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
Videos
Textbook Question
Chapter 15.1, Problem 15.37P
In a continuous printing process, paper is drawn into the presses at a constant speed v. Denoting by r the radius of the paper roll at any given time and by b the thickness of the paper, derive an expression for the angular acceleration of the paper roll.
Fig. P15.37
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Problem (8)
The belt shown moves over two pulleys without slipping. At the instant shown
the pulleys are rotating clockwise and the speed of point B on the belt is 4 m/s,
increasing at the rate of 32 m/s?. Determine, at this instant,
(a) the angular velocity and angular acceleration of each pulley,
(b) the acceleration of point P on pulley C.
B
160 mm
fi00 mm
please show presentation, drawing diagram, vector’s forces & position, etc.. and showing work steps. thank you
2) At the instant given, it is known that the
angular velocity of rod AB is 20 rad/s
clockwise. By use of Cartesian vector form,
determine (a) the angular velocity of rod BD,
(b) the velocity of the point D.
0.2 m
0.25 m
D
0.2 m
E
-0.6 m
B
Chapter 15 Solutions
Vector Mechanics for Engineers: Statics and Dynamics
Ch. 15.1 - A rectangular plate swings from arms of equal...Ch. 15.1 - Knowing that wheel A rotates with a constant...Ch. 15.1 - The brake drum is attached to a larger flywheel...Ch. 15.1 - The motion of an oscillating flywheel is defined...Ch. 15.1 - The motion of an oscillating flywheel is defined...Ch. 15.1 - As steam is slowly injected into a turbine, the...Ch. 15.1 - A small grinding wheel is attached to the shaft of...Ch. 15.1 - A connecting rod is supported by a knife-edge at...Ch. 15.1 - Prob. 15.7PCh. 15.1 - The angular acceleration of an oscillating disk is...
Ch. 15.1 - The angular acceleration of a shaft is defined by...Ch. 15.1 - The assembly shown consists of two rods and a...Ch. 15.1 - In Prob. 15.10, determine the velocity and...Ch. 15.1 - Prob. 15.12PCh. 15.1 - The rectangular block shown rotates about the...Ch. 15.1 - A circular plate of 120-mm radius is supported by...Ch. 15.1 - Prob. 15.15PCh. 15.1 - Prob. 15.16PCh. 15.1 - The earth makes one complete revolution on its...Ch. 15.1 - The sprocket wheel and chain shown are initially...Ch. 15.1 - Prob. 15.19PCh. 15.1 - Prob. 15.20PCh. 15.1 - The rated speed of drum B of the belt sander shown...Ch. 15.1 - The two pulleys shown may be operated with the V...Ch. 15.1 - A cyclist uses a stationary trainer during the...Ch. 15.1 - A gear reduction system consists of three gears A,...Ch. 15.1 - A belt is pulled to the right between cylinders A...Ch. 15.1 - Prob. 15.26PCh. 15.1 - Prob. 15.27PCh. 15.1 - A plastic film moves over two drums. During a 4-s...Ch. 15.1 - Cylinder A is moving downward with a velocity of 3...Ch. 15.1 - The system shown is held at rest by the...Ch. 15.1 - A load is to be raised 20 ft by the hoisting...Ch. 15.1 - A simple friction drive consists of two disks A...Ch. 15.1 - Prob. 15.33PCh. 15.1 - Two friction disks A and B are to be brought into...Ch. 15.1 - Two friction disks A and B are brought into...Ch. 15.1 - Steel tape is being wound onto a spool that...Ch. 15.1 - In a continuous printing process, paper is drawn...Ch. 15.2 - The ball rolls without slipping on the fixed...Ch. 15.2 - Three uniform rodsABC, DCE, and FGHare connected...Ch. 15.2 - Prob. 15.38PCh. 15.2 - An overhead door is guided by wheels at A and B...Ch. 15.2 - A painter is halfway up a 10-m ladder when the...Ch. 15.2 - Rod AB can slide freely along the floor and the...Ch. 15.2 - Rod AB can slide freely along the floor and the...Ch. 15.2 - Rod AB moves over a small wheel at C while end A...Ch. 15.2 - The disk shown moves in the xy plane. Knowing that...Ch. 15.2 - The disk shown moves in the xy plane. Knowing that...Ch. 15.2 - Prob. 15.46PCh. 15.2 - Velocity sensors are placed on a satellite that is...Ch. 15.2 - In the planetary gear system shown, the radius of...Ch. 15.2 - Prob. 15.49PCh. 15.2 - The outer gear C rotates with an angular velocity...Ch. 15.2 - Prob. 15.51PCh. 15.2 - A simplified gear system for a mechanical watch is...Ch. 15.2 - 15.53 and 15.54Arm ACB rotates about point C with...Ch. 15.2 - 15.53 and 15.54Arm ACB rotates about point C with...Ch. 15.2 - Knowing that at the instant shown the angular...Ch. 15.2 - Knowing that at the instant shown the velocity of...Ch. 15.2 - Knowing that the disk has a constant angular...Ch. 15.2 - The disk has a constant angular velocity of 20...Ch. 15.2 - The test rig shown was developed to perform...Ch. 15.2 - Prob. 15.60PCh. 15.2 - In the engine system shown, l = 160 mm and b = 60...Ch. 15.2 - In the engine system shown, l = 160 mm and b = 60...Ch. 15.2 - Knowing that the angular velocity of rod DE is a...Ch. 15.2 - In the position shown, bar AB has an angular...Ch. 15.2 - Prob. 15.65PCh. 15.2 - Prob. 15.66PCh. 15.2 - Prob. 15.67PCh. 15.2 - Prob. 15.68PCh. 15.2 - For the oil pump rig shown, link AB causes the...Ch. 15.2 - Both 6-in.-radius wheels roll without slipping on...Ch. 15.2 - The 80-mm-radius wheel shown rolls to the left...Ch. 15.2 - For the gearing shown, derive an expression for...Ch. 15.3 - The disk rolls without sliding on the fixed...Ch. 15.3 - Prob. 15.6CQCh. 15.3 - A juggling club is thrown vertically into the air....Ch. 15.3 - At the instant shown during deceleration, the...Ch. 15.3 - A helicopter moves horizontally in the x direction...Ch. 15.3 - Prob. 15.76PCh. 15.3 - Prob. 15.77PCh. 15.3 - Prob. 15.78PCh. 15.3 - In order to uncoil electrical wire from a spool...Ch. 15.3 - The arm ABC rotates with an angular velocity of 4...Ch. 15.3 - The double gear rolls on the stationary left rack...Ch. 15.3 - Prob. 15.82PCh. 15.3 - Rod ABD is guided by wheels at A and B that roll...Ch. 15.3 - Knowing that at the instant shown the angular...Ch. 15.3 - Knowing that at the instant shown the velocity of...Ch. 15.3 - A motor at O drives the windshield wiper mechanism...Ch. 15.3 - Prob. 15.88PCh. 15.3 - Small wheels have been attached to the ends of bar...Ch. 15.3 - Prob. 15.90PCh. 15.3 - The disk is released from rest and rolls down the...Ch. 15.3 - Prob. 15.92PCh. 15.3 - Two identical rods ABF and DBE are connected by a...Ch. 15.3 - Arm ABD is connected by pins to a collar at B and...Ch. 15.3 - Two rods ABD and DE are connected to three collars...Ch. 15.3 - Two 500-mm rods are pin-connected at D as shown....Ch. 15.3 - At the instant shown, the velocity of collar A is...Ch. 15.3 - Prob. 15.98PCh. 15.3 - Describe the space centrode and the body centrode...Ch. 15.3 - Describe the space centrode and the body centrode...Ch. 15.3 - Prob. 15.101PCh. 15.3 - Using the method of Sec. 15.3, solve Prob. 15.64....Ch. 15.3 - Using the method of Sec. 15.3, solve Prob. 15.65....Ch. 15.3 - Using the method of Sec. 15.3, solve Prob. 15.38....Ch. 15.4 - A rear-wheel-drive car starts from rest and...Ch. 15.4 - Fig. P15.105 and P15.106 15.105A 5-m steel beam is...Ch. 15.4 - For a 5-m steel beam AE, the acceleration of point...Ch. 15.4 - A 900-mm rod rests on a horizontal table. A force...Ch. 15.4 - In Prob. 15.107, determine the point of the rod...Ch. 15.4 - Knowing that point A is moving to the right at a...Ch. 15.4 - Knowing that at the instant shown crank BC has a...Ch. 15.4 - An automobile travels to the left at a constant...Ch. 15.4 - The 18-in.