
Engineering Mechanics: Dynamics
8th Edition
ISBN: 9781118885840
Author: James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher: WILEY
expand_more
expand_more
format_list_bulleted
Concept explainers
Question
Chapter 6.5, Problem 71P
To determine
Determine the distance
Expert Solution & Answer

Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Spur gears
Note : Exam is open notes &tables / Answer all questions.
Q.1. The press shown for Figure.1 has a rated load
of 22 kN. The twin screws have double start Acme
threads, a diameter of 50 mm, and a pitch of 6 mm.
Coefficients of friction are 0.05 for the threads and
0.08 for the collar bearings. Collar diameters are 90
mm. The gears have an efficiency of 95 percent and a
speed ratio of 60:1. A slip clutch, on the motor shaft,
prevents overloading. The full-load motor speed is
1720 rev/min.
(a) When the motor is turned on, how fast will the
press head move? (Vm= , Vser. =
)
(5M)
(b) What should be the horsepower rating of the
motor? (TR=, Tc= Pser. =
"
Bronze
bushings
Foot
Motor
Bearings
watt, Pm= watt, Pm= h.p.) (20M)
2['s
Fig.1
Worm
Collar
bearing
Problem 2 (55 pts). We now consider the FEM solution of Problem 1.(a) [5pts] Briefly describe the 4 steps necessary to obtain the approximate solution of thatBVP using the Galerkin FEM. Use the minimum amount of math necessary to supportyour explanations.(b) [20pts] Derive the weak form of the BVP.(c) [10pts] Assuming a mesh of two equal elements and linear shape functions, sketch byhand how you expect the FEM solution to look like. Also sketch the analytical solutionfor comparison. In your sketch, identify the nodal degrees of freedom that the FEMsolution seeks to find.(d) [10pts] By analogy with the elastic rod problem and heat conduction problem considered in class, write down the stiffness matrix and force vector for each of the twoelements considered in (c).(e) [10pts] Assemble the global system of equations, and verbally explain how to solve it.
An aluminum rod of length L = 1m has mass density ρ = 2700 kgm3 andYoung’s modulus E = 70GPa. The rod is fixed at both ends. The exactnatural eigenfrequencies of the rod are ωexactn =πnLqEρfor n=1,2,3,. . . .1. What is the minimum number of linear elements necessary todetermine the fundamental frequency ω1 of the system? Discretizethe rod in that many elements of equal length, assemble the globalsystem of equations KU = ω2MU, and find the fundamentalfrequency ω1. Compute the relative error e1 = (ω1 − ωexact1)/ωexact1.Sketch the fundamental mode of vibration.
Chapter 6 Solutions
Engineering Mechanics: Dynamics
Ch. 6.4 - Prob. 1PCh. 6.4 - In Prob. 6/1, if the plate is given a horizontal...Ch. 6.4 - The driver of a pickup truck accelerates from rest...Ch. 6.4 - A passenger car of an overhead monorail system is...Ch. 6.4 - The uniform box of mass m slides down the rough...Ch. 6.4 - The uniform slender bar of mass m and length L is...Ch. 6.4 - Prob. 7PCh. 6.4 - The frame is made from uniform rod which has a...Ch. 6.4 - Prob. 9PCh. 6.4 - Determine the value of P which will cause the...
