Engineering Mechanics: Dynamics (14th Edition)
14th Edition
ISBN: 9780133915389
Author: Russell C. Hibbeler
Publisher: PEARSON
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Chapter 16.3, Problem 33P
If the angular displacement of A it θA = (5t3 + 10t2) rad, where t is in seconds, determine the angular velocity and angular accelerator of B when t = 3 s.
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motor supplies 200 kW at 6 Hz to flange A of the shaft shown in Figure. Gear B transfers 125 W of power to operating machinery in the factory, and the remaining power in the shaft is mansferred by gear D. Shafts (1) and (2) are solid aluminum (G = 28 GPa) shafts that have the same diameter and an allowable shear stress of t= 40 MPa. Shaft (3) is a solid steel (G = 80 GPa) shaft with an allowable shear stress of t = 55 MPa. Determine:
a) the minimum permissible diameter for aluminum shafts (1) and (2)
b) the minimum permissible diameter for steel shaft (3).
c) the rotation angle of gear D with respect to flange A if the shafts have the minimum permissible diameters as determined in (a) and (b).
Chapter 16 Solutions
Engineering Mechanics: Dynamics (14th Edition)
Ch. 16.3 - Determine its constant angular acceleration and...Ch. 16.3 - Determine the angular acceleration when it has...Ch. 16.3 - Determine the time it takes to achieve an angular...Ch. 16.3 - If the angular displacement of the wheel is =...Ch. 16.3 - Determine the magnitude of the velocity and...Ch. 16.3 - Determine the velocity of the cylinder and the...Ch. 16.3 - Determine the magnitudes of the velocity and...Ch. 16.3 - If the disk is originally rotating at 0 = 12...Ch. 16.3 - It it is subjected to a constant angular...Ch. 16.3 - If it is subjected to a constant angular...
Ch. 16.3 - Determine the number of revolutions, the angular...Ch. 16.3 - Determine the number of revolutions it must...Ch. 16.3 - Also, find the number of revolutions of gear D to...Ch. 16.3 - Gears A, B, C, and D have radii of 15 mm, 50 mm,...Ch. 16.3 - Determine the magnitude of acceleration of point B...Ch. 16.3 - pulley A is given a constant angular acceleration...Ch. 16.3 - Starting from rest, determine the angular...Ch. 16.3 - If the engine turns pulley A at A = (20t + 40)...Ch. 16.3 - If the engine turns pulley A at A = 60 rad/s,...Ch. 16.3 - Determine the angular velocity of the disk and its...Ch. 16.3 - Determine the magnitudes of the normal and...Ch. 16.3 - Determine the magnitudes of the normal and...Ch. 16.3 - If this gear is initially turning at A = 15 rad/s,...Ch. 16.3 - If this gear is initially turning at A = 15 rad/s,...Ch. 16.3 - Determine the brushs angular velocity when t = 4...Ch. 16.3 - If this gear is initially turning at (A)0 = 20...Ch. 16.3 - Determine the magnitudes of the velocity and the n...Ch. 16.3 - If the motor turns gear A with an angular...Ch. 16.3 - If the motor turns gear A with an angular...Ch. 16.3 - and the meshed pinion gear B on the propeller...Ch. 16.3 - determine the magnitude of the velocity and...Ch. 16.3 - If the gears A and have the dimensions shown,...Ch. 16.3 - and the meshed pinion gear B on the propeller...Ch. 16.3 - and the meshed pinion gear B on the propeller...Ch. 16.3 - If the canisters are centered 200 mm apart on the...Ch. 16.3 - Determine the largest angular velocity of gear B...Ch. 16.3 - The shaft of the motor M turns with an angular...Ch. 16.3 - If A has a constant angular acceleration of A = 30...Ch. 16.3 - If the angular displacement of A it A = (5t3 +...Ch. 16.3 - This gear is connected to gear B, which is fixed...Ch. 16.3 - Express the result in Cartesian vector form.Ch. 16.3 - Determine the velocity and acceleration of point D...Ch. 16.3 - At the instant shown it is rotating about the y...Ch. 16.3 - Determine the magnitudes of the velocity and...Ch. 16.4 - Determine the angular velocity and angular...Ch. 16.4 - Determine the angular acceleration and angular...Ch. 16.4 - Determine the angular acceleration and angular...Ch. 16.4 - Determine the angular velocity and angular...Ch. 16.4 - Determine the angular velocity of the connecting...Ch. 16.4 - The cam rotates with a constant counterclockwise...Ch. 16.4 - The pin connection at O does not cause an...Ch. 16.4 - Determine the velocity of the follower rod AB as...Ch. 16.4 - The pin connection at O does not cause an...Ch. 16.4 - Determine the velocity and acceleration of the peg...Ch. 16.4 - Determine the velocity and acceleration of block...Ch. 16.4 - Determine the angular velocity and angular...Ch. 16.4 - If the slotted arm is causing A to move downward...Ch. 16.4 - If the wedge moves to the left with a constant...Ch. 16.4 - If the rollers do not slip, determine their...Ch. 16.4 - If no slipping occurs between the disk D and the...Ch. 16.4 - Determine the velocity and acceleration of...Ch. 16.5 - If roller A moves to the right with a constant...Ch. 16.5 - Determine the magnitude of the velocity of point B...Ch. 16.5 - The cable wraps around the inner core, and the...Ch. 16.5 - If crank OA rotates with an angular velocity of =...Ch. 16.5 - If rod AB slides along the horizontal slot with a...Ch. 16.5 - Determine the velocity of the peg at B at this...Ch. 16.5 - Determine the velocity of point B at this instant.Ch. 16.5 - If the block at C is moving downward at 4 ft/s,...Ch. 16.5 - Determine the velocity of block C and the angular...Ch. 16.5 - Determine the angular velocities of links A B and...Ch. 16.5 - Also, sketch the position of link BC when = 55,...Ch. 16.5 - Link BC rotates clockwise with an angular velocity...Ch. 16.5 - If the angular velocity of link AB is AB = 3...Ch. 16.5 - Determine the velocity of the gear rack C.Ch. 16.5 - If B is moving to the right at 8 ft/s and C is...Ch. 16.5 - Determine the angular velocity of the gear and the...Ch. 16.5 - Determine the velocity of point A on the rim of...Ch. 16.5 - Link CB is horizontal at this instant.Ch. 16.5 - Determine the velocity of the slider C at the...Ch. 16.5 - Determine the velocity of block C and the angular...Ch. 16.5 - If AB has an angular velocity AB = 8 rad/s,...Ch. 16.5 - If the slider block A is moving downward at vA = 4...Ch. 16.5 - If the slider block A is moving downward at A = 4...Ch. 16.5 - This gear has an inner hub C which is fixed to B...Ch. 16.5 - If link AB is rotating at AB =3 rad/s, determine...Ch. 16.5 - If link CD is rotating at CD = 5 rad/s, determine...Ch. 16.5 - By locking or releasing certain gears, it has the...Ch. 16.5 - If the ring gear A rotates clockwise with an...Ch. 16.5 - It consists of a driving piston A, three links,...Ch. 16.5 - Because of the rotational motion of lint AB and...Ch. 16.6 - Establish the location of the instantaneous center...Ch. 16.6 - Determine the angular velocity of the rod and the...Ch. 16.6 - Determine the angular velocity of link BC and...Ch. 16.6 - The gear rack B is fixed.Ch. 16.6 - If cable AB is unwound with a speed of 3 m/s, and...Ch. 16.6 - Determine the angular velocity of link BC and the...Ch. 16.6 - Determine the angular velocity of links BC and CD...Ch. 16.6 - Assume the geometry is known.Ch. 16.6 - Determine the angular velocity of link AB at the...Ch. 16.6 - Determine the angular velocity of the link CB at...Ch. 16.6 - Determine the velocities of the cylinders center C...Ch. 16.6 - Determine the velocities of points A and B on the...Ch. 16.6 - Determine the velocities of points A and B.Ch. 16.6 - If rod CD is rotating with an angular velocity CD...Ch. 16.6 - If bar AB has an angular velocity AB = 6 rad/s,...Ch. 16.6 - Under these conditions, what is the speed at A if...Ch. 16.6 - Due to slipping, points A and B on the rim of the...Ch. 16.6 - Determine the velocities of the center point C and...Ch. 16.6 - Determine the velocity of point D and the angular...Ch. 16.6 - Determine the velocity of point P, and the angular...Ch. 16.6 - If connected bar CD is rotating with an angular...Ch. 16.6 - Determine the speeds of points A, B, and C caused...Ch. 16.6 - Determine the velocity of the