Loose Leaf for Vector Mechanics for Engineers: Statics and Dynamics
12th Edition
ISBN: 9781259977206
Author: BEER, Ferdinand P., Johnston Jr., E. Russell, Mazurek, David, Cornwell, Phillip J., SELF, Brian
Publisher: McGraw-Hill Education
expand_more
expand_more
format_list_bulleted
Concept explainers
Textbook Question
Chapter 19.5, Problem 19.145P
One of the tail rotor blades of a helicopter has an unbalanced weight of 1 lb at a distance of e = 6 in. from the axis of rotation. The fuselage can be considered to be fixed and the tail rotor and tail can be modeled as an equivalent stiffness of 8800 lb/ft, weight of 165 lb, and damping ratio of 0.15. Knowing that the blades rotate at 500 rpm, determine the amplitude of vibration of the tail section.
Fig. P19.145
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
A simplified model of a washing machine is shown. A bundle of wet clothes forms a weight wb of 20 lb in the machine and causes a rotating unbalance. The rotating weight is 40 lb (including wb) and the radius of the washer basket e is 9 in. Knowing the washer has an equivalent spring constant k = 70 lb/ft and damping ratio and during the spin cycle the drum rotates at 250 rpm, determine the amplitude of the motion and the magnitude of the force transmitted to the sides of the washing machine.
A 36-lb motor is bolted to a light horizontal beam that has a static deflection of 0.075 in. due to the weight of the motor. Knowing that the unbalance of the rotor is equivalent to a weight of 0.64 oz located 6.25 in. from the axis of rotation, determine the amplitude of the vibration of the motor at a speed of 900 rpm, assuming (a ) that no damping is present, (b ) that the damping factor c/cc is equal to 0.055.
A machine of mass 75 kg is mounted on springs and is fitted with a dashpot to damp out vibrations. There are three springs each of stiffness 10 N/mm and it is found that the amplitude of vibration diminishes from 38.4 mm to 6.4 mm in two complete oscillations. Assuming that the damping force varies as the velocity, determine : 1. the resistance of the dash-pot at unit velocity ; 2. the ratio of the frequency of the damped vibration to the frequency of the undamped vibration ; and 3. the periodic time of the
damped vibration.
Chapter 19 Solutions
Loose Leaf for 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
- An 8-kg uniform disk of radius 200 mm is welded to a vertical shaft with a fixed end at B. The disk rotates through an angle of 3° when a static couple of magnitude 50N.m is applied to it. If the disk is acted upon by a periodic torsional couple of magnitude Tm=60N.m. determine the range of values of vf for which the amplitude of the vibration is less than the angle of rotation caused by a static couple of magnitude Tm.arrow_forwardA 45-kg motor is bolted to a light horizontal beam that has a static deflection of 6 mm due to the weight of the motor. The unbalance of the motor is equivalent to a mass of 110 g located 75 mm from the axis of rotation. Knowing that the amplitude of the vibration of the motor is 0.25 mm at a speed of 300 rpm, determine (a) the damping factor c/cc(b) the coefficient of damping c.arrow_forwardShow that for a small value of the damping factor c/cc , the maximum amplitude of a forced vibration occurs when Wf= Wn and that the corresponding value of the magnification factor is ½ (c/c2).arrow_forward
- A 400-kg motor supported by four springs, each of constant 150 kN/m, and a dashpot of constant c = 6500 N·s/m is constrained to move vertically. Knowing that the unbalance of the rotor is equivalent to a 23-g mass located at a distance of 100 mm from the axis of rotation, determine for a speed of 800 rpm (a ) the amplitude of the fluctuating force transmitted to the foundation, (b ) the amplitude of the vertical motion of the motor.arrow_forwardA 2-kg block is supported by a spring with a constant of k= 128 N/m and a dashpot with a coefficient of viscous damping of c=0.6 N.s/m. The block is in equilibrium when it is struck from below by a hammer that imparts to the block an upward velocity of 0.4 m/s. Determine (a) the logarithmic decrement,(b) the maximum upward displacement of the block from equilibrium after two cycles.arrow_forwardQ.4 A device to produce vibrations consists of the two counter-rotating wheels, each carrying an eccentric mass mo = 1 kg with a centre of mass at a distance e = 12 mm from its axis of rotation. The wheels are synchronized so that the vertical positions of the unbalanced masses are always identical. The total mass of the device is 10 kg. For an equivalent spring stiffness of 900 kN/m, determine the amplitude of the force transmitted to the fixed mountings due to the imbalance of the rotors at a speed of 1500 rev/min. Neglect damping. mo mo wwwwarrow_forward
- A slender 10-kg bar AB with a length of l = 0.6 m is connected to two collars of negligible weight. Collar A is attached to a spring with a constant of k = 1.5 kN/m and can slide on a horizontal rod, while collar B can slide freely on a vertical rod. Knowing that the system is in equilibrium when bar AB is vertical and that collar A is given a small displacement and released, determine the period of the resulting vibrations.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_forwardA 6-kg uniform cylinder can 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 = 4.2 kN/m, as shown. The bar is moved 12 mm to the right of the equilibrium position and released. Determine the period of vibration of the system. (Round the final answer to three decimal places.) The period of vibration of the system is ___s.arrow_forward
- A 6-kg uniform cylinder can roll without sliding on a horizontal surface and is attached by a pin at point C to the 4-kg horizontal bar AB to the 4-kg horizontal bar k= 5 kN/m, as shown. Knowing that the bar is moved 12 mm to the right of the equilibrium position and released, determine (a) the period of vibration of the system, (b) the magnitude of the maximum velocity of bar AB.arrow_forwardAn 800-g rod AB is bolted to a 1.2-kg disk. A spring of constant k = 12 N/m is attached to the center of the disk at A and to the wall at C . Knowing that the disk rolls without sliding, determine the period of small oscillations of the system.arrow_forwardA 360-lb motor is supported by springs of total constant 12.5 kips/ft. The unbalance of the rotor is equivalent to a 0.9-oz weight located 7.5 in. from the axis of rotation. Determine the range of speeds of the motor for which the amplitude of the fluctuating force exerted on the foundation is less than 5 lb.arrow_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
Ch 2 - 2.2.2 Forced Undamped Oscillation; Author: Benjamin Drew;https://www.youtube.com/watch?v=6Tb7Rx-bCWE;License: Standard youtube license