12th Edition

ISBN: 9781259977305

Author: BEER, Ferdinand P. (ferdinand Pierre), Johnston, E. Russell (elwood Russell), Cornwell, Phillip J., SELF, Brian P.

Publisher: Mcgraw-hill Education,

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Textbook Question

Chapter 15.1, Problem 15.7P

When studying whiplash resulting from rear-end collisions, the rotation of the head is of primary interest. An impact test was performed, and it was found that the angular acceleration of the bead is defined by the relation α = 700 cos θ + 70 sin θ , where a is expressed in rad/s² and θ in radians Knowing that the head is initially at rest, determine the angular velocity of the head when θ = 30 ° .

Chapter 15.1, Problem 15.7P, When studying whiplash resulting from rear-end collisions, the rotation of the head is of primary

Fig. P16.1

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Chapter 15.1, Problem 15.6P

Chapter 15.1, Problem 15.8P

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Chapter 15 Solutions

Vector Mechanics For Engineers

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 oscillation flvdee1 is defined by...Ch. 15.1 - The motion of an oscillation flywheel is defined...Ch. 15.1 - Prob. 15.4P 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 - When studying whiplash resulting from rear-end...Ch. 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. 15.10P Ch. 15.1 - Prob. 15.11P Ch. 15.1 - The rectangular block shown rotates about the...Ch. 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 - In Prob. 15.14, determine the velocity and...Ch. 15.1 - The earth makes one complete revolution around the...Ch. 15.1 - The earth makes one complete revolution on its...Ch. 15.1 - The sprocket wheel and chain shown initially at...Ch. 15.1 - Prob. 15.19P Ch. 15.1 - The belt sander shown is initially at rest. If the...Ch. 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 statior.ary trainer during the...Ch. 15.1 - gear reduction system consists of three gears A,...Ch. 15.1 - A belt is pulled to the right between cylinders A...Ch. 15.1 - Ring C has an inside radius of 55 mm and an...Ch. 15.1 - At the instant shown, the angular velocity of...Ch. 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 - Two friction wheels A and B are both rotating...Ch. 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 - Prob. 15.37P Ch. 15.2 - The ball rolls without slipping on the fixed...Ch. 15.2 - Three uniform rods—ABC, DCE, and FGH—are connected...Ch. 15.2 - An automobile travel, to the right at a constant...Ch. 15.2 - Prob. 15.39P 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 p1ane. Knowing that...Ch. 15.2 - Prob. 15.46P Ch. 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 - In the planetary gear system shown, the radius of...Ch. 15.2 - The outer gear C rotates with an angular velocity...Ch. 15.2 - In the simplified sketch of a ball bearing shown,...Ch. 15.2 - A simplified gear system for a mechanical watch is...Ch. 15.2 - Arm ACB rotates about point C with an angular...Ch. 15.2 - Arm ACB rotates about point C with an angular...Ch. 15.2 - Knowing that at the instant shown the angular...Ch. 15.2 - Prob. 15.56P 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 is shown was developed to perform...Ch. 15.2 - In the concentric shown, a disk of 2-in. radius...Ch. 15.2 - In the engine system shown, l=160mmandb=60mm ....Ch. 15.2 - In the engine system shown, l=160 mm and b=60 mm....Ch. 15.2 - Knowing that the angular velocity of rod DE is a...Ch. 15.2 - In the position shown bar AB has an anu1ar...Ch. 15.2 - Linkage DBEF is part of a windshield wiper...Ch. 15.2 - Roberts linkage is named after Richard Roberts...Ch. 15.2 - Roberts linkage is named after Richard Roberts...Ch. 15.2 - For the oil pump rig shown, link AB causes the...Ch. 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 - Bar BDE is pinned to two links, AB and CD. At the...Ch. 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 - A 60-mm-radius drum is rigidly attached to a...Ch. 15.3 - Prob. 15.77P Ch. 15.3 - In order to uncoil electrical wire from a...Ch. 