Engineering Mechanics: Dynamics (14th Edition)
14th Edition
ISBN: 9780133915389
Author: Russell C. Hibbeler
Publisher: PEARSON
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Chapter 22.6, Problem 75P
To determine
The spring’s maximum compression.
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A mass weighing 16 pounds stretches a spring 4 feet. The medium offers
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Chapter 22 Solutions
Engineering Mechanics: Dynamics (14th Edition)
Ch. 22.1 - A spring is stretched 175 mm by an 8-kg block. If...Ch. 22.1 - Prob. 2PCh. 22.1 - A spring is stretched 200 mm by a 15-kg block. If...Ch. 22.1 - When a 20-lb weight is suspended from a spring,...Ch. 22.1 - Prob. 5PCh. 22.1 - Prob. 6PCh. 22.1 - Prob. 7PCh. 22.1 - Prob. 8PCh. 22.1 - A 3-kg block is suspended from a spring having a...Ch. 22.1 - Prob. 10P
Ch. 22.1 - Prob. 11PCh. 22.1 - 22-12. Determine the natural period of vibration...Ch. 22.1 - The body of arbitrary shape has a mass m, mass...Ch. 22.1 - Determine the torsional stiffness k, measured in...Ch. 22.1 - Prob. 15PCh. 22.1 - Prob. 16PCh. 22.1 - If the natural periods of oscillation of the...Ch. 22.1 - Prob. 18PCh. 22.1 - Prob. 19PCh. 22.1 - A uniform board is supported on two wheels which...Ch. 22.1 - If the wire AB is subjected to a tension of 20 lb,...Ch. 22.1 - The bar has a length l and mass m. It is supported...Ch. 22.1 - The 20-kg disk, is pinned at its mass center O and...Ch. 22.1 - Prob. 24PCh. 22.1 - If the disk in Prob. 22-24 has a mass of 10 kg,...Ch. 22.1 - Prob. 26PCh. 22.1 - Prob. 27PCh. 22.1 - Prob. 28PCh. 22.1 - Prob. 29PCh. 22.2 - Determine the differential equation of motion of...Ch. 22.2 - Determine the natural period of vibration of the...Ch. 22.2 - Determine the natural period of vibration of the...Ch. 22.2 - Prob. 33PCh. 22.2 - Determine the differential equation of motion of...Ch. 22.2 - Prob. 35PCh. 22.2 - Prob. 36PCh. 22.2 - Prob. 37PCh. 22.2 - Prob. 38PCh. 22.2 - Prob. 39PCh. 22.2 - If the slender rod has a weight of 5 lb, determine...Ch. 22.6 - If the block-and-spring model is subjected to the...Ch. 22.6 - Prob. 42PCh. 22.6 - A 4-lb weight is attached to a spring having a...Ch. 22.6 - Prob. 44PCh. 22.6 - Prob. 45PCh. 22.6 - Prob. 46PCh. 22.6 - Prob. 47PCh. 22.6 - Prob. 48PCh. 22.6 - Prob. 49PCh. 22.6 - Prob. 50PCh. 22.6 - The 40-kg block is attached to a spring having a...Ch. 22.6 - The 5kg circular disk is mounted off center on a...Ch. 22.6 - Prob. 53PCh. 22.6 - Prob. 54PCh. 22.6 - Prob. 55PCh. 22.6 - Prob. 56PCh. 22.6 - Prob. 57PCh. 22.6 - Prob. 58PCh. 22.6 - Prob. 59PCh. 22.6 - The 450-kg trailer is pulled with a constant speed...Ch. 22.6 - Prob. 61PCh. 22.6 - Prob. 62PCh. 22.6 - Prob. 63PCh. 22.6 - The spring system is connected to a crosshead that...Ch. 22.6 - Prob. 65PCh. 22.6 - Prob. 66PCh. 22.6 - Prob. 67PCh. 22.6 - The 200-lb electric motor is fastened to the...Ch. 22.6 - Prob. 69PCh. 22.6 - If two of these maximum displacements can be...Ch. 22.6 - Prob. 71PCh. 22.6 - Prob. 72PCh. 22.6 - Prob. 73PCh. 22.6 - Prob. 74PCh. 22.6 - Prob. 75PCh. 22.6 - Prob. 76PCh. 22.6 - Prob. 77PCh. 22.6 - Prob. 78PCh. 22.6 - Prob. 79P
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- 8. A spring of 21 cm length reaches 30.8 cm after hanging a mass of 1/4 kilogram on it. The medium through which the mass moves provides a damping force equal to three times the instantaneous velocity. Find the equation of motion if the mass is released from the equilibrium position with a downward velocity of 2 m/s. Calculate the time at which the mass reaches its extreme displacement, and what is the position of the mass at that moment? (Use g = 9.8 m/s²) Sol.arrow_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_forwardWhen a tree branch bends, it can be assumed that acts as a spring, i.e there is a restoring force −kx in response to a vertical deflection x. Internal friction of wood provides the dominant cushioning and is independent of the hanging mass, that is, F = −bẋ with b constant. We observe that a monkey of mass m1 hangs from the branch. East monkey oscillates many times, up and down before damping off appreciably, and coming to equilibrium. Then a second monkey of mass m2 hangs from the first monkey, and we observe that the monkeys together also oscillate several times before the branch reaches equilibrium. So the new equilibrium position of the branch is three times larger than with a single monkey. Besides, the energy loss per cycle for a monkey is half that of the loss with two monkeys. Based on these observations, determine the mass of each monkey (m1 and m2) in terms of a elastic constant k of the branch and a friction coefficient of the wood b. (Note: k and b are data)arrow_forward
