Spring Constant [Please Check Work]

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SUMMARY

The discussion focuses on calculating the spring constant of a bungee cord used by a jumper with a mass of 98 kg. The jumper oscillates up and down, completing three cycles in 9.3 seconds. The initial calculation for the spring constant (k) was derived using the formula ω = √(k/m) and resulted in k = 44.732 N/m. However, the user later recognized the need to account for the total period of oscillation and the effects of gravity, indicating that the initial calculation was incorrect.

PREREQUISITES
  • Understanding of harmonic motion and oscillation principles
  • Familiarity with the formula for angular frequency ω = √(k/m)
  • Knowledge of the relationship between period and frequency
  • Basic concepts of gravitational force and its impact on oscillating systems
NEXT STEPS
  • Review the calculation of the period of oscillation for a bungee jumper
  • Learn how to incorporate gravitational force into spring constant calculations
  • Study the relationship between mass, spring constant, and oscillation frequency
  • Explore examples of spring constant calculations in real-world applications
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Physics students, educators, and anyone interested in understanding the dynamics of oscillating systems, particularly in the context of bungee jumping and spring mechanics.

BuGzlToOnl
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Homework Statement


A bungee jumper, whose mass is 98 kg, jumps from a tall building. After reaching his lowest point, he continues to oscillate up and down, reaching the low point two more times in 9.3 s. Ignoring air resistance and assuming that the bungee cord is an ideal spring, determine its spring constant.

Homework Equations


[tex]\omega[/tex]=[tex]\sqrt{k/m}[/tex]

[tex]\omega[/tex]=2[tex]\pi[/tex]/T

The Attempt at a Solution



2[tex]\pi[/tex]/9.3s = [tex]\sqrt{k/98kg}[/tex]

k = 44.732N/m [?]

I rewrote the equations so I can try to obtain.

The answer I got 44.732N/m, but that seems way to low, can anyone verify if its right/wrong and where I went wrong

EDIT: Well I think I'm wrong because I never used the fact that he reached the lowest point 3 times and didn't incorporate gravity. Not sure on how to approach this so any help would be appreciated.
 
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Hi BuGzlToOnl,

BuGzlToOnl said:

Homework Statement


A bungee jumper, whose mass is 98 kg, jumps from a tall building. After reaching his lowest point, he continues to oscillate up and down, reaching the low point two more times in 9.3 s. Ignoring air resistance and assuming that the bungee cord is an ideal spring, determine its spring constant.


Homework Equations


[tex]\omega[/tex]=[tex]\sqrt{k/m}[/tex]

[tex]\omega[/tex]=2[tex]\pi[/tex]/T



The Attempt at a Solution



2[tex]\pi[/tex]/9.3s = [tex]\sqrt{k/98kg}[/tex]

I don't believe the period is 9.3 seconds. Do you see what it needs to be?
 

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