Engineering Mechanics: Statics & Dynamics (14th Edition)
14th Edition
ISBN: 9780133915426
Author: Russell C. Hibbeler
Publisher: PEARSON
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Chapter 22.2, Problem 30P
To determine
The differential equation of motion of the block when it is displaced slightly and released.
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Chapter 22 Solutions
Engineering Mechanics: Statics & Dynamics (14th Edition)
Ch. 22.1 - A spring is stretched 175 mm by an 8-kg block. If...Ch. 22.1 - A spring has a stiffness of 800 N/m. If a 2-kg...Ch. 22.1 - Prob. 3PCh. 22.1 - Prob. 4PCh. 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 - While standing in an elevator, the man holds a...Ch. 22.1 - Determine the natural period of vibration of the...Ch. 22.1 - Prob. 13PCh. 22.1 - Prob. 14PCh. 22.1 - Prob. 15PCh. 22.1 - Prob. 16PCh. 22.1 - Prob. 17PCh. 22.1 - The uniform beam is supported at its ends by two...Ch. 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 - Prob. 23PCh. 22.1 - Prob. 24PCh. 22.1 - If the disk in Prob. 22-24 has a mass of 10 kg,...Ch. 22.1 - A flywheel of mass m which has a radius of...Ch. 22.1 - Prob. 27PCh. 22.1 - The platform AB when empty has a mass of 400 kg...Ch. 22.1 - The plate of mass m is supported by three...Ch. 22.2 - Prob. 30PCh. 22.2 - Prob. 31PCh. 22.2 - Prob. 32PCh. 22.2 - If the 20-kg wheel is displaced a small amount and...Ch. 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 - A block which has a mass m is suspended from a...Ch. 22.6 - A 4-lb weight is attached to a spring having a...Ch. 22.6 - A 4-kg block is suspended from a spring that has a...Ch. 22.6 - Use a block-and-spring model like that shown in...Ch. 22.6 - A 5-kg block is suspended from a spring having a...Ch. 22.6 - The uniform rod has a mass of m. If it is acted...Ch. 22.6 - Prob. 48PCh. 22.6 - The light elastic rod supports a 4-kg sphere. When...Ch. 22.6 - Find the differential equation for small...Ch. 22.6 - Prob. 51PCh. 22.6 - Prob. 52PCh. 22.6 - The fan has a mass of 25 kg and is fixed to the...Ch. 22.6 - In Prob. 22-53 , determine the amplitude of...Ch. 22.6 - Prob. 55PCh. 22.6 - Prob. 56PCh. 22.6 - Prob. 57PCh. 22.6 - Prob. 58PCh. 22.6 - Prob. 59PCh. 22.6 - Prob. 60PCh. 22.6 - Prob. 61PCh. 22.6 - Prob. 62PCh. 22.6 - Prob. 63PCh. 22.6 - Prob. 64PCh. 22.6 - Prob. 65PCh. 22.6 - Determine the magnification factor of the block,...Ch. 22.6 - Prob. 67PCh. 22.6 - The 200-lb electric motor is fastened to the...Ch. 22.6 - Prob. 69PCh. 22.6 - Prob. 70PCh. 22.6 - If the amplitude of the 50-lb cylinder's...Ch. 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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- The man pushes the 120-lb homogeneous crate with the horizontal force P. Determine the largest distance h for which the crate will slide without tipping.arrow_forwardA spring is stretched 175 mm by an 8-kg block. If the block is displaced 100 mm downward from its equilibrium position and given a downward velocity of 1.50 ms, determine the differential equation which describes the motion. Assume that positive displacement is downward. Also determine the position of the block when t = 0.22 s. (Show free-body diagram of the system.)arrow_forwardThe 20-kg block A rests on the 2-kg pan B. Both are supported by a spring having a stiffness k of 3 N/m that is attached to the bottom of the pan and to the ground. Determine the distance d the pan should be pushed down from the equilibrium position and then released from rest so that separation of the block will take place from the surface of the pan at the instant the spring becomes unstretched. Please show complete solution with FBD.arrow_forward
- The 8-kg block is moving with an initial speed of 5 m/s. If the coefficient ofkinetic friction between the block and plane is uk = 0.25, determine the maximum compressionin the spring when the block momentarily stops.arrow_forwardA 9-kg block is suspended from a spring having a stiffness of k = 200 N/m. If the block is given an upward velocity of 0.4 m/s when it is 95 mm above its equilibrium position, determine the equation which describes the motion. Assume that positive displacement is downward.arrow_forwardThe slender 10-kg bar AB is horizontal and at rest and the spring is unstretched. Determine the stiffness k of the spring so that the motion of the bar is momentarily stopped when it has rotated clockwise 90° after being released.arrow_forward
- The coefficients of static and kinetic friction between the 100 kg block and the inclined plane are 0.30 and 0.20, respectively. Determine (i) the friction force Facting on the block when P is applied with a magnitude of 200 N to the block at rest, (ii) the force P required to initiate motion up the incline from restarrow_forwardThe 5 kg cylinder is released from rest in the postion shown in the figure below. Determine the maximum compression xmax of the spring. The stiffness of the spring is 1800 N/m.arrow_forwardThe two springs are identical, withunstretched length 0.4 m. When the 150-kg mass issuspended at B, the length of each spring increases to0.6 m. What is the spring constant k?arrow_forward
- A brake mechanism is used to lower body A with a constant velocity of 3.0 m/s. The coefficient of friction between the brake and drum D is 0.40. Neglect the weight of the brake. Determine the mass of body A and the power dissipated by the brake. (hint: the normal force between the brake the and disk is not 1200 N)arrow_forwardTwo blocks A and B have a weight of 10 lb and 6 lb, respectively. They rest on the inclined plane whose coefficients of static friction are A=0.15 and B 0.25 respectively. Determine the angle of inclination X for which both blocks begin to slide. Also find the required elongation or compression in the spring connecting them for this to occur. The spring has a stiffness of k 2 lb/ft.arrow_forwardThe coefficient of static and kinetic friction between the 100-kg block and the inclined plane are 0.30 and 0.20 respectively. Determine (a) the friction forced F acting on the block when P is applied with a magnitude of 200 N to the block at rest (b) the force P required to impend motion up the incline.arrow_forward
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