-radius flywheel is rigidly attached to...Ch. 15.4 - 15.113 and 15.114A 3-in.-radius drum is rigidly...Ch. 15.4 - 15.113 and 15.114A 3-in.-radius drum is rigidly...Ch. 15.4 - A heavy crate is being moved a short distance...Ch. 15.4 - Prob. 15.116PCh. 15.4 - The 100-mm-radius drum rolls without slipping on a...Ch. 15.4 - In the planetary gear system shown, the radius of...Ch. 15.4 - The 200-mm-radius disk rolls without sliding on...Ch. 15.4 - Knowing that crank AB rotates about point A with a...Ch. 15.4 - Knowing that crank AB rotates about point A with a...Ch. 15.4 - In the two-cylinder air compressor shown, the...Ch. 15.4 - The right leg of an athlete on a rowing machine...Ch. 15.4 - Arm AB has a constant angular velocity of 16 rad/s...Ch. 15.4 - Arm AB has a constant angular velocity of 16 rad/s...Ch. 15.4 - A straight rack rests on a gear of radius r = 3...Ch. 15.4 - The elliptical exercise machine has fixed axes of...Ch. 15.4 - The elliptical exercise machine has fixed axes of...Ch. 15.4 - Knowing that the angular velocity of rod DE is a...Ch. 15.4 - Knowing that at the instant shown bar DE has an...Ch. 15.4 - 15.131 and 15.132Knowing that at the instant shown...Ch. 15.4 - 15.131 and 15.132Knowing that at the instant shown...Ch. 15.4 - 15.133 and 15.134Knowing that at the instant shown...Ch. 15.4 - 15.133 and 15.134Knowing that at the instant shown...Ch. 15.4 - Prob. 15.135PCh. 15.4 - For the oil pump rig shown, link AB causes the...Ch. 15.4 - Denoting by rA the position vector of a point A of...Ch. 15.4 - Prob. 15.138PCh. 15.4 - Prob. 15.139PCh. 15.4 - Prob. 15.140PCh. 15.4 - Prob. 15.141PCh. 15.4 - Prob. 15.142PCh. 15.4 - Prob. 15.143PCh. 15.4 - Crank AB rotates with a constant clockwise angular...Ch. 15.4 - Crank AB rotates with a constant clockwise angular...Ch. 15.4 - Solve the engine system from Sample Prob. 15.15...Ch. 15.4 - Prob. 15.147PCh. 15.4 - Prob. 15.148PCh. 15.4 - Prob. 15.149PCh. 15.5 - A person walks radially inward on a platform that...Ch. 15.5 - The motion of pin P is guided by slots cut in rods...Ch. 15.5 - The motion of pin P is guided by slots cut in rods...Ch. 15.5 - 15.152 and 15.153Two rotating rods are connected...Ch. 15.5 - 15.152 and 15.153Two rotating rods are connected...Ch. 15.5 - Pin P is attached to the wheel shown and slides in...Ch. 15.5 - Knowing that at the instant shown the angular...Ch. 15.5 - Prob. 15.156PCh. 15.5 - The motion of pin P is guided by slots cut in rods...Ch. 15.5 - Prob. 15.158PCh. 15.5 - Prob. 15.159PCh. 15.5 - Prob. 15.160PCh. 15.5 - Pin P is attached to the collar shown; the motion...Ch. 15.5 - Prob. 15.162PCh. 15.5 - Prob. 15.163PCh. 15.5 - At the instant shown, the length of the boom AB is...Ch. 15.5 - At the instant shown, the length of the boom AB is...Ch. 15.5 - Prob. 15.166PCh. 15.5 - Prob. 15.167PCh. 15.5 - Prob. 15.168PCh. 15.5 - 15.168 and 15.169A chain is looped around two...Ch. 15.5 - Prob. 15.170PCh. 15.5 - Prob. 15.171PCh. 15.5 - The collar P slides outward at a constant relative...Ch. 15.5 - Pin P