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 - An overhead door is guided by wheels at A and B...Ch. 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 - Prob. 15.85P Ch. 15.3 - A motor at O drives the windshield wiper mechanism...Ch. 15.3 - A motor at O drives the windshield wiper mechanism...Ch. 15.3 - Rod AB can slide freely along the floor and the...Ch. 15.3 - Small wheels have been attached to the ends of bar...Ch. 15.3 - Two slots have been cut in plate FG and the plate...Ch. 15.3 - The disk is released from rest and rolls down the...Ch. 15.3 - The pin at B is attached to member ABD and can...Ch. 15.3 - Two identical rods ABF and DBE are Connected by a...Ch. 15.3 - Ann 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. 15.98P Ch. 15.3 - Describe the space centrode and the body centrode...Ch. 15.3 - Describe the space centrode and the body centrode...Ch. 15.3 - Using the method of Sec. 15.3, solve Prob. 15.60.Ch. 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 - A 5-m steel beam is lowered by means of two cables...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 P...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 - automobile travels to the left at a constant speed...Ch. 15.4 - The 18-in.-radius flywheel is rigidly attached to...Ch. 15.4 - A 3-in.-radius drum is rigidly attached to a...Ch. 15.4 - A 3-in.-radius drum is rigidly attached to a...Ch. 15.4 - A heavy crate is being moved a sbo1 distance using...Ch. 15.4 - A wheel rolls without slipping on a fixed...Ch. 15.4 - The 100-nun-radius drum rolls without slipping on...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 - Prob. 15.123P 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 in....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. 15.129P Ch. 15.4 - Knowing that at the instant shown bar DE has an...Ch. 15.4 - Knowing that at the instant shown bar AB has a...Ch. 15.4 - Prob. 15.132P Ch. 15.4 - Prob. 15.133P Ch. 15.4 - Prob. 15.134P Ch. 15.4 - Roberts linkage is named after Richard Roberts...Ch. 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 - The drive disk of the Scotch crosshead mechanism...Ch. 15.4 - The wheels attached to the ends of rod AB roll...Ch. 15.4 - The wheels attached to the ends of rod AB roll...Ch. 15.4 - A disk of radius r rolls to the right with a...Ch. 15.4 - Ladder AB moves over a smooth corner at C while...Ch. 15.4 - Prob. 15.143P Ch. 15.4 - Crank4B rotates with a constant c1ockise angular...Ch. 15.4 - Crank 4B rotates with a constant clockwise angular...Ch. 15.4 - Solve the engine system from Sample Prob. 15.15...Ch. 15.4 - The position of rod AB is controlled by a disk of...Ch. 15.4 - A wheel of radius r rolls without slipping along...Ch. 15.4 - In Prob. 15. 148, show that the path of P is a...Ch. 15.5 - A person walks radially inward on a platform that...Ch. 15.5 - Prob. 15.150P Ch. 15.5 - Prob. 15.151P Ch. 15.5 - Two rotating rods are connected by slider block P....Ch. 15.5 - Two rotating rods are connected by slider block P....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 - Knowing that at the instant shown the anu1ar...Ch. 15.5 - The motion of pin P is guided by slots cut in...Ch. 15.5 - Four pins slide in four separate slots cut in a...Ch. 15.5 - Solve Prob. 15.158, assuming that the plate...Ch. 15.5 - The cage of a mine elevator moves downward at a...Ch. 15.5 - Prob. 15.161P Ch. 15.5 - A rocket sled is tested o a straight track that is...Ch. 15.5 - Prob. 15.163P Ch. 15.5 - Prob. 15.164P Ch. 15.5 - Prob. 15.165P Ch. 15.5 - In the automated welding setup shown, the position...Ch. 15.5 - In the automated welding setup shown, the position...Ch. 15.5 - A chain is looped around two gears of radius 40 mm...Ch. 15.5 - A chain is looped around two gears of radius 40 mm...Ch. 15.5 - Prob. 15.170P Ch. 15.5 - The human leg can be crudely approximated as two...Ch. 