Question

A bungee cord is essentially a very long rubber band that can stretch up to four times its unstretched length. However, its spring constant varies over its stretch. Take the length of the cord to be along the x-direction and define the stretch x as the length of the cord l minus its un-stretched length $l_0$; that is, $x=l-l_0$ (see below). Suppose a particular bungee cord has a spring constant, for 0 ≤ x ≤ 4.88m , of $k_1=204 N/m$ and for x ≥ 4.88m , of $k_2=111N/m$. (Recall that the spring constant is the slope of the force F(x) versus its stretch x.) (a) What is the tension in the cord when the stretch is 16.7 m (the maximum desired for a given jump)? (b) How much work must be done against the elastic force of the bungee cord to stretch it 16.7 m?


please explain if possible!

Answer 1

A) When the cord is stretched 16.7 m, the tension in the cord is 18537 N.

b) The work that must be done against the elastic force of the bungee cord to stretch it 16.7 m is 15.48 kJ.

What is the tension in the Bungee cord when stretched 16.7 m?

The tension or force in an elastic string is given by the formula:

• Force =  spring constant × extension

a) The force or tension in the cord = 111 N/m × 16.7

Tension = 18537 N

b) Work done in a string = ke²/2

where k = 111 N/m, e = 16.7

Work done = 111 × 16.7²/2 = 15,478.395 J

Work done = 15.48 kJ

In conclusion, the force constant of the cord is required to calculate the tension and work done against the elastic force of the cord.

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