## Solutions for Vector Mechanics for Engineers: Statics and Dynamics

Problem 2.1P:

Two forces are applied as shown to a hook. Determine graphically the magnitude and direction of...Problem 2.2P:

Two forces are applied as shown to a bracket support. Determine graphically the magnitude and...Problem 2.3P:

Two forces P and Q are applied as shown at point A of a hook support. Knowing that P = 75 N and Q =...Problem 2.4P:

Two forces P and Q are applied as shown at point A of a hook support. Knowing that P = 60 lb and Q =...Problem 2.5P:

A stake is being pulled out of the ground by means of two ropes as shown. Knowing that = 30,...Problem 2.6P:

A telephone cable is clamped at A to the pole AB. Knowing that the tension in the left-hand portion...Problem 2.7P:

A telephone cable is clamped at A to the pole AB. Knowing that the tension in the right-hand portion...Problem 2.8P:

A disabled automobile is pulled by means of two ropes as shown. The tension in rope AB is 2.2 kN,...Problem 2.9P:

A disabled automobile is pulled by means of two ropes as shown. Knowing that the tension in rope AB...Problem 2.10P:

Two forces are applied as shown to a hook support. Knowing that the magnitude of P is 35 N,...Problem 2.11P:

A steel tank is to be positioned in an excavation. Knowing that = 20, determine by trigonometry (a)...Problem 2.12P:

A steel tank is to be positioned in an excavation. Knowing that the magnitude of P is 500 lb,...Problem 2.13P:

A steel tank is to be positioned in an excavation. Determine by trigonometry (a) the magnitude and...Problem 2.14P:

For the hook support of Prob. 2.10, determine by trigonometry (a) the magnitude and direction of the...Problem 2.15P:

The barge B is pulled by two tugboats A and C. At a given instant, the tension in cable AB is 4500...Problem 2.16P:

Solve Prob. 2.1 by trigonometry.Problem 2.17P:

Solve Prob. 2.4 by trigonometry.Problem 2.18P:

For the stake of Prob. 2.5, knowing that the tension in one rope is 120 N, determine by trigonometry...# Browse All Chapters of This Textbook

Chapter 2 - Statics Of ParticlesChapter 2.1 - Addition Of Planar ForcesChapter 2.2 - Adding Forces By ComponentsChapter 2.3 - Forces And Equillibrium In A PlaneChapter 2.4 - Adding Forces In SpaceChapter 2.5 - Forces And Equillibrium In SpaceChapter 3 - Rigid Bodies: Equivalent Systems Of ForcesChapter 3.1 - Forces And MometsChapter 3.2 - Moment Of A Force About An AxisChapter 3.3 - Couples And Force-couple Systems

