- You’re an engineer for a company that makes bungee-jump cords and you’re asked

Question

- You’re an engineer for a company that makes bungee-jump cords and you’re asked to develop a formula for the work involved in stretching cords to double their length. Your cords have force-distance relations described by F = (kx + bx2 + cx3 + dx4),where k,b,c, and d are constants. (a) Given a cord with unstretched length L0, what is your formula? (b) Evaluate the work done in doubling the stretch of a 8 m cord with k = 420 N/m, b = 86 N/m2, c = 12 N/m3, and d = 0.5 N/m4.

7 You're an engineer for a company that makes bungee-jump cords and you're asked to develop a formula for the work involved in stretching cords to double their length Your cords have force-distance relations described by dr cro where k, c, and d are constants. b, (a) Given a cord with unstretched length Lo, what is your formula (b) Evaluate the work done in doubling the stretch of a 8 m cord with 120 N/m, 86 N/m2, c 12 N/m and d 0.5 N/m

Explanation / Answer

part a:

work done=integration of F.dx

=-(k*x+b*x^2+c*x^3+d*x^4)*dx

=-(0.5*k*x^2+(b*x^3/3)+0.25*c*x^4+0.2*d*x^5)

here in this case, integration will be from 0 to L0. (as length varies from L0 to 2*L0, stretching of the cord will vary from 0 to L0)

so work done=-(0.5*k*L0^2+(b*L0^3/3)+0.25*c*L0^4+0.2*d*L0^5)

part b:

given L0=8

k=420

b=-86

c=12

d=-0.5

work done=-(0.5*k*L0^2+(b*L0^3/3)+0.25*c*L0^4+0.2*d*L0^5)

=-7773.9 J

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