02-06ChapGere.0014

# 02-06ChapGere.0014 - L 1 d max 5 EA d max 2 2 L 5 EA d max...

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Problem 2.8-12 A bungee jumper having a mass of 55 kg leaps from a bridge, braking her fall with a long elastic shock cord having axial rigidity EA 5 2.3 kN (see figure). If the jumpoff point is 60 m above the water, and if it is desired to maintain a clearance of 10 m between the jumper and the water, what length L of cord should be used? Solution 2.8-12 Bungee jumper SECTION 2.8 Impact Loading 157 W 5 Mg 5 (55 kg)(9.81m/s 2 ) 5 539.55N EA 5 2.3kN Height: h 5 60m Clearance: C 5 10m Find length L of the bungee cord. P.E. 5 Potential energy of the jumper at the top of bridge (with respect to lowest position) 5 W ( L 1 d max ) U 5 strain energy of cord at lowest position C ONSERVATION OF ENERGY or Ê d max 2 2 2 WL EA d max 2 2 WL 2 EA 5 0 P . E . 5 U Ê W
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Unformatted text preview: ( L 1 d max ) 5 EA d max 2 2 L 5 EA d max 2 2 L S OLVE QUADRATIC EQUATION FOR d max : V ERTICAL HEIGHT h 5 C 1 L 1 d max S OLVE FOR L : S UBSTITUTE NUMERICAL VALUES : Numerator 5 h 2 C 5 60m 2 10m 5 50m 5 1.9586 L 5 50 m 1.9586 5 25.5 m 3 B 1 1 1 1 2 0.234587 1 / 2 R Denominator 5 1 1 (0.234587) W EA 5 539.55 N 2.3 kN 5 0.234587 L 5 h 2 C 1 1 W EA B 1 1 1 1 2 EA W 1 / 2 R h 2 C 5 L 1 WL EA B 1 1 1 1 2 EA W 1 / 2 R 5 WL EA B 1 1 1 1 2 EA W 1 / 2 R d max 5 WL EA 1 B WL EA 2 1 2 L WL EA R 1 / 2 h C A-PDF Split DEMO : Purchase from www.A-PDF.com to remove the watermark...
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## This note was uploaded on 09/20/2009 for the course COE 3001 taught by Professor Armanios during the Spring '08 term at Georgia Tech.

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