Vector Mechanics for Engineers: Statics and Dynamics
12th Edition
ISBN: 9781259638091
Author: Ferdinand P. Beer, E. Russell Johnston Jr., David Mazurek, Phillip J. Cornwell, Brian Self
Publisher: McGraw-Hill Education
expand_more
expand_more
format_list_bulleted
Concept explainers
Textbook Question
Chapter 19, Problem 19.168RP
A small ball of mass m attached at the midpoint of a tightly stretched elastic cord of length l can slide on a horizontal plane. The ball is given a small displacement in a direction perpendicular to the cord and released. Assuming the tension T in the cord to remain constant, (a) write the differential equation of motion of the ball, (b) determine the period of vibration.
Fig. P19.168
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
Problem 5.118
L2
02
The simple pendulum shown oscillates in the vertical plane (the plane of the figure) as
the pendulum cord is being steadily retracted through the opening at O with a constant
speed v. Consider the oscillations of the pendulum between positions O and ®, where
8, and 0, are the maximum swing angles of the pendulum at O and O, respectively. Let
L, and L, denote the lengths of the cord at 0 and ®, respectively, and let m denote the
L1
mass of the pendulum bob. Neglecting all forces except gravity and the tension in the
cord, determine the angular impulse relative to O provided to the pendulum bob in going
from 0 to 2.
Figure P5.118
A 1300-kg sports car has a center of gravity G located a distance h above a line connecting the front and rear axles. The car is suspended from cables that are attached to the front and rear axles as shown. Knowing that the periods of oscillation are 4.04 s when L = 4 m and 3.54 s when L = 3 m, determine h and the centroidal radius of gyration.
The 100-lb platform A is attached to springs B and D, each of which has a constant k = 120 lb/ft. Knowing that the frequency of vibration of the platform is to remain unchanged when an 80-lb block is placed on it and a third spring C is added between springs B and D , determine the required constant of spring C.
Chapter 19 Solutions
Vector Mechanics for Engineers: Statics and Dynamics
Ch. 19.1 - A particle moves in simple harmonic motion....Ch. 19.1 - A particle moves in simple harmonic motion....Ch. 19.1 - Prob. 19.3PCh. 19.1 - Prob. 19.4PCh. 19.1 - Prob. 19.5PCh. 19.1 - Prob. 19.6PCh. 19.1 - Prob. 19.7PCh. 19.1 - A simple pendulum consisting of a bob attached to...Ch. 19.1 - Prob. 19.9PCh. 19.1 - Prob. 19.10P
Ch. 19.1 - Prob. 19.11PCh. 19.1 - Prob. 19.12PCh. 19.1 - Prob. 19.13PCh. 19.1 - Prob. 19.14PCh. 19.1 - A 5-kg collar C is released from rest in the...Ch. 19.1 - Prob. 19.16PCh. 19.1 - Prob. 19.17PCh. 19.1 - An 11-lb block is attached to the lower end of a...Ch. 19.1 - Block A has a mass m and is supported by the...Ch. 19.1 - A 13.6-kg block is supported by the spring...Ch. 19.1 - Prob. 19.21PCh. 19.1 - 19.21 and 19.22A 50-kg block is supported by the...Ch. 19.1 - Prob. 19.23PCh. 19.1 - The period of vibration of the system shown is...Ch. 19.1 - Prob. 19.25PCh. 19.1 - Prob. 19.26PCh. 19.1 - From mechanics of materials, it is known that for...Ch. 19.1 - From mechanics of materials it is known that when...Ch. 19.1 - Prob. 19.29PCh. 19.1 - Prob. 19.30PCh. 19.1 - If h = 700 mm and d = 500 mm and each spring has a...Ch. 19.1 - Prob. 19.32PCh. 19.1 - Prob. 19.33PCh. 19.1 - Prob. 19.34PCh. 19.1 - Prob. 19.35PCh. 19.1 - Prob. 19.36PCh. 19.2 - The 9-kg uniform rod AB is attached to springs at...Ch. 19.2 - Prob. 19.38PCh. 19.2 - Prob. 19.39PCh. 19.2 - Prob. 19.40PCh. 19.2 - A 15-lb slender rod AB is riveted to a 12-lb...Ch. 19.2 - A 20-lb uniform cylinder can roll without sliding...Ch. 19.2 - A square plate of mass m is held by eight springs,...Ch. 19.2 - Prob. 19.44PCh. 19.2 - Prob. 19.45PCh. 19.2 - A three-blade wind turbine used for research is...Ch. 19.2 - A connecting rod is supported by a knife-edge at...Ch. 19.2 - A semicircular hole is cut in a uniform square...Ch. 19.2 - A uniform disk of radius r = 250 mm is attached at...Ch. 19.2 - A small collar of mass 1 kg is rigidly attached to...Ch. 19.2 - Prob. 19.51PCh. 19.2 - Prob. 19.52PCh. 19.2 - Prob. 19.53PCh. 19.2 - Prob. 19.54PCh. 19.2 - The 8-kg uniform bar AB is hinged at C and is...Ch. 19.2 - Prob. 19.56PCh. 19.2 - Prob. 19.57PCh. 19.2 - Prob. 19.58PCh. 19.2 - Prob. 19.59PCh. 19.2 - Prob. 19.60PCh. 19.2 - Two uniform rods, each of weight W = 24 lb and...Ch. 19.2 - A homogeneous rod of mass per unit length equal to...Ch. 19.2 - Prob. 19.63PCh. 19.2 - Prob. 19.64PCh. 19.2 - A 60-kg uniform circular plate is welded to two...Ch. 19.2 - Prob. 19.66PCh. 19.2 - Prob. 19.67PCh. 19.2 - The centroidal radius of gyration ky of an...Ch. 19.3 - Two blocks each have a mass 1.5 kg and are...Ch. 19.3 - Prob. 19.70PCh. 19.3 - Prob. 19.71PCh. 19.3 - Prob. 19.72PCh. 19.3 - Prob. 19.73PCh. 19.3 - Prob. 19.74PCh. 19.3 - Prob. 19.75PCh. 19.3 - Prob. 19.76PCh. 19.3 - Prob. 19.77PCh. 19.3 - Blade AB of the experimental wind-turbine...Ch. 19.3 - A 15-lb uniform cylinder can roll without sliding...Ch. 19.3 - Prob. 19.80PCh. 19.3 - Prob. 19.81PCh. 19.3 - Prob. 19.82PCh. 19.3 - Prob. 19.83PCh. 19.3 - Prob. 19.84PCh. 19.3 - A homogeneous rod of weight W and length 2l is...Ch. 19.3 - A 10-lb uniform rod CD is welded at C to a shaft...Ch. 19.3 - Prob. 19.87PCh. 19.3 - Prob. 19.88PCh. 19.3 - Prob. 19.89PCh. 19.3 - Prob. 19.90PCh. 19.3 - Prob. 19.91PCh. 19.3 - Prob. 19.92PCh. 19.3 - Prob. 19.93PCh. 19.3 - A uniform rod of length L is supported by a...Ch. 19.3 - Prob. 19.95PCh. 19.3 - Three collars each have a mass m and are connected...Ch. 19.3 - Prob. 19.97PCh. 19.3 - As a submerged body moves through a fluid, the...Ch. 19.4 - A 4-kg collar can slide on a frictionless...Ch. 19.4 - Prob. 19.100PCh. 19.4 - A collar with mass m that slides on a frictionless...Ch. 19.4 - Prob. 19.102PCh. 19.4 - The 1.2-kg bob of a simple pendulum of length l =...Ch. 19.4 - Prob. 19.104PCh. 19.4 - A precision experiment sits on an optical table...Ch. 19.4 - Prob. 19.106PCh. 19.4 - Prob. 19.107PCh. 19.4 - The crude-oil pumping rig shown is driven at 20...Ch. 19.4 - Prob. 19.109PCh. 19.4 - Prob. 19.110PCh. 19.4 - Prob. 19.111PCh. 19.4 - Rod AB is rigidly attached to the frame of a motor...Ch. 19.4 - Prob. 19.113PCh. 19.4 - Prob. 19.114PCh. 19.4 - A motor of weight 100 lb is supported by four...Ch. 19.4 - Prob. 19.116PCh. 19.4 - Prob. 19.117PCh. 19.4 - Prob. 19.118PCh. 19.4 - Prob. 19.119PCh. 19.4 - One of the tail rotor blades of a helicopter has...Ch. 19.4 - Prob. 19.121PCh. 19.4 - Prob. 19.122PCh. 19.4 - Prob. 19.123PCh. 19.4 - Prob. 19.124PCh. 19.4 - A 60-lb disk is attached with an eccentricity e =...Ch. 19.4 - A small trailer and its load have a total mass of...Ch. 19.5 - Prob. 19.127PCh. 19.5 - Prob. 19.128PCh. 19.5 - Prob. 19.129PCh. 19.5 - Prob. 19.130PCh. 19.5 - Prob. 19.131PCh. 19.5 - Prob. 19.132PCh. 19.5 - Prob. 19.133PCh. 19.5 - Prob. 19.134PCh. 19.5 - Prob. 19.135PCh. 19.5 - Prob. 19.136PCh. 19.5 - Prob. 19.137PCh. 19.5 - Prob. 19.138PCh. 19.5 - A machine element weighing 500 lb is supported by...Ch. 19.5 - Prob. 19.140PCh. 19.5 - Prob. 19.141PCh. 19.5 - Prob. 19.142PCh. 19.5 - Prob. 19.143PCh. 19.5 - A 36-lb motor is bolted to a light horizontal beam...Ch. 19.5 - One of the tail rotor blades of a helicopter has...Ch. 19.5 - Prob. 19.146PCh. 19.5 - Prob. 19.147PCh. 19.5 - Prob. 19.148PCh. 19.5 - Prob. 19.149PCh. 19.5 - Prob. 19.150PCh. 19.5 - The suspension of an automobile can be...Ch. 19.5 - Prob. 19.152PCh. 19.5 - Prob. 19.153PCh. 19.5 - Prob. 19.154PCh. 19.5 - 19.155 