A bungee jumper of mass 160kg falls from a cliff. The bungee cord has a natural length of 5.0m and a stiffness constant of 3.0N/m. The air resistance is a constant force of 4.0N, what's the speed of the jumper when the total length of cord is 5.9m?
This is an example of an energy consideration problem involving work done in the context of a Hooke's law situation. Firstly draw a diagram to show what's going on. Then recall that the work done by the air resistance on the jumper = the loss in TOTAL energy of the jumper. Consider first the initial energy, it will have GPE relative to where the length is 5.9m, GPE = mgh = mg(5.9), now at the point where the total length is 5.9m the cord has been extended by 0.9m so it will have Elastic potential AND kinetic energy, = 1/2 kX2 + 1/2 mv2 where k is the stiffness constant and X is the extension (=0.9m) . Remember that work done by the air resistance is = force x distance so = 5.9x4 = 23.6N Formulate these energies as previously discussed i.e. Work done by air resistance = initial GPE - final(EPE + KE) 23.6 = mg(5.9) - 1/2 kX2- 1/2 mv2 where v is the speed at that point and m is the mass(160kg)Rearrange this to make v the subject and substitute the values in for: m, k, X and g = 9.81m/s2 Doing this yields v = 11m/s (given to two significant figures as the minimum number of sig figs given in the question was 2.)