Ch. 6.4 - The uniform 5-kg bar AB is suspended in a vertical...Ch. 6.4 - Prob. 12PCh. 6.4 - Prob. 13PCh. 6.4 - Prob. 14PCh. 6.4 - Prob. 15PCh. 6.4 - Prob. 16PCh. 6.4 - The 1650-kg car has its mass center at G....Ch. 6.4 - Prob. 18PCh. 6.4 - A cleated conveyor belt transports solid...Ch. 6.4 - The thin hoop of negligible mass and radius r...Ch. 6.4 - Determine the magnitude P and direction θ of the...Ch. 6.4 - The mine skip has a loaded mass of 2000 kg and is...Ch. 6.4 - The block A and attached rod have a combined mass...Ch. 6.4 - The homogeneous rectangular plate weighs 40 lb and...Ch. 6.4 - A jet transport with a landing speed of 200 km/h...Ch. 6.4 - Prob. 26PCh. 6.4 - Prob. 27PCh. 6.4 - The 30,000-lb concrete pipe section is being...Ch. 6.4 - Determine the maximum counterweight W for which...Ch. 6.4 - The 1800-kg rear-wheel-drive car accelerates...Ch. 6.4 - The experimental Formula One race car is traveling...Ch. 6.4 - Two pulleys are fastened together to form an...Ch. 6.4 - The uniform 20-kg slender bar is pivoted at O and...Ch. 6.4 - The figure shows an overhead view of a...Ch. 6.4 - The uniform 100-kg beam is freely hinged about its...Ch. 6.4 - The motor M is used to hoist the 12,000-lb stadium...Ch. 6.4 - Prob. 38PCh. 6.4 - Each of the two drums and connected hubs of 8-in....Ch. 6.4 - Determine the angular acceleration and the force...Ch. 6.4 - The uniform 5-kg portion of a circular hoop is...Ch. 6.4 - The 30-in. slender bar weighs 20 lb and is mounted...Ch. 6.4 - The half ring of mass m and radius r is welded to...Ch. 6.4 - The uniform plate of mass m is released from rest...Ch. 6.4 - The uniform slender bar AB has a mass of 8 kg and...Ch. 6.4 - Prob. 46PCh. 6.4 - Prob. 47PCh. 6.4 - Prob. 48PCh. 6.4 - Prob. 49PCh. 6.4 - Prob. 50PCh. 6.4 - Prob. 51PCh. 6.4 - Prob. 52PCh. 6.4 - Prob. 53PCh. 6.4 - Prob. 54PCh. 6.4 - The solid cylindrical rotor B has a mass of 43 kg...Ch. 6.4 - Prob. 56PCh. 6.4 - Prob. 57PCh. 6.4 - The uniform slender bar is released from rest in...Ch. 6.4 - Prob. 59PCh. 6.4 - Prob. 61PCh. 6.4 - The uniform steel I-beam has a mass of 300 kg and...Ch. 6.4 - The gear train shown operates in a horizontal...Ch. 6.4 - Prob. 64PCh. 6.4 - Prob. 65PCh. 6.4 - Prob. 66PCh. 6.4 - The uniform 72-ft mast weighs 600 lb and is hinged...Ch. 6.4 - The robotic device consists of the stationary...Ch. 6.4 - Prob. 69PCh. 6.4 - Prob. 70PCh. 6.5 - The uniform slender bar rests on a smooth...Ch. 6.5 - The 64.4-lb solid circular disk is initially at...Ch. 6.5 - Prob. 73PCh. 6.5 - Prob. 74PCh. 6.5 - Prob. 75PCh. 6.5 - Prob. 76PCh. 6.5 - Prob. 77PCh. 6.5 - Determine the angular acceleration of each of the...Ch. 6.5 - The solid homogeneous cylinder is released from...Ch. 6.5 - The 30-kg spool of outer radius ro = 450 mm has a...Ch. 6.5 - Repeat Prob. 6/80 for the case where the cable...Ch. 6.5 - The fairing which covers the spacecraft package in...Ch. 6.5 - Prob. 83PCh. 6.5 - Prob. 85PCh. 6.5 - The system of Prob. 6/20 is repeated here. If the...Ch. 6.5 - Prob. 87PCh. 6.5 - Prob. 88PCh. 6.5 - Prob. 89PCh. 6.5 - Prob. 90PCh. 6.5 - Prob. 91PCh. 6.5 - The truck, initially at rest with a solid...Ch. 6.5 - Prob. 93PCh. 6.5 - The uniform rectangular 300-lb plate is held in...Ch. 6.5 - Prob. 96PCh. 6.5 - Prob. 97PCh. 6.5 - Prob. 98PCh. 6.5 - The yo-yo has a mass m and a radius of gyration k...Ch. 6.5 - Prob. 100PCh. 6.5 - Prob. 101PCh. 6.5 - Prob. 102PCh. 6.5 - Prob. 103PCh. 6.5 - Prob. 104PCh. 6.5 - The connecting rod AB of a certain...Ch. 6.5 - Prob. 107PCh. 6.5 - The four-bar mechanism lies in a vertical plane...Ch. 6.5 - The Ferris wheel at