and 19.156 Draw the electrical analog of...Ch. 19.5 - Prob. 19.156PCh. 19.5 - 19.157 and 19.158Write the differential equations...Ch. 19.5 - 19.157 and 19.158Write the differential equations...Ch. 19 - An automobile wheel-and-tire assembly of total...Ch. 19 - Prob. 19.160RPCh. 19 - Disks A and B weigh 30 lb and 12 lb, respectively,...Ch. 19 - A small trailer and its load have a total mass of...Ch. 19 - A 0.8-lb ball is connected to a paddle by means of...Ch. 19 - Prob. 19.164RPCh. 19 - A 4-lb uniform rod is supported by a pin at O and...Ch. 19 - Prob. 19.166RPCh. 19 - Prob. 19.167RPCh. 19 - A small ball of mass m attached at the midpoint of...Ch. 19 - Prob. 19.169RPCh. 19 - If either a simple or a compound pendulum is used...
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.Similar questions
- Two uniform rods, each of weight W = 1.2 lb and length l = 8 in., are welded together to form the assembly shown. Knowing that the constant of each spring is k = 0.6 lb/in. and that end A is given a small displacement and released, determine the frequency of the resulting motion.arrow_forwardA 2.3-kg object is suspended using two linear springs (k1 = 45 N/m and k2 = 21 N/m), as shown below. Due to aerodynamic effects and other losses, you observe that the amplitude of the vibration is halved after 5 complete cycles. If the initial mass was displaced 270 millimetres below the equilibrium position (i.e. negative initial displacement) and then released from rest, determine the position of the mass after 11 seconds. Give your answer in millimetres rounded to one decimal place. Enter positive values if the mass is above the equilibrium position and negative values if it is below the equilibrium position. k karrow_forwardProblem 38.3 Two uniform rods, each of weight W = 24 lb and length L = 2 ft, are welded together to form the assembly shown. Knowing that the constant of each spring is k = 3 lb/in. and that end A is given a small displacement and released, determine the frequency of the resulting motion. B wwarrow_forward
- A slender 12.7-kg rod can rotate in a vertical plane about a pivot at A. A spring of constant k= 89 N/m and of unstretched length 350 mm is attached to the rod as shown. Knowing that the rod is released from rest in position (1) (0 = 0°), it has rotated through 90° to reach position (2) (0 = 90°). 400 mm 0=0 200 mm 300 mm 200 mm 0=90 kinetic energy at position (1) (Joules) moment of inertia about the hinge (kg.m²) a. 0.8 о Б.0.97 c. 0.64 d. 1.13 е. 0.32 work due weight (N.m) wwwarrow_forwardQuestion 13.56 (Please do problem 13.56 only.) A spring with free length 1.2m is attached to a collar of mass of 20kg. if the collar is released from at position A to slide down the smooth vertical rod shown. If the lowest position readed by the collar is A2, where b=2m, determine the modulus k of the spring.arrow_forwardA slender 12.7-kg rod can rotate in a vertical plane about a pivot at A. A spring of constant k= 121 N/m and of unstretched length 370 mm is attached to the rod as shown. Knowing that the rod is released from rest in position (1) (0 =0°), it has rotated through 90° to reach position (2) ( e = 90°). 400 mm K 0=o 200 mm B 300 mm 200 mm 0=90arrow_forward
