2.30 c , is carried out in the xz plane. We obtain the following expressions for the corresponding scalar components:

Fx 5 Fh cos f 5 F sin uy cos f Fz 5 Fh sin f 5 F sin uy sin f

(2.17)

The given force F has thus been resolved into three rectangular vec-tor components F x , F y , F z , which are directed along the three coor-dinate axes. Applying the Pythagorean theorem to the triangles OAB and OCD of Fig. 2.30 , we write

F2 5 (OA)2 5 (OB)2 1 (BA)2 5 F2y 1 F2h

F2h 5 (OC)2 5 (OD)2 1 (DC)2 5 F2x 1 F

2z

Eliminating F2h from these two equations and solving for F , we obtain the following relation between the magnitude of F and its rectangular scalar components:

F 5 2F2x 1 F2y 1 F

2z (2.18)

(a)

A

B

C

z

y

xO

F

y

(b)

Fh

Fy A

B

C

z

y

xO

Fy

(c)

Fh

Fy

Fx

Fz

E

D

B

Cz

y

xO

Fig. 2.30

452.12 Rectangular Components of a Force in Space


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

Ejercicios Del Tema 1 y Tema 2 - Estatica Beer Jhonson 9ed

Documents

Phllip Jhonson

Asuhan Keperawatan Steven Jhonson

askep syndrom steven jhonson

Sindrom Steven Jhonson

Referat Steven Jhonson Sindrom

Schiffman08 9ed Tb

Case Report Steven Jhonson Syndrome

Steven Jhonson Syndrom

Phillip jhonson

Livro de Exercicios 9ed

Pratica Recurso Agravo 9ed

DOROTHY JHONSON CARAC

Ejercicios Resueltos Beer Jhonson

:;9B7H79?ãD :; 9ED

Steven Jhonson for persentation

CTO 9ed - Oftalmologia.pdf

Sumario Manual Prev 9ed

Steven Jhonson cuii

catalogo blocos de elevação jhonson

Cto 9ed urologia