an amusement park has an even...Ch. 6.6 - The slender rod of mass m and length l has a...Ch. 6.6 - The log is suspended by the two parallel 5-m...Ch. 6.6 - The assembly is constructed of homogeneous slender...Ch. 6.6 - Prob. 114PCh. 6.6 - Prob. 115PCh. 6.6 - The uniform semicircular bar of radius r = 75 mm...Ch. 6.6 - The homogeneous rectangular crate weighs 250 lb...Ch. 6.6 - The 24-lb disk is rigidly attached to the 7-lb bar...Ch. 6.6 - The two wheels of Prob. 6/78, shown again here,...Ch. 6.6 - The 15-kg slender bar OA is released from rest in...Ch. 6.6 - The light circular hoop of radius r contains a...Ch. 6.6 - Prob. 122PCh. 6.6 - The figure shows an impact tester used in studying...Ch. 6.6 - Prob. 124PCh. 6.6 - Prob. 125PCh. 6.6 - Prob. 126PCh. 6.6 - Prob. 127PCh. 6.6 - The uniform 40-lb bar with attached 12-lb wheels...Ch. 6.6 - Prob. 129PCh. 6.6 - The wheel consists of a 4-kg rim of 250-mm radius...Ch. 6.6 - The uniform slender bar ABC weighs 6 lb and is...Ch. 6.6 - Prob. 133PCh. 6.6 - The system is released from rest when the angle θ...Ch. 6.6 - The uniform 12-lb disk pivots freely about a...Ch. 6.6 - Prob. 137PCh. 6.6 - Prob. 138PCh. 6.6 - Prob. 139PCh. 6.6 - Prob. 140PCh. 6.6 - Prob. 141PCh. 6.6 - Prob. 142PCh. 6.6 - The homogeneous solid semicylinder is released...Ch. 6.6 - A small experimental vehicle has a total mass m of...Ch. 6.6 - Prob. 147PCh. 6.6 - The open square frame is constructed of four...Ch. 6.7 - The load of mass m is supported by the light...Ch. 6.7 - The uniform slender bar of mass m is shown in its...Ch. 6.7 - Prob. 151PCh. 6.7 - Prob. 152PCh. 6.7 - Prob. 153PCh. 6.7 - The load of mass m is given an upward acceleration...Ch. 6.7 - The cargo box of the food-delivery truck for...Ch. 6.7 - The sliding block is given a horizontal...Ch. 6.7 - Prob. 157PCh. 6.7 - Prob. 158PCh. 6.7 - Prob. 159PCh. 6.7 - Prob. 160PCh. 6.7 - The mechanical tachometer measures the rotational...Ch. 6.7 - Prob. 162PCh. 6.7 - Prob. 163PCh. 6.7 - Prob. 164PCh. 6.7 - Prob. 165PCh. 6.7 - Prob. 166PCh. 6.9 - Prob. 167RPCh. 6.9 - Prob. 168RPCh. 6.9 - Prob. 169RPCh. 6.9 - The frame of mass m is welded together from...Ch. 6.9 - Prob. 171RPCh. 6.9 - The cable drum has a mass of 800 kg with radius of...Ch. 6.9 - Prob. 173RPCh. 6.9 - Prob. 174RPCh. 6.9 - Prob. 175RPCh. 6.9 - Prob. 176RPCh. 6.9 - Prob. 177RPCh. 6.9 - The wad of clay of mass m is initially moving with...Ch. 6.9 - Prob. 179RPCh. 6.9 - Prob. 180RPCh. 6.9 - Prob. 181RPCh. 6.9 - Prob. 182RPCh. 6.9 - Prob. 183RPCh. 6.9 - Two small variable-thrust jets are actuated to...Ch. 6.9 - Prob. 185RPCh. 6.9 - Each of the two 300-mm uniform rods A has a mass...Ch. 6.9 - Prob. 187RPCh. 6.9 - The slender bar of mass m and length l is released...Ch. 6.9 - Prob. 189RPCh. 6.9 - Prob. 190RPCh. 6.9 - Prob. 191RPCh. 6.9 - Prob. 192RPCh. 6.9 - Prob. 193RPCh. 6.9 - Prob. 194RPCh. 6.9 - The 165-lb ice skater with arms extended...Ch. 6.9 - Prob. 196RPCh. 6.9 - Prob. 197RPCh. 6.9 - The body of the spacecraft weighs 322 lb on earth...Ch. 6.9 - Prob. 199RPCh. 6.9 - Prob. 200RPCh. 6.9 - Prob. 201RPCh. 6.9 - The uniform cylinder is rolling without slip with...Ch. 6.9 - Prob. 203RPCh. 6.9 - The 30-kg wheel has a radius of gyration about its...Ch. 6.9 - The mass m is traveling with speed v when it...Ch. 6.9 - Prob. 206RPCh. 6.9 - Prob. 207RPCh. 6.9 - Prob. 208RPCh. 6.9 - The nose-wheel assembly is raised by the...Ch. 6.9 - Prob. 210RPCh. 6.9 - Prob. 211RPCh. 6.9 - Prob. 212RPCh. 6.9 - Prob. 213RPCh. 6.9 - Prob. 214RPCh. 6.9 - Prob. 215RPCh. 6.9 - Prob. 216RPCh. 6.9 - Prob. 217RPCh. 6.9 - Prob. 218RPCh. 6.9 - Prob. 219RPCh. 6.9 - Prob. 220RPCh. 6.9 - The slender rod of mass m1 and length L has a...Ch. 6.9 - Prob. 222RPCh. 6.9 - Prob. 226RPCh. 6.9 - Prob. 228RPCh. 6.9 - Prob. 229RPCh. 6.9 - Prob. 230RP
