Vector Mechanics for Engineers: Dynamics
11th Edition
ISBN: 9780077687342
Author: Ferdinand P. Beer, E. Russell Johnston Jr., Phillip J. Cornwell, Brian Self
Publisher: McGraw-Hill Education
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Textbook Question
Chapter 15.3, Problem 15.99P
Describe the space centrode and the body centrode of rod ADD of Prob. 15.83. (Hint: The body centrode need not lie on a physical portion of the rod)
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5) In ice figure skating, a couple execute a “top” (see picture). The centre of mass of the woman (58 kg) is situated 1.3 m from the axis of rotation which is vertical and passes through the centre of mass of the man (85 kg). They are spinning at a constant angular velocity equal to 3.1415 rad/s and the man and woman have moments of inertia, about their own centres of mass, equal to 1.6 and 2.5 kg.m2 respectively. Then the woman grabs the neck of the man. At this point, her moment of inertia decreases to 1.4 kg.m2 and her body centre of gravity is 0.9 m from the axis of rotation. Determine the new angular velocity.
Hints: This is a conservation of angular momentum problem, and needs the parallel axis theorem to determine moments of inertia about the axis of rotation. The skaters are moving as one body with one angular velocity, but they each have their own moments of inertia given relative to their own CoMs. For the man, that’s fine…the axis they’re rotating about passes through his…
3. A simple connecting rod mechanism has a rod 250mm long and a crank radius of 75 mm. The connecting rod
has a mass of 1.5kg, its centre of gravity is 75mm from the large end and it has a radius of gyration about the
centre of gravity of 100mm.
When the crank angle is 30° and the crankshaft speed is 3000rpm clockwise:
(a) (i) Show by kinematic analysis that the angular acceleration of the connecting rod is 13,940 rad/s²
(clockwise)
(ii) Show also that the acceleration of the centre of gravity (C) in the X and Y direction is respectively, fcx
= 6759m/s² (to the right) and fcy = 2590.8m/s² (downwards).
Hence, find the magnitude and direction of the forces acting on the frame of the engine due to the inertia of
the connecting rod as follows:
(b) The force exerted by the cylinder wall on the piston at B
(c) The force on the main bearing at O
(d) The torque input or output at the crank
B
Figure 3. Connecting rod mechanism
C
A
30°
O
ASAP, answer A, B and C, I will LIKE if all are answered. Thanks
A. The mass moment of inertia of a cylinder about its central axis perpendicular to a circular cross section is
a. Directly proportional to its radius
b. Directly proportional to its length
c. Independent of its radius
d. Independent of its length
B. A projectile is thrown with a speed of 120ft/sec in a direction 41 degrees above the horizontal. Determine the highest point to which it rises ymax.
A. 90.25
B. 102.14
C. 103.17
D. 96.24
C. A 60 lb ball is dropped from a height of 48ft. What is the velocity of the ball just before impact?
a. 9.8 ft/s
b. 55.6 ft/s
c. 39.3 ft/s
d. 31 ft/s
Chapter 15 Solutions
Vector Mechanics for Engineers: 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 lager 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 - The rotor of a gas turbine is rotating at a speed...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 - The bent rod ABCD rotates about a line joining...Ch. 15.1 - In Prob. 15.10, determine the velocity and...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 - A series of small machine components being moved...Ch. 15.1 - A series of small machine components being moved...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 - Three belts move over tow pulleys without slipping...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 - Ring B has an inside radius r2and hangs from the...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. 15.37PCh. 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 - The motion of rod AB is guided by pins attached at...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 - The plate shown moves in the xy plane. Knowing...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 - Arm AB rotates with an angular velocity of 20...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 velocity of...Ch. 15.2 - Knowing that at the instant shown the angular...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 at the instant shown the angular...Ch. 15.2 - In the position shown, bar AB has angular velocity...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 - In the position shown, bar DE has a constant...Ch. 15.2 - 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 - 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. 15.77PCh. 15.3 - The spool of tape shown and its frame assembly are...Ch. 15.3 - The spool of tape shown and its frame are pulled...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 - Rod BDE is partially guided by a roller at D that...Ch. 15.3 - Rod BDE is partially guided by a roller at D that...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 25-in. rods are pin-connected at D as shown....Ch. 15.3 - Two rods ABD and DE are connected to three collars...Ch. 15.3 - At the instant shown, the velocity of collar A is...Ch. 15.3 - Two rods AB and DE are connected as shown. Knowing...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 at the instant shown crank BC has a...Ch. 15.4 - End A of rod AB moves to the right with a constant...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 - 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 - The disk shown has a constant angular velocity of...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 - Knowing that at the instant shown bar AB has a...Ch. 15.4 - Knowing that at the instant shown bar DE has a...Ch. 15.4 - Knowing that at the instant shown bar AB has a...Ch. 15.4 - Knowing that at the instant shown bar AB has a...Ch. 15.4 - Knowing that at the instant shown bar AB has...Ch. 15.4 - Knowing that at the instant shown bar AB has...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 - Rod AB moves over a small wheel at C while end A...Ch. 15.4 - Rod AB moves over a small wheel at C while end A...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 - Pin P is attached to the collar shown; the motion...Ch. 15.5 - Pin P is attached to the collar shown; the motion...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. 15.161PCh. 15.5 - A rocket sled is tested o a straight track that is...Ch. 15.5 - Prob. 15.163PCh. 15.5 - Prob. 15.164PCh. 15.5 - At the instant shown the length of the boom AB is...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. 15.170PCh. 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. 15.176PCh. 15.5 - Prob. 15.177PCh. 15.5 - In Prob. 15.177, determine the angular velocity...Ch. 15.5 - Prob. 15.179PCh. 15.5 - Prob. 15.180PCh. 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 - Plate ABD and rod OB are rigidly connected and...Ch. 15.6 - At the instant considered, the radar antenna shown...Ch. 15.6 - Prob. 15.188PCh. 15.6 - The disk of a portable sander rotates at the...Ch. 15.6 - Prob. 15.190PCh. 15.6 - Prob. 15.191PCh. 15.6 - In the system shown, disk A is free to rotate...Ch. 15.6 - Prob. 15.193PCh. 15.6 - A gun barrel of length OP=4m is mounted on a...Ch. 15.6 - Prob. 15.195PCh. 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 - In the planetary gear system shown, gears A and B...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 - The rectangular plate shown rotates at the...Ch. 15.7 - The rectangular plate shown rotates at the...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 - The vertical plate shown is welded to arm EFG, and...Ch. 15.7 - The vertical plate shown is welded to arm EFG, and...Ch. 15.7 - A disk of 180-mm radius rotates at the constant...Ch. 15.7 - A disk of 180-mm radius rotates at the constant...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 - Knowing that inner gear A is stationary and outer...Ch. 15 - Knowing that at the instant shown bar AB has an...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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