- A slender 12.7-kg rod can rotate in a vertical plane about a pivot at A. A spring of constant k= 121 N/m and of unstretched length 370 mm is attached to the rod as shown. Knowing that the rod is released from rest in position (1) (0 = 0°), it has rotated through 90° to reach position (2) ( e = 90°). 400 mm K -0=0 200 mm B 300 mm 200 mm 0=90 kinetic energy at position (1) (Joules) moment of inertia about the hinge (kg.m2) a. 0,8 O b. 0.97 c. 0.64 d. 1.13 O e. 0.32 work due weight (N.m) work due to spring (N.m) a. -5,57 b. -6.68 C. -4.45 d. -7.79 e. -2.23 angular velocity in position (2) (rad/s) О а. 5.71 b. 6.85 C. 4.57 d. 7,99 O e. 2.28 O o o C ооarrow_forwardProblem 22.77 The 20-kg block is subjected to the action of the harmonic force F = (90 cos 6t) N, where t is in seconds. (Figure 1) Figure k = 400 N/m WWW k = 400 N/m O 0 20 kg O O O O F90 cos 6tr C c = 125 N.s/m 1 of 1 Part A Write the equation which describes the steady-state motion. Express your answer in terms of t. Express your answer using three significant figures. Express the phase in radians and the final result in meters. x = Submit 15. ΑΣΦΑ Provide Feedback Request Answer vec ? marrow_forwardThe period of oscillation of the system shown in Fig. a is observed to be 0.5 s. After the spring of stiffness kz is added to the system as shown in Fig. b, the period of oscillation is observed to be 0.31 s. Determine the value kz of the added spring and the mass of the block. ki=2000 N/m. m k2 k1 (a) (b) ww-arrow_forward
- As a submerged body moves through a fluid, the particles of the fluid flow around the body and thus acquire kinetic energy. In the case of a sphere moving in an ideal fluid, the total kinetic energy acquired by the fluid is where p is the mass density of the fluid, V is the volume of the sphere, and v is the velocity of the sphere. Consider a 500-g hollow spherical shell of radius 80 mm that is held submerged in a tank of water by a spring of constant 500 N/m. (a ) Neglecting fluid friction, determine the period of vibration of the shell when it is displaced vertically and then released. (b) Solve part a, assuming that the tank is accelerated upward at the constant rate of 8 m/s2.arrow_forwardA 6-kg uniform cylinder is assumed to roll without sliding on a horizontal surface and is attached by a pin at point C to the 4-kg horizontal bar AB. The bar is attached to two springs, each having a constant of k = 3.5 kN/m, as shown. Knowing that the coefficient of static friction between the cylinder and the surface is 0.5, determine the maximum amplitude of the motion of point C that is compatible with the assumption of rolling.arrow_forward(c) A spool of mass 60 kg is supported on two rollers at A and B as shown in Figure Q1(c). Neglect the mass of the inelastic cable, friction and the mass of the rollers at A and B. Knowing that a constant pulling force P is applied in order to unwind 6 m of cable in 3 s starting from rest. The radius of gyration for the spool is (600+a) mm, where a =8 Explain with calculation on ways to increase the acceleration of cable being pulledarrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University PressMechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSONThermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
- Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEYMechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningEngineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY
Elements Of Electromagnetics
Mechanical Engineering
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Oxford University Press
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:9780134319650
Author:Russell C. Hibbeler
Publisher:PEARSON
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:9781259822674
Author:Yunus A. Cengel Dr., Michael A. Boles
Publisher:McGraw-Hill Education
Control Systems Engineering
Mechanical Engineering
ISBN:9781118170519
Author:Norman S. Nise
Publisher:WILEY
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Cengage Learning
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:9781118807330
Author:James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:WILEY
Introduction to Undamped Free Vibration of SDOF (1/2) - Structural Dynamics; Author: structurefree;https://www.youtube.com/watch?v=BkgzEdDlU78;License: Standard Youtube License