Chapter 3.4 - Simplifying Systems Of ForcesChapter 4 - Equilibrium Of Rigid BodiesChapter 4.1 - Equilibrium In Two DimensionsChapter 4.2 - Two Special CasesChapter 4.3 - Equillibrium In Three DimensionsChapter 5 - Distributed Forces: Centroids Abd Centers Of GravityChapter 5.1 - Planar Centers Of Gravity And CentroidsChapter 5.2 - Further Considerations Of CentroidsChapter 5.3 - Additional Applications Of CentroidsChapter 5.4 - Centers Of Gravity And Centroids Of VolumesChapter 6 - Analysis Of StructuresChapter 6.1 - Analysis Of TrussesChapter 6.2 - Other Truss AnalysesChapter 6.3 - FramesChapter 6.4 - MachinesChapter 7 - Internal Forces And MomentsChapter 7.1 - Internal Forces In MembersChapter 7.2 - BeamsChapter 7.3 - Relations Among Load, Shear, And Bending MomentChapter 7.4 - CablesChapter 7.5 - Catenary CablesChapter 8 - FrictionChapter 8.1 - The Laws Of Dry FrictionChapter 8.2 - Wedges And ScrewsChapter 8.3 - Friction On Axles, Disks, And WheelsChapter 8.4 - Belt FrictionChapter 9 - Distributed Forces: Moments Of InertiaChapter 9.1 - Moments Of Inertia Of AreasChapter 9.2 - Parallel-axis Theorem And Composite AreasChapter 9.3 - Transformation Of Moments Of InertiaChapter 9.4 - Mohr's Circle For Moments Of InertiaChapter 9.5 - Mass Moments Of InertiaChapter 9.6 - Additional Concepts Of Mass Moments Of InertiaChapter 10 - Method Of Virtual WorkChapter 10.1 - The Basic MethodChapter 10.2 - Work, Potential Energy, And StabilityChapter 11 - Kinematics Of ParticlesChapter 11.1 - Rectilinear Motion Of ParticlesChapter 11.2 - Special Cases And Relative MotionChapter 11.3 - Graphical SolutionsChapter 11.4 - Curvilinear Motion Of ParticlesChapter 11.5 - Non-rectangular ComponentsChapter 12 - Kinetics Of Particles: Newton’s Second LawChapter 12.1 - Newton’s Second Law And Linear MomentumChapter 12.2 - Angular Momentum And Orbital MotionChapter 12.3 - Applications Of Central-force MotionChapter 13 - Kinetics Of Particles: Energy And Momentum MethodsChapter 13.1 - Work And EnergyChapter 13.2 - Conservation Of EnergyChapter 13.3 - Impulse And MomentumChapter 13.4 - ImpactsChapter 14 - Systems Of ParticlesChapter 14.1 - Applying Newton’s Second Law And Momentum Principles To Systems Of ParticlesChapter 14.2 - Energy And Momentum Methods For A System Of ParticlesChapter 14.3 - Variable Systems Of ParticlesChapter 15 - Kinematics Of Rigid BodiesChapter 15.1 - Translation And Fixed-axis RotationChapter 15.2 - General Plane Motion: VelocityChapter 15.3 - Instantaneous Center Of RotationChapter 15.4 - General Plane Motion: AccelerationChapter 15.5 - Analyzing Motion With Respect To A Rotating FrameChapter 15.6 - Motion Of A Rigid Body In SpaceChapter 15.7 - Motion Relative To A Moving Reference FrameChapter 16 - Plane Motion Of Rigid Bodies: Forces And AccelerationsChapter 16.1 - Kinetics Of A Rigid BodyChapter 16.2 - Constrained Plane MotionChapter 17 - Plane Motion Of Rigid Bodies: Energy And Momentum MethodsChapter 17.1 - Energy Methods For A Rigid BodyChapter 17.2 - Momentum Methods For A Rigid BodyChapter 17.3 - Eccentric ImpactChapter 18 - Kinetics Of Rigid Bodies In Three DimensionsChapter 18.1 - Energy And Momentum Of A Rigid BodyChapter 18.2 - Motion Of A Rigid Body In Three DimensionsChapter 18.3 - Motion Of A GyroscopeChapter 19 - Mechanical VibrationsChapter 19.1 - Vibrations Without DampingChapter 19.2 - Free Vibrations Of Rigid BodiesChapter 19.3 - Applying The Principle Of Conservation Of EnergyChapter 19.4 - Forced VibrationsChapter 19.5 - Damped Vibrations

# Sample Solutions for this Textbook

We offer sample solutions for Vector Mechanics for Engineers: Statics and Dynamics homework problems. See examples below:

Chapter 2.1, Problem 2.1PChapter 2.2, Problem 2.22PChapter 2.2, Problem 2.36PChapter 2.3, Problem 2.50PChapter 2.3, Problem 2.57PChapter 2.3, Problem 2.65PThe following figure gives the sketch of the system given in the problem. The tension in the cables...Write the equation to find the magnitude of the vector AB. |AB|=ABx2+ABy2+ABz2 (I) Write the...Chapter 2.5, Problem 2.107P

