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 11 m long, and that the cords stretch in the jump an additional 24 m for a jumper whose mass is 120 kg, the heaviest adult you will allow to use your bungee jump (heavier customers would hit the ground).
(a) What is the jumper's speed at this instant, when the tension is greatest in the cords?
v = __0__ m/s
(b) Focus on this instant of greatest tension and, starting from a fundamental principle, determine the spring stiffness ks for each of the two cords.
ks = _____ N/m
(c) 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.)
FT = ____ N
(d) What is the maximum acceleration |ay| = |dvy/dt| (in "g's") that the jumper experiences? (Note that |dpy/dt| = m|dvy/dt| if v is small compared to c.)
|ay| = ____ g's (acceleration in m/s2 divided by 9.8 m/s2)"
Answers & Comments
Verified answer
Measuring the heights from the final equilibrium position.
The potential energy at the top most point was mgh = 120*9.8*35 = 41160
All this energy is converted as the stings p.e at the bottom most point/
1/2 k x^2 = 1/2 k 24^2 = 41160
b)
k = 143 N/m
c)
The force needed to extend 24 m is 143*24 = 3432 N
Assuming each string has the same spring constant, then each can support half the above value = 1716N
d)
The max upward acceleration a =1716/120 = 14.3 m/s^2.
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