02-06ChapGere.0009

02-06ChapGere.0009 - linearly elastic behavior of the...

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Problem 2.8-5 Solve the preceding problem if the block weighs W 5 1.0 lb, h 5 12 in., and k 5 0.5 lb/in. Solution 2.8-5 Block dropping onto a spring 152 CHAPTER 2 Axially Loaded Members W 5 1.0lb h 5 12in. k 5 0.5lb/in. (a) M AXIMUM SHORTENING OF THE SPRING (b) I MPACT FACTOR (E Q . 2-61) 5 4.6 Impact factor 5 d max d st 5 9.21 in. 2.0 in. 5 9.21 in. Eq. (2-53): Ê d max 5 d st B 1 1 ¢ 1 1 2 h d st 1 / 2 R d st 5 W k 5 1.0 lb 0.5 lb / in. 5 2.0 in. h k W Problem 2.8-6 A small rubber ball (weight W 5 450 mN) is attached by a rubber cord to a wood paddle (see figure). The natural length of the cord is L 0 5 200 mm, its cross-sectional area is A 5 1.6 mm 2 , and its modulus of elasticity is E 5 2.0 MPa. After being struck by the paddle, the ball stretches the cord to a total length L 1 5 900 mm. What was the velocity v of the ball when it left the paddle? (Assume
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Unformatted text preview: linearly elastic behavior of the rubber cord, and disregard the potential energy due to any change in elevation of the ball.) Solution 2.8-6 Rubber ball attached to a paddle g 5 9.81m/s 2 E 5 2.0MPa A 5 1.6mm 2 L 5 200mm L 1 5 900mm W 5 450mN W HEN THE BALL LEAVES THE PADDLE KE 5 Wv 2 2 g W HEN THE RUBBER CORD IS FULLY STRETCHED : C ONSERVATION OF ENERGY S UBSTITUTE NUMERICAL VALUES : 5 13.1 m / s v 5 (700 mm) B (9.81 m / s 2 )(2.0 MPa)(1.6 mm 2 ) (450 mN)(200 mm) v 5 ( L 1 2 L ) B gEA WL v 2 5 gEA WL ( L 1 2 L ) 2 KE 5 U Wv 2 2 g 5 EA 2 L ( L 1 2 L ) 2 U 5 EA d 2 2 L 5 EA 2 L ( L 1 2 L ) 2 A-PDF Split DEMO : Purchase from www.A-PDF.com to remove the watermark...
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