Chapter 2.5, Problem 2.112PChapter 2.5, Problem 2.115PChapter 2, Problem 2.127RPChapter 2, Problem 2.136RPChapter 3.1, Problem 3.17PWrite an expression to calculate the moment of the force at the origin O due to the force acting at...Chapter 3.1, Problem 3.20PChapter 3.2, Problem 3.61PChapter 3.2, Problem 3.64PChapter 3.2, Problem 3.65PChapter 3.3, Problem 3.76PChapter 3.3, Problem 3.79PChapter 3.3, Problem 3.85PChapter 3.4, Problem 3.104PChapter 3.4, Problem 3.120PWrite the equation of the distance between AC. dAC=r12+r22+r32 (I) Here, the distance between AC is...The diagram for the force-couple system is given below: Refer fig 1. Write the equation of resultant...Chapter 3, Problem 3.147RPThe z-component of the replaced equivalent couple M2z is zero, magnitude of F1 is 77 N and moment M1...Chapter 4.1, Problem 4.23PTake vectors along positive x and y axis are positive. Let A is the reaction at the point A , B is...Chapter 4.1, Problem 4.27PChapter 4.1, Problem 4.50PGiven information: The size of the identical plates is 500 mm×750 mm. Number of plates is 8. The...Chapter 4.1, Problem 4.60PChapter 4.2, Problem 4.69PChapter 4.2, Problem 4.71PChapter 4.2, Problem 4.90PChapter 4.3, Problem 4.105PChapter 4.3, Problem 4.106PChapter 4.3, Problem 4.107PThe tension in the cable DCE can be represented as TCD and TCE respectively. The total tension on...Chapter 4.3, Problem 4.129PThe free-body diagram is shown in figure 1. The weight of the truck is 3200 lb and it is lifting...The free-body diagram is shown in figure 1. Write the expression for the tension in the cable....Chapter 5.1, Problem 5.16PChapter 5.1, Problem 5.17PChapter 5.1, Problem 5.29PChapter 5.2, Problem 5.43PChapter 5.2, Problem 5.44PChapter 5.2, Problem 5.48PChapter 5.3, Problem 5.80PGiven that the width of the dam section w is 1 ft. The height of the dam at the point C is h=18 ft....Sketch the free body diagram of the dam as shown in the Figure 1. Write the equation for the...Refer Fig. P5.21 and Fig. 1. Let the element of volume of the disk be of radius r and thickness dx....Chapter 5.4, Problem 5.132PChapter 5.4, Problem 5.133PRefer Figure 1 and Figure 2. Consider an elemental section of the given section. Write an expression...Chapter 5, Problem 5.137RPChapter 5, Problem 5.138RPThe free-body diagram of the entire truss is shown in figure 1. Refer to figure 1 and use symmetry....The free-body diagram of the entire truss is shown in figure 1. Refer to figure 1 and use symmetry....Chapter 6.1, Problem 6.38PChapter 6.1, Problem 6.39PChapter 6.2, Problem 6.47PChapter 6.2, Problem 6.56PChapter 6.2, Problem 6.70PChapter 6.3, Problem 6.88PChapter 6.3, Problem 6.89PChapter 6.3, Problem 6.103PChapter 6.3, Problem 6.104PChapter 6.3, Problem 6.121PChapter 6.4, Problem 6.157PTake all vectors along the x axis and y axis as positive. Let P is the force exerted on the bucket...Chapter 6.4, Problem 6.159PChapter 6.4, Problem 6.162PChapter 6, Problem 6.164RPChapter 6, Problem 6.165RPSketch the free body diagram for the internal forces acting on the frame and pulley system as shown...Chapter 7.1, Problem 7.16PChapter 7.2, Problem 7.35PChapter 7.2, Problem 7.60PRefer Figure 1. Write an expression to calculate the counter clockwise moment at point A. ΣMA=0...Chapter 7.3, Problem 7.86PChapter 7.3, Problem 7.87PRefer Fig P7.88. Write the equation for change in shear moment with distance. dVdx=−w (I) Here, V is...Chapter 7.4, Problem 