Bungee Cord Damping and Unstretched Length Calculation

  • Thread starter Thread starter aks_sky
  • Start date Start date
  • Tags Tags
    Bungee
AI Thread Summary
The discussion revolves around calculating the damping constant and unstretched length of a bungee cord used in a jump scenario. An individual weighing 80 kg experiences varying cord lengths during oscillations, with the lowest point reaching 90m and eventually resting at 50m. The period of small oscillations is given as 6 seconds, leading to the use of the formula T=2π√(m/k) to find the spring constant. The participant is uncertain about how to determine the change in length (Delta L) due to the varying lengths of the cord. Clarification on these calculations and alternative methods for finding the damping constant is sought.
aks_sky
Messages
53
Reaction score
0
I am a bit confused in this problem.

A person of mass 80 kg takes a bungee jump. At the lowest point of the jump the bungee cord is 90m in length and then at the lowest point of the next oscillation the cord has a length of 80m. when the person does eventually come to rest the length of the cord is 50m. the period of the small oscillations just before the person comes to rest is 6s. find the damping constant for the cord and its unstretched length.


What i tried:

Well i have been given the Period of the small oscillations which is 6s. Now to find the spring constant i use this:
<br /> T=2\cdot\pi\cdot\sqrt{\frac{m}{k}}<br />
And then if use this next equation, The only thing i am not sure about is the Delta L. Since the length of the cord changes in the question.
<br /> mg=k\Delta L<br />

Can someone help me clear up on the rope length and the unstretched part. I am just a but confused. and is there an easier way also to find the damping constant since i will have all the relevant parameters?
 
Physics news on Phys.org
anybody know?
 
ok then. thank you!
 
TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
Thread 'Variable mass system : water sprayed into a moving container'
Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
Back
Top