Question

Engineers desire to model the magnitude of the elastic force of a bungee cord using the equation F(x) = a[x⁹ - (9x⁹)²], where x is the stretch of the cord along its length and a is a constant. If it takes 22.0 kJ of work to stretch the cord by 16.7 m, determine the value of the constant a.

Answer 1

To determine the value of the constant a in the equation for the elastic force of the bungee cord, we can use the given information that it takes 22.0 kJ of work to stretch the cord by 16.7 m.

To determine the value of the constant a in the equation for the elastic force of the bungee cord, we can use the given information that it takes 22.0 kJ of work to stretch the cord by 16.7 m.

We can solve for a by substituting the given values into the equation and solving for a:

22.0 kJ = a(16.79 - (9(16.7)9)2)

Simplifying the equation and solving for a will give us the value of the constant a.