7.99PThe free body diagram for the portion AC is depicted below: Refer fig 1, Write the equation of net...The figure 1 below shows the cable and which makes the curve due the load w. Write the expression...Given information: The length of the cable AB is L=10 ft. The value of angle θ is 30°. The collar at...Given information: The length of the cable AB is L=10 ft. The value of angle θ is 45°. The collar at...Chapter 7, Problem 7.154RPGiven information: The moment applied at A is M=0. Calculation: Show the free-body diagram of the...Chapter 8.1, Problem 8.13PGiven information: The mass of the package A, B, and C is mA=mB=mC=4 kg. The static coefficient of...Chapter 8.1, Problem 8.37PChapter 8.1, Problem 8.42PChapter 8.1, Problem 8.43PChapter 8.2, Problem 8.64PChapter 8.2, Problem 8.65PWrite the equation of the magnitude of the couple as follows; M=23μkPsinθR23−R13R22−R12 Here, the...Chapter 8.3, Problem 8.97PChapter 8.4, Problem 8.118PGiven information: The mass of the block C is mC=100 kg. The coefficient of static friction is...Chapter 8.4, Problem 8.121PChapter 8, Problem 8.134RPGiven information: The weight of the cabinet is W=120 lb. The coefficient of static friction between...Given information: The curve equation is x2a2+y2b2=1. Calculation: Sketch the vertical strip shaded...Given information: The equation of the curve is y2=c+k2x2 The equation of the curve is y1=k1x2...Chapter 9.1, Problem 9.24PChapter 9.2, Problem 9.41PCalculation: Sketch the cross section as shown in Figure 1. Refer to Figure 1. Find the area (A1) of...Chapter 9.2, Problem 9.48PChapter 9.3, Problem 9.79PChapter 9.3, Problem 9.82PSketch the cross section as shown in Figure 1. Express the product of inertia as shown below:...Calculation: Sketch the cross section shown in Figure 1. Refer to Figure 1. Find the area (A1) of...Given information: The thickness (t) of sheet steel is 2 mm. The density ρ of steel is 7,850 kg/m3....Chapter 9.5, Problem 9.137PChapter 9.5, Problem 9.145PGiven information: The mass of the cylinder is denoted by m. The length of the circular cylinder is...Calculation: Refer to problem 9.145 and 9.149. Ix=26.4325×10−3 kg⋅m2Iy=31.1726×10−3...Given information: Refer Problem 9.168. Show the moment of inertia as follows:...Chapter 9, Problem 9.185RPSketch the cross section as shown in Figure 1. Refer to Figure 9.13. The moment of inertia I¯x about...Given information: The spring constant is k=15 kN/m. Calculation: Show the free-body diagram of the...Chapter 10.1, Problem 10.6PGiven information: The magnitude of the force P is 4 kN. The distance between the point A and B is...Chapter 10.1, Problem 10.22PFind the force at A; Show the free-body diagram of the continuous beam as in Figure 1. Consider the...Given information: The weight of the slender rod AB is W=300 lb. The length of the slender rod AB is...Chapter 10.2, Problem 10.97PChapter 10.2, Problem 10.98PChapter 10.2, Problem 10.100PChapter 10, Problem 10.101RPChapter 11.1, Problem 11.4PChapter 11.1, Problem 11.5PChapter 11.1, Problem 11.29PChapter 11.2, Problem 11.57PGiven information: The relative change in position of block C with respect to block A (yC/A) is 280...Chapter 11.3, Problem 11.61PChapter 11.3, Problem 11.64PChapter 11.4, Problem 11.96PChapter 11.4, Problem 11.121PChapter 11.4, Problem 11.127PGiven Information: The small boat travel north at the speed (vB)y of 15 km/h at an angle (θ) of 50°...Chapter 11.5, Problem 