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) How will you model this problem?
b. Given a cord with un-stretched length 4, what is the formula for the work done?
c. Evaluate the work done in doubling the stretch of an 8 m cord with k= 420N/m, b = -86N/m2, c = 12N/m3, and d=-0.50N/m4

a) Definition of work, definite integration, b) , c)

Explanation:

a) The bungee-jump cord is modelled by using the integral form of the physical definition of works, as the force varies with the elongation. A definite integral is used because initial and final lengths are supposed to be known.

b) The formula for the work done is:

Where .

c) The value for x is:

The work done to stretch the cord is:

The negative sign is because the reactive nature of the elastic forces, which is antiparallel to displacement direction.

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