Problem

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

While the stiffness of an elastic cord can be quite 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 δ (measured in ft) is the displacement of the cord from its unstretched length, considering a bungee cord whose unstretched length is 150 ft, and letting k = 2.58 lb/ft, determine the value of the constant β such that a bungee jumper weighing 170 lb and starting from rest gets to the bottom of a 400 ft tower with zero speed.