While the stiffness of an elastic cord can be nearly constant (i.e., the force versus disp...

While the stiffness of an elastic cord can be nearly constant (i.e., the force versus displacement curve is a straight line) over a large range of stretch, as a bungee cord is stretched, it softens; that is, the cord tends to get less stiff as it gets longer. Assuming a softening force-displacement relation of the form kδ − βδ3, where k = 2.58 lb/ft and β = 0.000013 lb/ft3 and where δ (measured in ft) is the displacement of the cord from its unstretched length, and considering a bungee cord whose unstretched length is 150 ft, determine

(a) the expression of the cord’s potential energy as a function of δ;

(b) the velocity at the bottom of a 400 ft tower of a bungee jumper weighing 170 lb and starting from rest;

(c) the maximum acceleration, expressed in g’s, felt by the bungee jumper in question.

Figure P4.45