Explanation Given: The mass of the cylinder is 20 kg . Initially the cylinder is at rest h = 0 . The stiffness of the spring is k . The unstretched length of the spring is s 0 = 1 m . Draw the free body diagram of cylinder as shown in Figure (1). Write the formula for kinetic energy ( T ) . T = 1 2 m v 2 (I) Here, m is the mass and v is the velocity. Refer Figure (1). Write the formula for elastic potential energy ( V e ) . V e = 1 2 k ( s 1 − s 0 ) 2 (II) Here, k is the stiffness of the spring and s 1 , s 0 is the final and initial displacement. Write the formula for gravitational potential energy ( V g ) . V g = m g h (III) Here, m is the mass of the cylinder, g is the acceleration due to gravity and s is the displacement. Write the formula total potential energy ( V ) . V = V g + V e (IV) Here, V g is gravitational potential energy and V e is elastic potential energy. Write the formula for conservation of energy. T 1 + V 1 = T 2 + V 2 (V) Here, T 1 , T 2 are the initial and final kinetic energy and V 1 , V 2 are the initial and final potential energy. Conclusion: At Initial: Calculate the initial kinetic energy and potential energy of the cylinder. The cylinder is at rest ( h = 0 ) . The kinetic energy of the cylinder is T 1 = 0 . When the unstretched length of the spring is s 0 = 1 m . At rest, The gravitational potential energy of the cylinder is V g = 0 . Calculate the elastic potential energy ( V e ) at rest. Substitute 2 m for s 1 and 1 m for s 0 in Equation (II) V e = 2 1 2 ( k ) ( 2 m − 1 m ) 2 = k ( 1 ) = k Calculate the total potential energy ( V 1 ) . Substitute V 1 for V , k for V e and 0 for V g in Equation (IV). V 1 = 0 + k = k At Final: Calculate the final kinetic energy

Engineering Mechanics: Dynamics (14th Edition)

14th Edition

ISBN: 9780133915389

Author: Russell C. Hibbeler

Publisher: PEARSON

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Chapter 14.5, Problem 96P

To determine

The stiffness of the spring when h=0.5 m .

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Chapter 14.5, Problem 95P

Chapter 14.5, Problem 97P

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Chapter 14 Solutions

Engineering Mechanics: Dynamics (14th Edition)

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Ch. 14.3 - If it is originally at rest, determine the...Ch. 14.3 - If it is originally at rest, determine the...Ch. 14.3 - Determine the required height h of the roller...Ch. 14.3 - How far will the truck skid if it is traveling 80...Ch. 14.3 - Show that this is so, by considering the 10-kg...Ch. 14.3 - A force of F = 250 N is applied to the end at B....Ch. 14.3 - If the block has a mass of 20 kg and is suspended...Ch. 14.3 - Determine how far the block must slide before its...Ch. 14.3 - If the 6-kg collar is orginally at rest, determine...Ch. 14.3 - Select the proper value of k so that the maximum...Ch. 14.3 - Determine the speed of the brick just before it...Ch. 14.3 - Determine the speed of block A after it moves 5 ft...Ch. 14.3 - If the kinetic coefficient of friction between the...Ch. 14.3 - Determine the angle at which the box leaves the...Ch. 14.3 - If the cord is subjected to a constant force of F=...Ch. 14.3 - Determine the maximum distance A will fall before...Ch. 14.3 - If the cord is subjected to a constant force of F=...Ch. 14.3 - The barrier stopping force is measured versus the...Ch. 14.3 - The coefficient of kinetic friction between both...Ch. 14.3 - If the coefficient of kinetic friction between the...Ch. 14.3 - The 8-Kg block is moving with an initial speed of...Ch. 14.3 - At a given instant the 10-lb block A is moving...Ch. 14.3 - The 5-lb cylinder is falling from A with a speed...Ch. 14.3 - The propelling action is obtained by drawing the...Ch. 14.3 - By design the car cannot fall off the track,...Ch. 14.3 - If the coefficient of kinetic friction along AB is...Ch. 14.3 - Prob. 29P Ch. 14.3 - If the can is prevented from moving, determine the...Ch. 14.3 - Determine the placement R of the can from the end...Ch. 14.3 - If it starts from rest when the attached spring is...Ch. 14.3 - Neglect the size of the block.Ch. 14.3 - As shown, the spring is confined by the plate P...Ch. 14.3 - Determine his speed when he reaches point B on the...Ch. 14.3 - As shown, it is confined by the plate and wall...Ch. 14.3 - If the track is to be designed so that the...Ch. 14.3 - Neglect friction.Ch. 14.3 - Neglect friction and the size of the pulley.Ch. 14.3 - Neglect friction and the size of the pulley.Ch. 14.3 - An elastic cord having a stiffness k = 2 lb/ft is...Ch. 14.4 - In initially, the block is at rest.Ch. 14.4 - When s = 0, the 20-kg block is moving at v = 1...Ch. 14.4 - The load weighs 100 lb and the efficiency of the...Ch. 14.4 - If the block is traveling up the inclined plane...Ch. 14.4 - determine the power input to the motor, which...Ch. 14.4 - which is increasing at a rate of aP = 6 m/s2....Ch. 14.4 - Assuming the wheels do not slip on the ground,...Ch. 14.4 - Determine the power Input for a motor necessary to...Ch. 14.4 - If mechanical friction and wind resistance are...Ch. 14.4 - manufactures a turbojet engine that is placed in a...Ch. 14.4 - If the car is brought to a stop, determine how...Ch. 14.4 - If the steps are 125 mm high and 250 mm in length,...Ch. 14.4 - Determine the power generated. 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The stiffness of the spring when h = 0.5 m .

Solution Summary: The author explains how to determine the stiffness of the spring at h=0.5m.

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Chapter 14 Solutions