slides in a circular slot cut in the plate...Ch. 15.5 - Prob. 15.174PCh. 15.5 - Prob. 15.175PCh. 15.5 - Knowing that at the instant shown the rod attached...Ch. 15.5 - Prob. 15.177PCh. 15.5 - In Prob. 15.177, determine the angular velocity...Ch. 15.5 - At the instant shown, bar BC has an angular...Ch. 15.5 - Prob. 15.180PCh. 15.5 - Rod AB passes through a collar that is welded to...Ch. 15.5 - Prob. 15.182PCh. 15.5 - Prob. 15.183PCh. 15.6 - The bowling ball shown rolls without slipping on...Ch. 15.6 - Prob. 15.185PCh. 15.6 - Prob. 15.186PCh. 15.6 - Prob. 15.187PCh. 15.6 - The rotor of an electric motor rotates at the...Ch. 15.6 - Prob. 15.189PCh. 15.6 - Prob. 15.190PCh. 15.6 - In the system shown, disk A is free to rotate...Ch. 15.6 - Prob. 15.192PCh. 15.6 - Prob. 15.193PCh. 15.6 - A radar system is used to track a new experimental...Ch. 15.6 - A 3-in.-radius disk spins at the constant rate 2 =...Ch. 15.6 - Prob. 15.196PCh. 15.6 - The cone shown rolls on the zx plane with its apex...Ch. 15.6 - At the instant shown, the robotic arm ABC is being...Ch. 15.6 - Prob. 15.199PCh. 15.6 - Prob. 15.200PCh. 15.6 - Several rods are brazed together to form the...Ch. 15.6 - In Prob. 15.201, the speed of point B is known to...Ch. 15.6 - Prob. 15.203PCh. 15.6 - Prob. 15.204PCh. 15.6 - Rod BC and BD are each 840 mm long and are...Ch. 15.6 - Rod AB is connected by ball-and-socket joints to...Ch. 15.6 - Prob. 15.207PCh. 15.6 - Prob. 15.208PCh. 15.6 - Prob. 15.209PCh. 15.6 - Prob. 15.210PCh. 15.6 - Prob. 15.211PCh. 15.6 - Prob. 15.212PCh. 15.6 - Prob. 15.213PCh. 15.6 - Prob. 15.214PCh. 15.6 - In Prob. 15.205, determine the acceleration of...Ch. 15.6 - In Prob. 15.206, determine the acceleration of...Ch. 15.6 - In Prob. 15.207, determine the acceleration of...Ch. 15.6 - Prob. 15.218PCh. 15.6 - Prob. 15.219PCh. 15.7 - A flight simulator is used to train pilots on how...Ch. 15.7 - A flight simulator is used to train pilots on how...Ch. 15.7 - Prob. 15.222PCh. 15.7 - Prob. 15.223PCh. 15.7 - Prob. 15.224PCh. 15.7 - The bent rod shown rotates at the constant rate of...Ch. 15.7 - The bent pipe shown rotates at the constant rate 1...Ch. 15.7 - The circular plate shown rotates about its...Ch. 15.7 - Prob. 15.228PCh. 15.7 - Prob. 15.229PCh. 15.7 - Prob. 15.230PCh. 15.7 - Prob. 15.231PCh. 15.7 - Using the method of Sec. 15.7A, solve Prob....Ch. 15.7 - Prob. 15.233PCh. 15.7 - Prob. 15.234PCh. 15.7 - Prob. 15.235PCh. 15.7 - The arm AB of length 16 ft is used to provide an...Ch. 15.7 - The remote manipulator system (RMS) shown is used...Ch. 15.7 - A disk with a radius of 120 mm rotates at the...Ch. 15.7 - Prob. 15.239PCh. 15.7 - Prob. 15.240PCh. 15.7 - Prob. 15.241PCh. 15.7 - The cylinder shown rotates at the constant rate 2...Ch. 15.7 - Prob. 15.243PCh. 15.7 - Prob. 15.244PCh. 15.7 - Prob. 15.245PCh. 15.7 - Prob. 15.246PCh. 15.7 - Prob. 15.247PCh. 15 - A wheel moves in the xy plane in such a way that...Ch. 15 - Two blocks and a pulley are connected by...Ch. 15 - A baseball pitching machine is designed to deliver...Ch. 15 - The flywheel OD on the elliptical machine analyzed...Ch. 15 - The roller at point A on the elliptical machine...Ch. 15 - Knowing that at the instant shown rod AB has zero...Ch. 15 - Rod AB is attached to a collar at A and is fitted...Ch. 15 - Prob. 15.255RPCh. 15 - A disk of 0.15-m radius rotates at the constant...Ch. 15 - Prob. 15.257RPCh. 15 - Prob. 15.258RPCh. 15 - In the position shown, the thin rod moves at a...