gear rack C.Ch. 16.6 - If the hub gear H and ring gear R have angular...Ch. 16.6 - What is the angular velocity of the spur gear?Ch. 16.6 - Determine the angular velocity of rod CD at the...Ch. 16.6 - If bar CD is rotating with an angular velocity of...Ch. 16.6 - If the link rotates about the fixed point B at 4...Ch. 16.7 - if the sun gear D is rotating clockwise at D = 5...Ch. 16.7 - The angular velocity is given.Ch. 16.7 - Determine the angular acceleration of the rod and...Ch. 16.7 - Determine the acceleration of point A.Ch. 16.7 - At the instant shown, the center O of the gear...Ch. 16.7 - Determine the angular acceleration of the gear at...Ch. 16.7 - Determine the angular acceleration of link BC at...Ch. 16.7 - Determine the angular acceleration of link BC and...Ch. 16.7 - Determine the velocity sod acceleration of the...Ch. 16.7 - Determine the acceleration of the top of the...Ch. 16.7 - Determine the acceleration of the bottom A of the...Ch. 16.7 - Determine the velocity and acceleration of the...Ch. 16.7 - Determine the velocity and acceleration of the...Ch. 16.7 - At the instant shown, point A has the motion...Ch. 16.7 - Determine the angular velocity and angular...Ch. 16.7 - Determine the angular velocity and angular...Ch. 16.7 - Determine the angular acceleration of link AB and...Ch. 16.7 - Determine the angular acceleration of link CD if...Ch. 16.7 - Determine the velocity and acceleration of point A...Ch. 16.7 - Determine the velocity and acceleration of point B...Ch. 16.7 - If it is pulled with a constant velocity v,...Ch. 16.7 - If it does not slip at A, determine the...Ch. 16.7 - If it does not slip at A, determine the...Ch. 16.7 - As cord CF unwinds from the inner rim of the...Ch. 16.7 - Determine the velocity and acceleration of point B...Ch. 16.7 - Determine the angular velocity and angular...Ch. 16.7 - If link DE has the angular motion shown, determine...Ch. 16.7 - If member AB has the angular motion shown,...Ch. 16.7 - If member AB has the angular motion shown,...Ch. 16.7 - Determine the acceleration of points A and B on...Ch. 16.7 - At a given instant, A has a velocity of vA = 4...Ch. 16.7 - Determine the angular acceleration of rod AB at...Ch. 16.8 - Determine the acceleration of A at the instant...Ch. 16.8 - If at the same instant the disk has the angular...Ch. 16.8 - At the same instant, the boom is extending with a...Ch. 16.8 - Prob. 131PCh. 16.8 - Prob. 132PCh. 16.8 - Determine the velocity and acceleration of a water...Ch. 16.8 - At the instant shown, the cord is pulled down...Ch. 16.8 - Prob. 135PCh. 16.8 - Determine the velocity and acceleration of point C...Ch. 16.8 - Prob. 137PCh. 16.8 - Determine the magnitudes of the velocity and...Ch. 16.8 - If link AD is rotating at a constant rate of AD =...Ch. 16.8 - Determine the angular velocity and angular...Ch. 16.8 - If rod AB has an angular velocity of 2 rad/s and...Ch. 16.8 - Prob. 142PCh. 16.8 - If the gears center O moves with the velocity and...Ch. 16.8 - Prob. 144PCh. 16.8 - Prob. 145PCh. 16.8 - Also at this instant the car mounted at the end of...Ch. 16.8 - If the slider block C is fixed to the disk that...Ch. 16.8 - Determine the velocity and acceleration of car A...Ch. 16.8 - Determine the velocity and acceleration of car B...Ch. 16.8 - Link AB has a pin at B which is confined to move...Ch. 16.8 - Prob. 151PCh. 16.8 - The star wheel A makes one sixth of a revolution...Ch. 16.8 - If the tires do not slip on the pavement,...Ch. 16.8 - Determine the velocity and deceleration of the...Ch. 16.8 - Determine the speed of block B when it has risen s...Ch. 16.8 - At the instant shown, it has an acceleration of...Ch. 16.8 - If bar AB has an angular velocity AB = 6 rad/s,...Ch. 16.8 - If the cable does not slip on the pulley's...Ch. 16.8 - Determine the acceleration of the pin at C and the...Ch. 16.8 - If it does not slip at A, determine the...Ch. 16.8 - Determine the velocity and acceleration of the...
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