Question

A bungee cord exerts a nonlinear elastic force of magnitude F(x) = k1x + k2x^3, where x is the distance the cord is stretched, k1=204 N/m and k2=-0.233 N/m^3. How much work must be done on the cord to stretch it 16.7 m?

a) 6,000 J
b) 8,000 J
c) 10,000 J
d) 12,000 J

Answer 1

The amount of work done on the bungee cord to stretch it 16.7 m is approximately 6000 J.

Step-by-step explanation:

To find the work done on the bungee cord, we can use the formula:

W = ∫F(x) dx

where F(x) is the force applied at each point and dx is the infinitesimal distance over which the force is applied.

Given that F(x) = k1x + k2x^3, we can integrate this expression over the range of x from 0 to 16.7:

W = ∫(k1x + k2x^3) dx = (k1/2)x^2 + (k2/4)x^4

Substituting the values of k1 = 204 N/m, k2 = -0.233 N/m^3, and x = 16.7 m, we get:

W = (204/2)(16.7)^2 + (-0.233/4)(16.7)^4

W ≈ 6000 J

Therefore, the amount of work done on the bungee cord to stretch it 16.7 m is approximately 6000 J.