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
- 6) Bar BDE is attached to two links AB and CD. Knowing that at the instant shown link AB rotates with a constant angular velocity of 3 rad/s clockwise, determine the acceleration (a) of point D, (b) of point E. 19.1 cm 19.1 cm C -30.5 cm -22.9 cm- B ODarrow_forward15.113 The 360-mm-radius flywheel is rigidly attached to a 30-mm- radius shaft that can roll along parallel rails. Knowing that at the instant shown the center of the shaft has a velocity of 24 mm/s and an acceleration of 10 mm/s, both directed down to the left, determine the acceleration (a) of point A, (b) of point B. A 2₂x 360 mm- 20° Barrow_forwardRequired information NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. For a 5-m steel beam AE, the acceleration of point A is 2.5 m/s² downward and the angular acceleration of the beam is 1.5 rad/s2 counterclockwise. Knowing that at the instant considered the angular velocity of the beam is zero, determine the acceleration of cable B and cable D. A -1.5 m- B Determine the acceleration of cable B The acceleration of cable Bis 2 m 1.375 5 m/s2. D -1.5 m- Earrow_forward
- please solve explaning each step in the process thanksarrow_forwardIn a continuous printing process, paper is drawn into the presses at a constant speed v. Denoting by r the radius of the paper roll at any given time and by b the thickness of the paper, derive an expression for the angular acceleration of the paper roll.arrow_forward25.4 cm 30° O B 50.8 cm- 30° DO PROBLEM 15.81 Knowing that at the instant shown the angular velocity of bar DC is 18 rad/s counterclockwise, determine (a) the angular velocity of bar AB, (b) the angular velocity of bar BC, (c) the velocity of the midpoint of bar 25.4 cm BC. сarrow_forward
- Review questions please explain in full detail.arrow_forward1.- 4 A 3-in.-radius drum is rigidly attached to a 5-in. radius drum as shown. One of the drums rolls without sliding on the surface shown, and a cord is wound around the other drum. Knowing that at the instant shown end D of the cord has a velocity of 8 in./s and an acceleration of 30 in./s², both directed to the left, determine the accelerations of points A, B, and C of the drums. 5 in. 3 in G Darrow_forwardTHIS IS A SUPPLEMENTAL STUDY PROBLEM GIVEN AS AN EXTRA EXAMPLETHIS IS NOT A GRADED ASSIGNMENTarrow_forward
- Problem (5) The rectangular block shown rotates about the diagonal OA with a constant angular velocity of 6.76 rad/s. Knowing that the rotation is counterclockwise as viewed from A, determine the velocity and acceleration of point B at the instant shown. 240 mm 100 mm 312 mm B 312 mmarrow_forwardIn a four bar mechanism, the dimensions of the links are given as AB = 50 mm, BC = 66 mm, CD = 56 mm and AD = 100 mm. At a given instant when <DAB=600 . The angular velocity of link AB is 10.5r/s in CCW direction. Determine, (i) velocity of point C, (ii) velocity of point E on link BC when BE = 40 mm, (iii) the angular velocity of link BC and CD; (iv) the velocity of an offset point F on link BC, if BF = 45 mm, CF = 30 mm and BCF is read clockwise. (v) the velocity of an offset point G on link CD, if CG = 24 mm, DG = 44 mm and DCG is read clockwise (arrow_forwardPb 1) The angular velocity and angular acceleration of link 2 of the linkage shown are 20 rad/s cw and 600 rad/s² cw, respectively. Noting that the lengths AO2, AC and BA are all equal to 10 cm, determine: (a) VB, VC, @3 (b) aB, ac, α3. Bo 2 15° 3 Ans: 388 cm/s downward, 104 cm/s right, 20 rad/s ccw, 13600 cm/s² downward, 5000 cm/s² left, 600 rad/s² ccw Pb 2) In the mechanism shown, the angular velocity of link 2 is 130 rpm CW (constant). Using graphical method, determine: (a) VE, VF, 3, 4, 5, (b) aɛ, af, α3, A4, α5. D 3 2 C 60° 7 A E 5 AB = 1.8' BC = 3.75' CD = 3.75' AD = 4.5' AE= 4.35' DE=6.0' EF= 11.1' F Ans: 34 ft/s, 37 ft/s, 10.93 rad/s cw, 8 rad/s cw, 1.1 rad/s ccw, 288 ft/s2, 90 ft/s2, 51.2 rad/s² ccw, 18.7 rad/s² cw, 27.6 rad/s² ccwarrow_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 Press
Mechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSON
Thermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEY
Mechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage Learning
Engineering 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