C. What is the value of the stiffness constant (aka “elastic constant” or “sprin

Question

C. What is the value of the stiffness constant (aka “elastic constant” or “springconstant”) for the bungee cord that satisfies the problem described above? Remember, usethe energy model (re-read the problem description). Circle the best answer. Relevant work is required

A. k = 100 N/m

B. k = 125 N/m

C. k = 150 N/m

D. k = 175 N/m

E. k = 200 N/m

F. k = 225 N/m

G. k = 250 N/m

(15 points total) A 50kg bungee jumper steps off of a bridge (from rest) with a 30-meter (un-stretched length) bungee attached to her body harness, with its the other end attached safely to the bridge by her feet. The jumper reaches the very bottom of her bounce (comes to rest at a total of 50 meters below where she stepped off the bridge. Your ultimate goal will be to find the bungee cord's stiffness constant (a.k.a. astic constant or spring constant Hints: Use the energy model and g 10m/sa. nclude the bungee cord and jumper in your system ignore the mass of the bungee cord and any friction or air resistance. If you pick the best times to evaluate the energy, this problem is very simple. a. (5 points) Which sketch of the problem best matches what is described in the problem statement above? Circle the best answer. Showing work is optional but you REALLY want to take your time with this. v 0 Un-stretched Length Un-stretched Length L 30m Ls 30 200m v 0 50m b. 5 points Which two energy types are changing from the initial time: when the jumper steps off the bridge (from rest) to the final time: at the bottom of the bounce (at rest? Note: just consider energies AT those initial and final times do NOT consider changes that occur in between those 2 times. Circle the best answer. Support your answer with carefully drawn energy bar graphs to receive points. i. Kinetic energy and gravitational energy ii. Kinetic energy and elastic energy iii. Gravitational energy and elastic energy iv. Fear energy and enjoyment energy (don't circle this one)

Explanation / Answer

a] Total distance covered from the point of release on the bridge = 50 m

unstretched length of the cord = 30 m

therefore, the extension produced in the cord will be: 50 - 30 = 20 m

this is accurately shown in figure [ii]

b] Since initial and final positions both have v = 0, the kinetic energy does not change.

The energies changing are Gravitational Potential Energy and Elastic Potential Energy. [answer : iii]

c] Total change in potential energy = 50(50)(10) = 25000 J

this will be equal to the change in elastic potential energy since v = 0 on both the extreme points.

so, 25000 = (1/2)kx2

x = 50 - 30 = 20 m

so, 25000 = (1/2)k(20)2

=> k = 125 N/m.

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