Design a \"bungee jump\" apparatus for adults. A bungee jumperfalls from a high platform with two elastic cords tied to theankles. The jumper falls freely for a while, with the cords slack.Then the jumper falls an additional distance with the cordsincreasingly tense. Assume that you have cords that are 11 m long,and that the cords stretch in the jump an additional 23 m for ajumper whose mass is 140 kg, the heaviest adult you will allow touse your bungee jump (heavier customers would hit the ground). (a)It will help you a great deal in your analysis to make a series of5 simple diagrams, like a comic strip, showing the platform, thejumper, and the two cords at the following times in the fall andthe rebound: 1 while cords are slack (shown here as an example toget you started) 2 when the two cords are just starting to stretch3 when the two cords are half stretched 4 when the two cords arefully stretched 5 when the two cords are again half stretched, onthe way up On each diagram, draw and label vectors representing theforces acting on the jumper, and the jumper's velocity. Make therelative lengths of the vectors reflect their relative magnitudes.(b) At what instant is there the greatest tension in the cords?(How do you know?) When the person has fallen 11 m. At the bottom,when the person has fallen 34 m. When the person has fallen between0 m and 11 m. When the person has fallen between 11 m and thebottom. At the top, when the person has fallen 0 m. (c) What is thejumper's speed at this instant, when the tension is greatest in thecords? m/s (d) Is the jumper's momentum changing at this instant ornot? (That is, is nonzero or zero?) (e) Which of the followingstatements is a valid basis for answering part (d) correctly? Sincethe momentum is zero, the momentum isn't changing. If the momentumweren't changing, the momentum would remain zero forever. After avery short time the momentum will be upward (and nonzero). Sincethe net force must be zero when the momentum is zero, and since isequal to the net force, must be zero. A very short time ago themomentum was downward (and nonzero). The number of significantdigits is set to 3; the tolerance is +/-2% (f) Focus on thisinstant of greatest tension and, starting from a fundamentalprinciple, determine the spring stiffness for each of the twocords. N/m (g) What is the maximum tension that each one of the twocords must support without breaking? (This tells you what kind ofcords you need to buy.) N (h) What is the maximum acceleration (in\"g's\") that the jumper experiences? (Note that | if is smallcompared to .) g's (acceleration in m/s2 divided by 9.8 m/s2) (i)What is the direction of this maximum acceleration? (j) Whatapproximations or simplifying assumptions did you have to make inyour analysis which might not be adequately valid? (Don't check anyapproximations or simplifying assumptions which in fact havenegligible effects on your numerical results.) Assume that thegravitational force hardly changes from the top of the jump to thebottom. Neglect air resistance, despite fairly high speeds. Assumethe speeds are very small compared to the speed of light. Assumetension in cord proportional to stretch, even for the very largestretch occurring here.