11.141PChapter 11.5, Problem 11.163PChapter 11.5, Problem 11.164PChapter 11.5, Problem 11.179PChapter 11.5, Problem 11.180PChapter 11, Problem 11.182RPChapter 11, Problem 11.192RPCalculation: Sketch the general diagram of systems as shown in Figure (1). Write total length of...Chapter 12.1, Problem 12.18PChapter 12.1, Problem 12.19PChapter 12.1, Problem 12.22PChapter 12.1, Problem 12.28PChapter 12.1, Problem 12.31PChapter 12.1, Problem 12.52PChapter 12.1, Problem 12.65PChapter 12.2, Problem 12.85PGiven information: The altitude of circular orbit of the satellite from the surface of the earth (r)...Given information: The mass of the Venus is 0.82 times the mass of the earth. The radius of...Chapter 12, Problem 12.122RPChapter 12, Problem 12.133RPChapter 13.1, Problem 13.12PGiven information: The initial speed of the train (v1) is 30mi/h. The coefficient of kinetic...Chapter 13.1, Problem 13.26PChapter 13.1, Problem 13.29PChapter 13.1, Problem 13.30PChapter 13.2, Problem 13.64PChapter 13.2, Problem 13.73PChapter 13.2, Problem 13.101PGiven information: The altitude between the earth to point A (h1) is 200mi. The altitude between the...Given information: The altitude of the space vehicle in a circular orbit (hA) is 225mi. The altitude...Chapter 13.2, Problem 13.116PChapter 13.3, Problem 13.129PChapter 13.3, Problem 13.130PChapter 13.3, Problem 13.149PChapter 13.3, Problem 13.150PChapter 13.4, Problem 13.162PGiven information: The weight of the block A (WA) is 0.8lb. The weight of the block B (WB) is 0.8lb....Chapter 13.4, Problem 13.184PChapter 13.4, Problem 13.188PChapter 13, Problem 13.190RPChapter 13, Problem 13.201RPChapter 14.1, Problem 14.11PChapter 14.1, Problem 14.12PChapter 14.1, Problem 14.14PChapter 14.2, Problem 14.48PChapter 14.2, Problem 14.53PGiven information: The discharge of coal from first conveyor belt at the rate Q=150 kg/s. The...Chapter 14.3, Problem 14.99PChapter 14.3, Problem 14.100PGiven information: Consider the initial mass of the rocket is denoted by m0. The rate of consumption...Chapter 14, Problem 14.105RPChapter 15.1, Problem 15.3PGiven information: The initial speed (ω0) of sprocket wheel and the chain is 600...Chapter 15.1, Problem 15.35PChapter 15.2, Problem 15.45PChapter 15.2, Problem 15.57PChapter 15.2, Problem 15.71PChapter 15.3, Problem 15.80PGiven information: The angular velocity of the arm DE is ωDE=3 rad/s(Clockwise). Calculation: Show...Chapter 15.3, Problem 15.93PChapter 15.4, Problem 15.123PChapter 15.4, Problem 15.128PChapter 15.4, Problem 15.133PGiven information: The constant angular velocity of AB is ωAB=4 rad/s(Clockwise)=−4k. Calculation:...Chapter 15.5, Problem 15.154PChapter 15.5, Problem 15.176PGiven information: The constant angular velocity of the bar AD is ωAD=4 rad/s. The angular velocity...Chapter 15.6, Problem 15.202PGiven information: The collar B moves towards D at a constant speed of vB=50 mm/s. The length of rod...Given information: The collar B moves towards D at a constant speed of vB=50 mm/s. The length of rod...Given information: The side length of the square plate is 2r. The shaft rotates with a constant...Given information: The radius of disk is r=130 mm. The length of rod CD is lCD=500 mm. The constant...Chapter 15, Problem 15.248RPGiven information: The value of the angle is θ=90°. Calculation: Consider the value of the angle as...Chapter 16.1, Problem 16.20PChapter 16.1, Problem 16.34PChapter 