Design a “bungee jump” apparatus for adults. A bungee jumper falls from a high platform with two elastic cords tied to the
ankles. The jumper falls freely for a while, with the cords slack. Then the jumper falls an additional distance with the cords
increasingly tense. Assume that you have cords that are 10 m long, and that the cords stretch in the jump an additional 24 m
for a jumper whose mass is 80 kg, the heaviest adult you will allow to use your bungee jump (heavier customers would hit
the ground).
(a) It will help you a great deal in your analysis to make a series of 5 simple diagrams, like a comic strip, showing the
platform, the jumper, and the two cords at the following times in the fall and the rebound:
▪ while cords are slack (shown here as an example to get you started)
▪ when the two cords are just starting to stretch
▪ when the two cords are half stretched
▪ when the two cords are fully stretched
▪ when the two cords are again half stretched, on the way up
On each diagram, draw and label vectors representing the forces acting on the jumper, and the jumper's velocity.
Make the relative lengths of the vectors reflect their relative magnitudes.
(b) At what instant is there the greatest tension in the cords? (How do you know?)
(c) What is the jumper's speed at this instant, when the tension is greatest in the cords?
(d) Is the jumper's momentum changing at this instant or not? (That is, is dpy/dt nonzero or zero?) Give a valid physics
reason for your answer. Check to make sure that the magnitudes of the velocity and force vectors shown in your
diagram number 4 are consistent with your analysis of parts (c) and (d).
(e) Focus on this instant of greatest tension and, starting from a fundamental principle, determine the spring stiffness ks
for each of the two cords.
(f) What is the maximum tension that each one of the two cords must support without breaking? (This tells you what
kind of cords you need to buy.)
(g) What is the maximum acceleration |ay| = |dvy/dt| (in “g's”; acceleration divided by 9.8 m/s2) that the jumper
experiences? (Note that |dpy/dt| = m|dvy/dt| if v is small compared to c.)
(h) What is the direction of this maximum acceleration?
(i) What approximations or simplifying assumptions did you have to make in your analysis that might not be adequately
valid?