227_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

227_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: Sec_2.8-2.12.qxd 9/25/08 11:44 AM Page 221 SECTION 2.8 Impact Loading Solution 2.8-12 Bungee jumper max: SOLVE QUADRATIC EQUATION FOR 2 WL WL WL 1/2 + ca b + 2L a bd EA EA EA dmax WL 2EA 1/2 c1 + a1 + bd EA W VERTICAL HEIGHT h C h W Mg (55 kg)(9.81 m/s2) 1+ 60 m Clearance: C W 2EA 1/2 c1 + a1 + bd EA W W EA 539.55 N 2.3 kN Potential energy of the jumper at the top of bridge (with respect to lowest position) Numerator W(L U Denominator max) EAd2 max 2L or d2 max h C 60 m L W(L + dmax) 2WL d EA max EAd2 max 2L 2WL2 EA 0 50 m 1.9586 10 m 50 m 1 + (0.234587) 1.9586 CONSERVATION OF ENERGY U ; 0.234587 * c1 + a1 + strain energy of cord at lowest position P.E. C SUBSTITUTE NUMERICAL VALUES: 10 m Find length L of the bungee cord. P.E. 2EA 1/2 WL c1 + a1 + bd EA W h L 2.3 kN Height: h L+ SOLVE FOR L: 539.55 N EA C + L + dmax 25.5 m ; 1/2 2 bd 0.234587 221 ...
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