Question
no guessing please!
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 k delta - beta delta 3. where delta (measured in ft) is the displacement of the cord from its unstretched length, considering a bungee cord whose unstretched length is 150ft. and letting k = 2.58 lb/ft. determine the value of the constant beta such that a bungee jumper weighing 170 lb and starting from rest gets to the bottom of a 400 ft tower with zero speed.
Explanation / Answer
initial energy = 0.5*1413 * 10^2 = 70650 J
final energy = intial + work done = 70650 + 400000 = 470650 J
so .. o.5 * 1413 * v^2 = 470650
so final velcotu = v = 25.810294 m/sec