16.1, Problem 16.37PChapter 16.1, Problem 16.39PThe force pulled between cylinders A and B (P) is 2.00 lb. The weight of the cylinder A (WA) is 5...Chapter 16.1, Problem 16.43PChapter 16.1, Problem 16.44PThe weight of the cylinder A (WA) is 5 lb. The weight of the cylinder B (WB) is 5 lb. The weight of...Given information: The weight of the ladder is W=40 lb. The length of the ladder is l=30 ft. The...Chapter 16.2, Problem 16.127PChapter 16.2, Problem 16.134PChapter 16.2, Problem 16.135PGiven information: The mass of the rod BC is mBC=6 kg. The mass of the disk is md=10 kg. The mass of...Chapter 16.2, Problem 16.138PChapter 16.2, Problem 16.141PChapter 16.2, Problem 16.142PChapter 16, Problem 16.153RPChapter 16, Problem 16.161RPChapter 17.1, Problem 17.12PChapter 17.1, Problem 17.14PChapter 17.1, Problem 17.16PGiven information: The mass of the turbine disk is mturbine=30 kg. The centroidal radius of gyration...Chapter 17.1, Problem 17.45PGiven information: The mass (m) of the tube AB is 1.6 kg. The initial angular velocity (ω1) of the...Given information: The mass (mR) of the rod AB is 4 kg. The mass (mT) of the tube CD is 6 kg. The...Chapter 17.2, Problem 17.89PChapter 17.2, Problem 17.91PChapter 17.3, Problem 17.111PChapter 17.3, Problem 17.115PGiven information: The weight (WS) of the sphere is 3 lb. The radius (r) of the sphere is 3 in.. The...Chapter 17.3, Problem 17.133PChapter 17, Problem 17.135RPChapter 18.1, Problem 18.32PGiven information: The weight of the space probe (w′) is 3,000 lb. The radius of gyration along x...Given information: The mass of the square plate is m. The side of a square plate is a. The angular...Chapter 18.1, Problem 18.54PGiven information: The weight (W) of the disk is 6 lb. The radius (r) of the disk is 3 in.. The...Given information: The weight (W) of the disk is 6 lb. The radius (r) of the disk is 3 in.. The...Chapter 18.2, Problem 18.103PChapter 18.2, Problem 18.104PGiven information: The weight of geostationary satellite (W) is 800 lb. The angular velocity of the...Given information: The position of the sphere β is zero. The rate of precession ϕ˙0=17g/11a....Given information: The position of the sphere β is zero. The largest value of β in the ensuing...Chapter 18, Problem 18.147RPGiven Information: The weight of the disk (W) is 6 lb. The constant angular velocity (ω1) with...Given Information: The mass (m1) of the electromagnet is 150 kg. The mass (m2) of the scrap steel is...Chapter 19.1, Problem 19.15PGiven Information: The cord length (lAB) of the bob is 1.2 m. At rest the angle (θA) is 5°. The...Chapter 19.2, Problem 19.37PChapter 19.2, Problem 19.47PChapter 19.2, Problem 19.50PGiven information: The length of rod AB and CD is l. The mass of the gear C is m. The mass of the...Given information: The length of rod AB and CD is l. The mass of the gear C is m. The mass of the...Given information: The mass (mS) of the sphere is 2 kg. The mass (mABC) of the bar ABC is 1.5 kg....Given information: The weight of the bob (WB) is 2.75 lb. The weight of the collar (WC) is 3 lb. The...Chapter 19.4, Problem 19.112PCalculation: Since (c>cc) which is over damped, the wavelength λ1 and λ2 is less than zero. The...Given information: The magnitude of periodic force (P) is P=Pmsinωft. Calculation: The expression...Chapter 19.5, Problem 19.151PChapter 19, Problem 19.159RPChapter 19, Problem 19.165RP

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