Question

A bungee cord exerts a nonlinear elastic force of magnitudeF(x) = k1x + k2x3,where x is the distance the cord is stretched,k1 = 209 N/mandk2 = −0.240 N/m3.How much work (in kJ) must be done on the cord to stretch it 18.0 m?

Answer 1

To find the work done on the bungee cord to stretch it 18.0 m, you can calculate the area under the force vs. displacement curve by integrating the force function. The work is approximately -1.43 kJ.

Step-by-step explanation:

To find the work done on the bungee cord to stretch it 18.0 m, we need to calculate the area under the force vs. displacement curve. This can be done by integrating the force function, F(x) = k1x + k2x³, with respect to x from 0 to 18.0 m.

The work done on the cord is given by the formula:

work = ∫(k1x + k2x³)dx

Integrating this function from 0 to 18.0 m, we calculate the work to be approximately -1.43 kJ.