- 4. A mass-spring system exhibits a period of 5 s and a measured mass of 20 kg. Calculate the spring stiffness k.arrow_forwardThe maximum permissible recoil distance of a gun is specified as 0.5 m. If the initial recoil velocity is to be between 8 m/s and 10 m/s, find the mass of the gun and the spring stiffness of the recoil mechanism. Assume that a critically damped dashpot is used in the recoil mechanism and the mass of the gun has to be at least 500 kg.arrow_forwardA mass m is attached to both a spring (with given spring constant k) and a dashpot (with given damping constant c). The mass is set in motion with initial position x0 and initial velocity v0. Find the position function x(t) and determine whether the motion is over-damped, critically damped, or under-damped.arrow_forward
- рис Q2. A railroad bumper (which it is used to stop the railroad car) is designed as a spring in parallel with viscous damping. What is the bumper's damping coefficient such that the system has a damping ration of 1.25 when the bumper is engaged by 20,000 kg railroad car and has a stiffness of 2×10 N/m. The railroad car is traveling at initial speed of 20 m/s when it engages the bumper. What is the time at the maximum deflection occurs when dx/dt=0. brings eacharrow_forwardA mass weighing 4 pounds is attached to a spring whose constant is 2 Ib/ft. The medium offers a damping force that is numerically equal to the instantaneous velocity. The mass is initially released from a point 1 foot above the equilibrium position with a downward velocity of 14 ft/s. Determine the time (in s) at which the mass passes through the equilibrium position. (Use g = 32 ft/s? for the acceleration due to gravity.) Find the time (in s) after the mass passes through the equilibrium position at which the mass attains its extreme displacement from the equilibrium position. What is the position (in ft) of the mass at this instant? ftarrow_forwardA weight of 32 pounds is suspended from a spring with a modulus of 5 lb/ft. From equilibrium position, the weight is pulled down 4 inches below and then released. Given that the damping force in pounds is numerically equal to four times the instantaneous velocity, what is the position of the weight after sec.arrow_forward
- e(+) 3r S.E.P. The homogeneous disc with a mass of 4m and radius of 3r is supported at point 0. For small oscillations, find the equations of motion of the two – degree – of – freedom system in terms of the given parameters (k,m,r), and show them in the matrix form. The system is in the static equilibrium position at the instant given. 4m 3 2k Sm Ta(+) 5k Зт wwarrow_forwardA set of scales consists of an instrumented spring from which the mass of the measured object can be deduced, and a damper to reduce oscillations of the readings. The mass of the scales is small and the damper is chosen to give critical damping when a 10-kg object is weighed. If a mass of 20 kg is placed on the scales, what is the damping ratio and how many cycles of vibration will occur before the reading on the scales settles to within 1% of the correct value?arrow_forward(b) A small generator of mass m is supported by four anti- vibration springs to reduce vibration levels being transmitted to the floor. Each spring has a stiffness of k N/m. Draw free body diagrams for: (i) The static equilibrium position for the system (ii) The dynamic case when the mass is displaced downwards by a deflection of x m and released. If the mass of the small generator m is 12 kg and (ii) each spring has a stiffness of 800 N/m and the vibration described as simple harmonic motion, calculate the frequency of vibration in Hz and time period of vibration.arrow_forward
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