Explanation Given information: Diameter of the cylinder is d = 0.5 ft = 6 in . . Length of the cylinder is L = 1.5 ft = 18 in . The cylinder is made up of Am 1004-T61 magnesium. Weight of the block hitting the cylinder is 800 lb. Speed of the block is v = 2 ft/sec = 24 in ./sec . Neglect the mass of the cylinder. Young’s modulus or modulus of elasticity is E m g = 6.48 ( 10 3 ) ksi = 6.48 ( 10 6 ) psi . The acceleration due to gravity is g = 32.2 ft/sec 2 = ( 32.2 × 12 ) in ./sec 2 . Explanation: Area of the cylinder: Determine the area of the cylinder ( A ) using the formula. A = π d 2 4 (1) Here, d is diameter of the cylinder. Stiffness: Determine the stiffness of the spring ( k ) when the load is applied on top of the post using the equation. k = A E L (2) Here, E is Young’s modulus of the magnesium and L is the length of the cylinder. Conservation of energy: Express the equation for conservation of energy as follows: U e = U i 1 2 m v 2 = 1 2 k Δ max 2 (3) Here, m is mass of the block, v is velocity, W is the weight of the cylinder, and Δ max is the maximum displacement. Maximum dynamic force developed in the cylinder ( P max ) : Determine the maximum dynamic force developed in the cylinder using the equation. P max = k Δ max (4) Maximum stress in the cylinder ( σ max ) : Determine the maximum stress developed in the cylinder using the formula. σ max = P max A (5) Mass of the cylinder: Determine the mass of the cylinder using the relation. m = W g (6) Show the calculation of values as follows: Conclusion: Substitute 6 in. for d in Equation (1). A = π × 6 2 4 = 28

Mechanics of Materials, Student Value Edition Plus Mastering Engineering with Pearson eText -- Access Card Package (10th Edition)

10th Edition

ISBN: 9780134326054

Author: Russell C. Hibbeler

Publisher: PEARSON

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Any functioning component, such as machine parts, structural members, pressure vessels, and so on, are all under the influence of more than one force. When anybody is under the influence of more than one force such as shear forces, bending moments, axial…

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Chapter 14.4, Problem 14.52P

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The maximum stress in the cylinder.

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Chapter 14.4, Problem 14.51P

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Mechanics of Materials, Student Value Edition Plus Mastering Engineering with Pearson eText -- Access Card Package (10th Edition)

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The maximum stress in the cylinder.

Solution Summary: The author explains how the cylinder is made up of Am 1004-T61 magnesium.

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