PEARSON ETEXT ENGINEERING MECH & STATS
15th Edition
ISBN: 9780137514724
Author: HIBBELER
Publisher: PEARSON
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Chapter 22, Problem 59P
To determine
The angular velocity of the flywheel.
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A smooth disk with a mass of 3 kg is placed on a cylindrical surface.It can move without slipping. This cylinder has a mass of 2 kgproperly connected to the AB bar at its midpoint. AB bar is also middleIt is connected to a spring with a constant k = 300 N/m. EUrod can move freely around point A. Boccurs when the tip is given a small displacement and released.Calculate the period of the vibration.
Determine the characteristic equation and the periods of vibration of the indicated system.
Important problem. The motor produces
a counterclockwise torque 1 N.m on the
attached disk A. A Part of this torque is
transferred to the disk C through the belt after
amplification. The disk A has mass 0.5 kg.
and the disk C has mass = 4.5 kg. Find:
(50 m
5omm
pully C
I.
The difference tension between the
palley A
Te
belt parts (7- T).
II.
The angular acceleration of the disk
С.
The angular acceleration of disk A.
The angular velocity of the disk C after 5 seconds from the motion start.
The transferred torque to the disk C.
III.
IV.
V.
Chapter 22 Solutions
PEARSON ETEXT ENGINEERING MECH & STATS
Ch. 22 - A spring is stretched 175 mm by an 8-kg block. If...Ch. 22 - A spring has a stiffness of 800 N/m. If a 2-kg...Ch. 22 - Prob. 3PCh. 22 - Prob. 4PCh. 22 - Prob. 5PCh. 22 - Prob. 6PCh. 22 - Prob. 7PCh. 22 - Prob. 8PCh. 22 - A 3-kg block is suspended from a spring having a...Ch. 22 - Prob. 10P
Ch. 22 - Prob. 13PCh. 22 - Prob. 14PCh. 22 - Prob. 16PCh. 22 - Prob. 17PCh. 22 - A uniform board is supported on two wheels which...Ch. 22 - Prob. 24PCh. 22 - Prob. 30PCh. 22 - Prob. 31PCh. 22 - Prob. 32PCh. 22 - Determine the differential equation of motion of...Ch. 22 - Prob. 36PCh. 22 - If the block-and-spring model is subjected to the...Ch. 22 - A block which has a mass m is suspended from a...Ch. 22 - A 4-lb weight is attached to a spring having a...Ch. 22 - A 4-kg block is suspended from a spring that has a...Ch. 22 - A 5-kg block is suspended from a spring having a...Ch. 22 - Prob. 48PCh. 22 - The light elastic rod supports a 4-kg sphere. When...Ch. 22 - Find the differential equation for small...Ch. 22 - Prob. 52PCh. 22 - The fan has a mass of 25 kg and is fixed to the...Ch. 22 - In Prob. 22-53 , determine the amplitude of...Ch. 22 - Prob. 55PCh. 22 - Prob. 56PCh. 22 - Prob. 57PCh. 22 - Prob. 58PCh. 22 - Prob. 59PCh. 22 - Prob. 60PCh. 22 - Prob. 61PCh. 22 - Prob. 62PCh. 22 - Prob. 65PCh. 22 - Determine the magnification factor of the block,...Ch. 22 - Prob. 67PCh. 22 - The 200-lb electric motor is fastened to the...Ch. 22 - Prob. 70PCh. 22 - Prob. 72PCh. 22 - Prob. 73PCh. 22 - Prob. 74PCh. 22 - Prob. 75PCh. 22 - Prob. 76PCh. 22 - Prob. 79P
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- 22-18. The uniform beam is supported at its ends by two springs A and B, each having the same stiffness k. When nothing is supported on the beam, it has a period of vertical vibration of 0.83 s. If a 50-kg mass is placed at its center, the period of vertical vibration is 1.52 s. Compute the stiffness of each spring and the mass of the beam. B.arrow_forwardThe body of arbitrary shape has a mass m, mass center at G, and a radius ofgyration about G of . If it is displaced a slight amount from its equilibriumposition and released, determine the natural period of vibration.arrow_forwardThe uniform rod ABC weighs 5 lbf and is attached to wo springs as shown. If end c is given a small displacement and released, determine the frequency of vibration of the rod. Use Energy Method. k = 3 lby/in. k = 4 lbg/in. A 15 in. 15 in.arrow_forward
- If k = 23 kip/in and W = 329 kip, determine the period of vibration in seconds.arrow_forwarda. Find the equation of motion of the system below using Lagrange's equation and find the natural frequency at the end. Assume that the rod is massless. L ти k₁ www k2 marrow_forward*22-20. A uniform board is supported on two wheels which rotate in opposite directions at a constant angular speed. If the coefficient of kinetic friction between the wheels and board is u, determine the frequency of vibration of the board if it is displaced slightly, a distance x from the midpoint between the wheels, and released. Ex-| p- -p-arrow_forward
- 22-71. If the amplitude of the 50-lb cylinder's steady-state vibration is 6 in., determine the wheel's angular velocity w. 9 in. -c = 25 lb-s/ft k = 200 lb/ft k = 200 lb/ft Prob. 22-71 0000arrow_forward14. For the system shown to the right, the disk of mass m rolls without slip and z measures the displaccment of the disk from the unstretchcd position of the spring. 3k a) find the cquations of motion; b) if the system is inderdamped, whiat is the frequency of the frec vibrations of this system in terms of the parancters k, с, and m;arrow_forwardThe 30kg cylinder causes a static deflection of 50mm in the coiled spring. If the cylinder is depressed an additional 25mm from equilibrium position, and released from rest, calculate a) the resulting natural frequency of the vertical vibration in cycles per second * 30 kgarrow_forward
- The turbine rotor of a ship weighs 200 kN has a radius of gyration of 0.8 m. If the ship pitches with simple harmonic motion having amplitude of 8 degrees and time period of 15 seconds, determine the maximum couple that tends to shear the holding down bolts of the turbine. Also determine the maximum acceleration of the ship during pitching.arrow_forwardm Base The response for the block is a sine harmonic function and its amplitude is 0.458 m The response for the block is a cosine harmonic function and its amplitude is 0.019 m The response for the block is a cosine harmonic function and its amplitude is 1.56 m The response for the block is a cosine harmonic function and its amplitude is 0.119 marrow_forwardThe restroom door is equipped with a torsional spring and a torsional viscousdamper so that it automatically returns to its closed position after being opened. The door has amass of 60 kg and a centroidal moment of inertia about an axis parallel to the axis of the door’srotation of 7.2 kg m2. The torsional spring has a stiffness of 25 Nm/rad. a. What is the damping coefficient such that the system is critically damped?b. A man with an armload of packages, but in a hurry, kicks the closed door to cause it to open.What angular velocity must his kick impart to cause the door to open 700? c. How long after his kick will the door return to within 5 0 of completely closing? D. Repeat parts a through c if the door is designed with a damping ratio, ζ = 1.3.arrow_forward
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