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
- Problem 1 (65 pts, suggested time 50 mins). An elastic string of constant line tension1T is pinned at x = 0 and x = L. A constant distributed vertical force per unit length p(with units N/m) is applied to the string. Under this force, the string deflects by an amountv(x) from its undeformed (horizontal) state, as shown in the figure below.The PDE describing mechanical equilibrium for the string isddx Tdvdx− p = 0 . (1)(a) [5pts] Identify the BCs for the string and identify their type (essential/natural). Writedown the strong-form BVP for the string, including PDE and BCs.(b) [10pts] Find the analytical solution of the BVP in (a). Compute the exact deflectionof the midpoint v(L/2).(c) [15pts] Derive the weak-form BVP.(d) [5pts] What is the minimum number of linear elements necessary to compute the deflection of the midpoint?(e) [15pts] Write down the element stiffness matrix and the element force vector for eachelement.arrow_forwardProblem 1 (35 pts). An elastic string of constant line tension1 T is pinned at x = 0 andx = L. A constant distributed vertical force per unit length p (with units N/m) is appliedto the string. Under this force, the string deflects by an amount v(x) from its undeformed(horizontal) state, as shown in the figure below.Force equilibrium in the string requires thatdfdx − p = 0 , (1)where f(x) is the internal vertical force in the string, which is given byf = Tdvdx . (2)(a) [10pts] Write down the BVP (strong form) that the string deflection v(x) must satisfy.(b) [2pts] What order is the governing PDE in the BVP of (a)?(c) [3pts] Identify the type (essential/natural) of each boundary condition in (a).(d) [20pts] Find the analytical solution of the BVP in (a).arrow_forwardProblem 2 (25 pts, (suggested time 15 mins). An elastic string of line tension T andmass per unit length µ is pinned at x = 0 and x = L. The string is free to vibrate, and itsfirst vibration mode is shown below.In order to find the frequency of the first mode (or fundamental frequency), the string isdiscretized into a certain number of linear elements. The stiffness and mass matrices of thei-th element are, respectivelyESMi =TLi1 −1−1 1 EMMi =Liµ62 11 2 . (2)(a) [5pts] What is the minimum number of linear elements necessary to compute the fundamental frequency of the vibrating string?(b) [20pts] Assemble the global eigenvalue problem and find the fundamental frequency ofvibration of the stringarrow_forward
- I need part all parts please in detail (including f)arrow_forwardProblem 3 (10 pts, suggested time 5 mins). In class we considered the mutiphysics problem of thermal stresses in a rod. When using linear shape functions, we found that the stress in the rod is affected by unphysical oscillations like in the following plot E*(ux-a*T) 35000 30000 25000 20000 15000 10000 5000 -5000 -10000 0 Line Graph: E*(ux-a*T) MULT 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Arc length (a) [10pts] What is the origin of this issue and how can we fix it?arrow_forwardanswer the questions and explain all of it in words. Ignore where it says screencast and in class explanationarrow_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
Dynamics - Lesson 1: Introduction and Constant Acceleration Equations; Author: Jeff Hanson;https://www.youtube.com/watch?v=7aMiZ3b0Ieg;License: Standard YouTube License, CC-BY