Vector Mechanics for Engineers: Statics and Dynamics
11th Edition
ISBN: 9780073398242
Author: Ferdinand P. Beer, E. Russell Johnston Jr., David Mazurek, Phillip J. Cornwell, Brian Self
Publisher: McGraw-Hill Education
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Textbook Question
Chapter 15.2, Problem 15.70P
Both 6-in.-radius wheels roll without slipping on the horizontal surface. Knowing that the distance AD is 5 in., the distance BE is 4 in., and D has a velocity of 6 in./s to the right, determine the velocity of point E.
Fig. P15.70
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5
Both 6-in.-radius wheels roll without slipping on
the horizontal surface. Knowing that the distance
AD is 5 in., the distance BE is 4 in. and D has a
velocity of 6 in./s to the right, determine the
velocity of Point E.
A
14 in.
6 in.D
В
E
6 in.
A
The 18-in.-radius fly wheel is rigidly attached to a 1.5-in. -radius
shaft that can roll along parallel rails. Knowing that at the instant
shown the center of the shaft has a velocity of 1.2 in/s and an
acceleration of 0.5 in/s?, both directed down to the left,
determine the acceleration (a) of point A, (b) of point B.
18 in.
20
В
15.113 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°
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 - Prob. 15.1PCh. 15.1 - The motion of an oscillating flywheel is defined...Ch. 15.1 - The motion of an oscillating flywheel is defined...Ch. 15.1 - 15.4 The rotor of a gas turbine is rotating at a...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 - Prob. 15.10PCh. 15.1 - Prob. 15.11PCh. 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 - Prob. 15.18PCh. 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 - Prob. 15.23PCh. 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 - Prob. 15.39PCh. 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 - 15.50 Arm AB rotates with an angular velocity of...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 - 15.55 Knowing that at the instant shown the...Ch. 15.2 - Prob. 15.56PCh. 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 - Prob. 15.63PCh. 15.2 - Prob. 15.64PCh. 15.2 - Prob. 15.65PCh. 15.2 - Prob. 15.66PCh. 15.2 - Prob. 15.67PCh. 15.2 - Prob. 15.68PCh. 15.2 - 15.69 In the position shown, bar DE has a constant...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 - Prob. 15.79PCh. 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 - 15.84 Rod BDE is partially guided by a roller at D...Ch. 15.3 - Prob. 15.85PCh. 15.3 - Prob. 15.86PCh. 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 - 15.95 Two 25-in. rods are pin-connected at D as...Ch. 15.3 - Prob. 15.96PCh. 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 - 15.109 Knowing that at the instant shown crank BC...Ch. 15.4 - Prob. 15.110PCh. 15.4 - Prob. 15.111PCh. 15.4 - The 18-in.-radius flywheel is rigidly attached to...Ch. 15.4 - 15.113 and 15.114 A 3-in.-radius drum is rigidly...Ch. 15.4 - Prob. 15.114PCh. 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 - 15.123 The disk shown has a constant angular...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 - Prob. 15.129PCh. 15.4 - Prob. 15.130PCh. 15.4 - 15.131 and 15.132 Knowing that at the instant...Ch. 15.4 - 15.132 Knowing that at the instant shown bar AB...Ch. 15.4 - Prob. 15.133PCh. 15.4 - Prob. 15.134PCh. 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 - Prob. 15.150PCh. 15.5 - Prob. 15.151PCh. 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 - Prob. 15.194PCh. 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 - Prob. 15.242PCh. 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 - Prob. 15.251RPCh. 15 - Prob. 15.252RPCh. 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...
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- 2. An overhead door is guided by wheels at A and B that roll in horizontal and vertical tracks. Knowing that when 0 = 40° the velocity of wheel B is 1.5 ft/s upward, determine (a) the angular velocity of the door, (b) the velocity of end D of the door. 5ft 5 ftarrow_forward15.119 The 200-mm-radius disk rolls without sliding on the surface shown. Knowing that the distance BG is 160 mm and that at the instant shown the disk has an angular velocity of 8 rad/s counterclockwise and an angular acceleration of 2 rad/s² clockwise, determine the acceleration of A. A Fig. P15.119 800 mm B 200 mm Garrow_forwardplease solve explaning each step in the process thanksarrow_forward
- ) An overhead door is guided by wheelsn at A and B that roll in horizontal and vertical tracks. Knowing that when θ= 40° the velocity of wheel B is 0.5 m/s upward, determine (a) the angular velocity of the door, (b) the velocity of end D of the door.arrow_forward15.127 Knowing that at the instant shown rod AB has a constant an- gular velocity of 6 rad/s clockwise, determine the acceleration of point D. 4.5 in. 4.5 in. 4.5 in. B A 11.25 in. - D C 11.25 in.. Earrow_forwardProblem (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_forward
- 15.123 Knowing that crank AB rotates about point A with a constant angular velocity of 900 rpm clockwise, determine the acceleration of the pis- ton P when 0 = 60°. D 2 in. B 6 in.arrow_forward15.152 and 15.153 Pin P is attached to the collar shown; the motion of the pin is guided by a slot cut in rod BD and by the collar that slides on rod AE. Knowing that at the instant considered the rods rotate clockwise with constant angular velocities, determine for the given data the velocity of pin P. 15.152 AE 15.153 @AE 8 rad/s, wBD = 3 rad/s = 7 rad/s, @BD 4.8 rad/s 500 mm 30° B Fig. P15.152 and P15.153 Earrow_forwardProblem (6) The bent rod ABCD rotates about a line joining points A and E with a constant angular velocity of 12 rad/s. Knowing that the rotation is clockwise as viewed from E, determine the velocity and acceleration of corner C. 20cm A 25cm B 15cm 15cm 41cmarrow_forward
- 15.109 At the instant shown the angular velocity of the wheel is 2 rad/s clockwise and its angular acceleration is 3 rad/s² counterclockwise. Knowing that the wheel rolls without slipping, determine the location of the point on the wheel with zero acceleration at this instant. Fig. P15.109 600 mmarrow_forward15.115 and 15.116 A 60-mm-radius drum is rigidly attached to a 100-mm-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 160 mm/s and an acceleration of 600 mm/s², both directed to the left, determine the accel- erations of points A, B, and C of the drums. a D 100 mm G 60 mm 40 B Carrow_forward15.82 An overhead door is guided by wheels at A and B that roll in hori- zontal and vertical tracks. Knowing that when 0 = 40° the velocity of wheel B is 1.5 ft/s upward, determine (a) the angular velocity of the door, (b) the velocity of end D of the door. A 5 ft 5 ft Fig. P15.82arrow_forward
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