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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Chapter 15.5, Problem 15.177P
To determine
The angular velocity and angular acceleration of disk S.
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Link 2 of the mechanism shown rotates about the z-axis w.r.t.
the ground (Link 1) at a constant +2rad/s. Link 3 rotates
about a pin joint currently aligned with the y-axis at a
constant -3rad/s. What is the angular velocity of the link?
Angular velocity (rad/s): type your answer.... i+
type your answer...
j+ type your answer...
k. Answer with
integers. Include a minus sign if necessary. Don't include a
plus sign.
Z
A
2
3
— X
►
Problem (3)
radius r = 70 mm and is attached to block B as
shown. If the angular velocity of gear D is 20 rpm
A straight rack rests on a gear of
A
counterclockwise when 0 = 20°, determine:
(a) The velocity of block B
(b) The angular velocity of rack AB
Solve the problem one time using the relative velocity equation and another time using the
Instantaneous Center (IC) method. You should get the same answers.
Q1: The crank of a slider crank mechanism rotates clockwise at a constant speed
of 300 r.p.m. The crank is 150 mm and the connecting rod is 600 mm long.
Determine the angular velocity and angular acceleration of the connecting rod, at
a crank angle of 45° from inner dead center position.
A
immin
B
150 mm
45°
I.D.C.
Q2: The turning moment diagram of a four-stroke engine assumed to be
represented by four triangles in each stroke. The areas of these triangles are as
follows: Suction stroke = 700 N.m; Compression stroke = 2940 N.m; Expansion
stroke = 11900 N.m; Exhaust stroke = 1120 N.m. All the areas excepting
Expansion stroke are negative. Determine the moment of inertia of the flywheel
to keep the speed between 98 r.p.m. and 102 r.p.m. Also find the size of a rim-
type flywheel, given that density of flywheel material is 8150 kg/m³; the
allowable tensile stress of the flywheel material is 7.5 MPa. The rim cross-section
is rectangular; one side being four times the length of the other.…
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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