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 - Rod AD is bent in the shape of an are of a circle...Ch. 15.5 - Solve Prob. 15.l74 when =90 .Ch. 15.5 - Prob. 15.176P Ch. 15.5 - Prob. 15.177P Ch. 15.5 - In Prob. 15.177, determine the angular velocity...Ch. 15.5 - Prob. 15.179P Ch. 15.5 - Prob. 15.180P Ch. 15.5 - Rod AB passes through a collar that is welded to...Ch. 15.5 - Solve Prob. 15.181 assuming block A moves to the...Ch. 15.5 - In Prob. 15.157, determine the acceleration of pin...Ch. 15.6 - The bowling ball shown rolls without slipping on...Ch. 15.6 - The bowling ball shown rolls without slipping on...Ch. 15.6 - Prob. 15.186P Ch. 15.6 - At the instant considered, the radar antenna shown...Ch. 15.6 - Prob. 15.188P Ch. 15.6 - The disk of a portable sander rotates at the...Ch. 15.6 - Prob. 15.190P Ch. 15.6 - Prob. 15.191P Ch. 15.6 - In the system shown, disk A is free to rotate...Ch. 15.6 - Prob. 15.193P Ch. 15.6 - A radar system is used to track a new experimental...Ch. 15.6 - Prob. 15.195P Ch. 15.6 - A 3-in-radius disk spins at the constant rate 2=4...Ch. 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. 15.199P Ch. 15.6 - In Prob. 15.199, determine (a) the common angular...Ch. 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 - Rod AB of length 25 in. is connected by ball...Ch. 15.6 - Rod AB has a length of 13 in. and is connected by...Ch. 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 - Rod AB of length 29 in. is connected by...Ch. 15.6 - Rod AB of length 300 mm is connected by ball...Ch. 15.6 - Rod AB of length 300 mm is connected by...Ch. 15.6 - Two shafts AC and EG, which lie in the vertical yz...Ch. 15.6 - Solve Prob. 15.210, assuming that the arm of the...Ch. 15.6 - Rod BC has a length of 42 in. and is connected by...Ch. 15.6 - Rod AB has a length of 275 mm and is connected by...Ch. 15.6 - For the mechanism of Prob.15.204, determine the...Ch. 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 - In Prob. 15.208, determine the acceleration of...Ch. 15.6 - In Prob. 15.209, determine the acceleration of...Ch. 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. 15.222P Ch. 15.7 - Prob. 15.223P Ch. 15.7 - Rod AB is welded to the 0.3-m-radius plate that...Ch. 15.7 - The bent rod shown rotates at the constant rate of...Ch. 15.7 - The bent pipe shown rotates at the constant rate...Ch. 15.7 - The circular plate shown rotates about its...Ch. 15.7 - Manufactured items are spray-painted as they pass...Ch. 15.7 - Solve Prob. 15.227, assuming that at the instant...Ch. 15.7 - Solve Prob. 15.225, assuming that at the instant...Ch. 15.7 - Using the method of Sec. 15.7A, solve Prob....Ch. 15.7 - Using the method of Sec. 15.7A, solve Prob....Ch. 15.7 - Using the method of Sec. 15.7A, solve Prob....Ch. 15.7 - The 400-mm bar AB is made to rotate at the...Ch. 15.7 - The 400-mm bar AB is made to rotate at the rate...Ch. 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 - The crane shown rotates at the constant rate...Ch. 15.7 - Prob. 15.240P Ch. 15.7 - Prob. 15.241P Ch. 15.7 - Prob. 15.242P Ch. 15.7 - Prob. 15.243P Ch. 15.7 - A square plate of side 2r is welded to a vertical...Ch. 15.7 - Two disks, each of 130-mm radius, are welded to...Ch. 15.7 - In Prob. 15.245, determine the velocity and...Ch. 15.7 - The position of the stylus tip A is controlled by...Ch. 15 - A wheel moves in the xy plane in such a way that...Ch. 15 - Two blocks and a pulley e connected by...Ch. 15 - A baseball pitching machine is designed to deliver...Ch. 15 - The flywheel OD on the elliptical machine analyzed...Ch. 15 - Prob. 15.252RP 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 - flows through a curved pipe .AB that rotates with...Ch. 15 - A disk of 0.15-m radius rotates at the constant...Ch. 15 - Two rods AE and BD pass through holes drilled into...Ch. 15 - Rod BC of length 24 in. is connected by ball...Ch. 15 - In the positions shown, the thin rod moves at a...

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Solution Summary: The author explains the angular velocity of the head when theta =30°.

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