Solutions for Vector Mechanics For Engineers
Problem 11.CQ3P:
Two model rockets are fired simultaneously from a ledge and follow the trajectories shown....Problem 11.CQ4P:
Ball A is thrown straight up. Which of the following statements about the ball are true at the...Problem 11.CQ5P:
Ball A is thrown straight up with an initial speed v0 and reaches a maximum elevation h before...Problem 11.CQ6P:
Two cars are approaching an intersection at constant speeds as shown. What velocity will car B...Problem 11.CQ7P:
Blocks A and B are released from rest in the positions shown. Neglecting friction between all...Problem 11.89P:
A ball is thrown so that the motion is defined by the equations x=5t and y=2+6t4.9t2 , where x and y...Problem 11.90P:
The motion of a vibrating particle is defined by the position vector r=10(1e3t)i+(4e2tsin15t)j ,...Problem 11.91P:
The motion of a particle is defined by the equations x=(4cost1)(2cost) and y=3sint(2cost) , where x...Problem 11.92P:
The motion of a particle is defined by the equations x=10t5sint and y=105cost , where x and y are...Problem 11.93P:
Engineers are examining how shock absorber designs affect the displacement of a mountain biker's hip...Problem 11.94P:
A girl operates a radio-controlled model car in a vacant parking lot. The girl's position is at the...Problem 11.97P:
An airplane used to drop water on brushfires is flying horizontally in a straight line at 130 knots...Problem 11.98P:
A ski jumper starts with a horizontal take-off velocity of 25 m/s and lands on a straight landing...Problem 11.99P:
A baseball pitching machine "throws" baseballs with a horizontal velocity v0. Knowing that height h...Problem 11.100P:
While delivering newspapers, a girl throws a newspaper with a horizontal velocity v0. Determine the...Problem 11.101P:
A pump is located near the edge of the horizontal platform shown. The nozzle at A discharges water...Problem 11.102P:
In slow pitch softball, the underhand pitch must reach a maximum height of between 1.8 m and 3.7 m...Problem 11.103P:
A volleyball player serves the ball with an initial velocity v0 of magnitude 13.40 m/s at an angle...Problem 11.104P:
A golfer hits a golf ball with an initial velocity of 140 ft/s at an angle of 25° with the...Problem 11.105P:
A homeowner uses a snowblower to clear his driveway. Knowing that the snow is discharged at an...Problem 11.106P:
At halftime of a football game, souvenir balls are thrown to the spectators with a velocity v0....Problem 11.107P:
A basketball player shoots when she is 16 ft from the backboard. Knowing that the ball has an...Problem 11.108P:
A tennis player serves the ball at a height h=2.5 m with an initial velocity of v0 at an angle of 5°...Problem 11.109P:
The nozzle at A discharges cooling water with an initial velocity v0 at an angle of 6° with the...Problem 11.110P:
While holding one of its ends, a worker lobs a coil of rope over the lowest limb of a tree. If he...Problem 11.115P:
An oscillating garden sprinkler which discharges water with an initial velocity v0 of 8 m/s is used...Problem 11.116P:
A nozzle at A discharges water with an initial velocity of 36 ft/s at an angle with the horizontal....Problem 11.117P:
The velocities of skiers A and B are as shown. Determine the velocity of A with respect to B.Problem 11.118P:
The three blocks shown move with constant velocities. Find the velocity of each block, knowing that...Problem 11.119P:
Three seconds after automobile B passes through the intersection shown, automobile A passes through...Problem 11.120P:
Shore-based radar indicates that a ferry leaves its slip with a velocity v=18km/h70 , while...Problem 11.121P:
Airplanes A and B are flying at the same altitude and are tracking the eye of hurricane C. The...Problem 11.123P:
Knowing that at the instant shown block B has a velocity of 2 ft/s to the right and an acceleration...Problem 11.124P:
Knowing that at the instant shown block A has a velocity of 8 in./s and an acceleration of 6 in./s2,...Problem 11.125P:
A boat is moving to the right with a constant deceleration of 0.3 m/s2 when a boy standing on the...Problem 11.126P:
The assembly of rod A and wedge B starts from rest and moves to the right with a constant...Problem 11.127P:
Coal discharged from a dump truck with an initial velocity (vc)0=5ft/s50 falls onto conveyor belt B....Problem 11.128P:
Conveyor belt A, which forms a 20° angle with the horizontal, moves at a constant speed of 4 ft/s...Problem 11.129P:
During a rainstorm, the paths of the raindrops appear to form an angle of 30° with the vertical and...Problem 11.130P:
Instruments in airplane A indicate that; with respect to the air, the plane is headed 30° north of...Browse All Chapters of This Textbook
Chapter 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 Motion
Chapter 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 - Translations 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 VibrationsChapter B - Mass Moment Of Inertia
Book Details
A primary objective in a first course in mechanics is to help develop a student's ability first to analyze problems in a simple and logical manner and then to apply basic principles to their solutions. A strong conceptual understanding of these basic mech
Sample Solutions for this Textbook
We offer sample solutions for Vector Mechanics For Engineers homework problems. See examples below:
Chapter 11.1, Problem 11.12PChapter 11.1, Problem 11.19PChapter 11.1, Problem 11.29PChapter 11.2, Problem 11.57PChapter 11.2, Problem 11.60PGiven: The particle starts from origin with an initial displacement of x0=−48 ft. Concept used: The...Chapter 11.3, Problem 11.76PChapter 11.4, Problem 11.90PChapter 11.4, Problem 11.91P
Chapter 11.4, Problem 11.92PGiven information: Initial velocity v0=75 m/s Rocket lands at distance d=100 m from point A For a...Given information: Time t=3 s r=3+0.5cos(4θ) θ=−π4t2+πt Concept used: Velocity vr=r˙, vθ=rθ˙...Given information: Length of rope is defined as, r=600−18t5/2 Constant velocity of the boat is 15 kn...Given information: R=A(t+1)θ=Btz=Ct(t+1) The cylindrical co-ordinates of velocity are defined as:...Given information: According to problem 11.95 : r=(Rtcosωnt)i+ctj+(Rtsinωnt)k The first derivative...Given information: According to problem 11.96, r=(Atcost)i+(A t2+1)j+(Btsint)k A=3, B=1 The first...Chapter 11, Problem 11.182RPGiven information: Distance between A and B is equal to 5 m r¨=−1.0 m/s2 θ¨=−0.5 rad/s2 Velocity of...Chapter 12.1, Problem 12.18PChapter 12.1, Problem 12.19PGiven information: Mass of block A =10 kg Mass of block B=C =5 kg Time t=2sec Let the position...Given information: Weight of panel =40 lb Weight of the counterweight =25 lb First, we draw the free...Chapter 12.1, Problem 12.31PGiven: ρ=150 mm=0.15 m m=0.5 kg First of all, a=an=v2ρ Where, ρ=150 mm=0.15 m ←+∑Fx=ma :...Chapter 12.1, Problem 12.47PChapter 12.1, Problem 12.66PChapter 12.1, Problem 12.70PGiven information: ms = 500 kgh = 4500 kmrm = 1737 kmmm = 0.01230 me Formula used: F = GMmr2...Chapter 12.2, Problem 12.91PChapter 12.3, Problem 12.105PGiven information: rA=9.3×103mi vA=20,000ft/s rC=5600mi MVenus=0.82MEarth If the trajectory is an...Given information: rA=202×106mi rB=92×106mi rA'=164.5×106mi rB'=85.5×106mi MSun=332.8×103×MEarth If...Chapter 12, Problem 12.122RPChapter 12, Problem 12.133RPChapter 13.1, Problem 13.12PChapter 13.1, Problem 13.22PChapter 13.1, Problem 13.42PChapter 13.1, Problem 13.43PChapter 13.1, Problem 13.45PConsider the diagram of the suspended ball by an inextensible cord. Let us consider at point “A” as...Given: V(x,y,z)=−(x2+y2+z2)1/2 x component: Px=−∂V∂x Px=−∂[−(x2+y2+z2)1/2]∂x Px=x(x2+y2+z2)−1/2 y...Given information: h1 = 225 miϕB = 60oh2 = 40 mi Formula used: GM = gR2 T = 12mv2 V = −GMmr L = mvr...Given information: The altitude of the space vehicle at point A, ha = 225mi. The altitude of the...Given information: Max altitude αR Initial velocity v0 Radius of planet R Launch angle ϕ0 Escape...Given information: Radius rmin Speed vmax Planet mass M Concept used: Following formulae will be...Chapter 13.3, Problem 13.145PGiven information: Weight of hammer is 1.5 lb. The velocity of the rivet is 20 ft/s. “A force acting...Given information: Weight of the bullet, mB=0.5 oz Weight of A and C, mA=mC=3 lb Coefficient of...Given information: Speed of the ball =vx=2 →ms−1 Mass of the ball =m=75g Mass of the plate =M=400g...Given information: Mass of each bumper car is equal to 200 kg. Riders A, B and C have mass of 40 kg,...Given information: α=45° Rock A falls from a distance of 20 m. h=30 md=20 m The total linear...Chapter 13.4, Problem 13.182PChapter 13.4, Problem 13.188PChapter 13, Problem 13.190RPChapter 13, Problem 13.201RPChapter 14.1, Problem 14.10PChapter 14.1, Problem 14.14PChapter 14.1, Problem 14.30PChapter 14.2, Problem 14.53PChapter 14.2, Problem 14.54PChapter 14.3, Problem 14.74PChapter 14.3, Problem 14.75PChapter 14.3, Problem 14.80PChapter 14.3, Problem 14.100PChapter 14, Problem 14.105RPChapter 14, Problem 14.116RPChapter 15.1, Problem 15.3PChapter 15.1, Problem 15.24PChapter 15.1, Problem 15.26PChapter 15.2, Problem 15.45PGiven information: (vA)x=12 in/s(vB)x=− 4 in/s(vC)y=−24 in/s The relative velocity of A with respect...Chapter 15.2, Problem 15.59PChapter 15.3, Problem 15.84PGiven information: At the instant shown, the velocity of collar D is 1.6 m s−1, upward. Concept...Chapter 15.3, Problem 15.97PChapter 15.4, Problem 15.128PGiven information: Angular velocity of bar AB is 10 rad/s clockwise. Angular acceleration of bar AB...Given information: Angular velocity of bar AB is 10 rad/s clockwise. Angular acceleration of bar AB...Chapter 15.4, Problem 15.135PGiven information: Constant angular velocity of rod AE is 6 rad/s clockwise. The constant relative...Chapter 15.5, Problem 15.173PGiven information: Angular velocity of rod AP is 5 rad/s counter clockwise. Angular acceleration of...Chapter 15.6, Problem 15.202PChapter 15.6, Problem 15.218PChapter 15.6, Problem 15.219PChapter 15.7, Problem 15.244PChapter 15.7, Problem 15.245PChapter 15, Problem 15.248RPChapter 15, Problem 15.257RPChapter 16.1, Problem 16.36PChapter 16.1, Problem 16.37PChapter 16.1, Problem 16.39PChapter 16.1, Problem 16.44PChapter 16.1, Problem 16.45PChapter 16.1, Problem 16.71PChapter 16.1, Problem 16.72PChapter 16.1, Problem 16.74PGiven: Weight of rod AB is 2 lb. Weight of rod BC is 4 lb. Angular velocity is 10 rad/s. Angle θ is...Chapter 16.2, Problem 16.116PGiven information: Pole length, L=20ft Weight, W=100lb Angular velocity, ω=1rad/s Horizontal force,...Given information: Rod BC mass, m = 6kg Disk mass, m = 10kg Rod CD mass, m = 5kg Disk AB velocity...Chapter 16.2, Problem 16.136PChapter 16.2, Problem 16.138PChapter 16.2, Problem 16.141PGiven information: The attached rod A mass is=0.8kg And length is=160mm Rod BP mass is=1kg Length...Chapter 16, Problem 16.153RPGiven information: Cylinder weight with hole = 16 lb Cylinder weight without hole = 15 lb Angular...Chapter 17.1, Problem 17.11PChapter 17.1, Problem 17.12PGiven information: Mass of block (mb) = 15kg. Mass of cylinder (ma) = 5kg. Radius of gyration (k) =...Chapter 17.1, Problem 17.35PChapter 17.1, Problem 17.45PGiven: Wheel is initially at rest and it is relased from an indined surface from rest. Wheel radius...Given: Mass of cylinder, m = 6 kg Radius of cylinder, r = 125 mm = 0.125 m Angular velocity of...Given information: Mass of coller A = mA=1.8 kg. Mass of coller B = mB=0.7 kg. The velocity of...Given: The weight of collar = ωc=4lb=1.814kg Mass of ring = ωr=6lb=2.721kg The radius of the ring,...Chapter 17.3, Problem 17.111PChapter 17.3, Problem 17.118PChapter 17.3, Problem 17.120PGiven: Mass of block is m, mass of the disk is M and Falling distance is h. Concept used:...Chapter 17, Problem 17.135RPGiven information:...Given information: The mass of each L-shaped arm is 5 kg, speed of assembly is 360 rpm. The below...Given information: The mass of the each plate is 4 kg and the corresponding impulse is −(2.4 N⋅s)k....Given information: The mass of the each plate is 4 kg and the corresponding impulse is (2.4 N⋅s)j....Given information: Mass of circular plate is m, falling velocity of the plate is v¯0, impact is...Given information: The weight of the space probe is 3000 lb, the weight of the meteorite is 5 oz,...Given information: The total mass is 600 g, the distance between the bearing is 150 mm and the...Given information: The total mass is 600 g, the distance between the bearing is 150 mm, the time is...Given information: Angular velocity of disk in z-direction is 60 rad/s, radius of the disk is 3 in...Given information: Angular velocity of disk in z-direction is 60 rad/s, radius of the disk is 3 in...Chapter 18.2, Problem 18.104PGiven information: The below figure represent the schematic diagram of the system. Figure-(1) Write...Chapter 18.3, Problem 18.129PChapter 18.3, Problem 18.130PGiven information: The height of the solid cone is 180 mm, the radius of the circular cone is 60 mm,...Write the expression for the force. F=mrω2 Here, the mass is m, the speed is ω and the radius is r....Chapter 18, Problem 18.150RPChapter 19.1, Problem 19.10PGiven information: Mass of block m=3 lb Spring constant k=2 lb/in. Velocity v=90 in./s For simple...Given information: Angle θ=5° Length of cord l=40 in. The equation of a simple harmonic motion in...Given information: Weight of rod AB = 9Kg Spring constant kA=kB=850 Ν/m The free body diagram of the...Given information: Weight of rod W=15 lb Weight of disc Wdisc=12 lb Spring constant k=30 lb/in.=360...Given information: Mass of collar mC=1 Κg Mass of rod mR=3 Κg Length of rod L=750 mm The forces...Given information: The mass of gear C is m, and the mass of gear A is 4m. Calculations: For the...Given information: The mass of gear C is m, and the mass of gear A is 4m. Calculations: For the...Given information: Mass of the hollow-spherical shell is 500-g. Radius of the spherical shell is 80...Given: Mass of attached sphere is 2 kg. Spring constant is 3.6 kN/m. Vertical deflection is...Given: Amplitude of vibration when 1 collar is on the spring is 15 mm. Amplitude of vibration when 2...Given information: The system is underdamped, the time period between two successive points is...Given information: The mass of the block A is 2.4 kg, the mass of the block B is 0.9 kg, the spring...Given information: The weight of two counter rotating eccentric mass exciters is 14 oz, the radius...Given information: The weight of the wheel is 47 lb, the torsional spring constant of the wire is...Given information: The mass of the motor is 400 kg, the constant of the spring is 150 kN/m, the...Chapter B, Problem B.1PGiven information: The diameter of the formed steel wire is 18 in and the specific weight of the...Chapter B, Problem B.56PGiven information: The diameter of the formed steel wire is 18 in, unit vector is (−3i−6j+2k)/7 and...Chapter B, Problem B.71PGiven information: The thin bent plate with uniform density, the weight of both the plates is W, the...Chapter B, Problem B.73PGiven information: The mass per unit length of the steel is 0.056 kg/m. Draw the diagram for the...
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