How Far Will a Bungee Cord Stretch During a Jump?

[coglon]

I am stumped... very hard question:
"A 70.0kg woman does a bungee jump. The length of the bungee cord is 5.00m and it has a spring constant of 122.08 N/m. Assume the gravitational field strength is 9.81 N/kg.

a)What is the maximun distance the bungee cord will stretch and how far will the jumper be below her initial start point?

b)How much is the total mechanical energy of the system?

c)How far will the bungee cord be stretched when the jumper is moving at her maximun speed? What is this point called? <- I think its called the equilibrium point.

d)What is the maximun speed the jumper will atain."

So as you can see this is a very difficult question. I've taken some stabs at it with no luck. Heres what I've done so far.. but it might be wrong: I found that the initial speed will begin when cord starts to stretch so after 5m of free fall I found Velocity intial would be 9.9m/s then I started my equations:

Total Energy Mechnical (Emt) = Potential Energy Gravity (-ΔEpg) + Kinetic Energy (ΔEk)
Emt= -ΔEpg + ΔEk
Emt -ΔEpg = Eps (Potential spring Energy)
mgh= 1/2kx² height= x+5 where x is the stretch of the bungee cord
mg(x+5)=1/2kx²
√(2mg(x+5))/x= x
as you can see I am going nowhere... what i got lead to a quadratique equation... I don't know if I need to use one or not

Could some one help me solve this question or atleast get me started.

Thanks for help

Cogon,

 

[Pyrrhus]

I think maybe you should find the speed at the point when the woman as covered 5 meters, using Free Fall, and the probably relate that to when it has covered x distance.

Yes there's Gravitational Potential Energy and Spring Energy, but also kinetic energy.

 

[Atheist]

k, some hints:
- draw a scetch of the process and try to distinguish different phases (the phase before he jumps would be the 1st one, for example).
- try Emt = Epg(h) + Ek(h) + Eps(h). Beware of my different sign-convention but you should be able to translate to yours. Ask yourself why all of the three "contributing energies" are only dependent of the height!
- above energy Emt is conserved as it´s the total energy (not 100% sure what "total mechanical energy" is supposed to be but most probably that).

specific hints:
a) What makes that point special? It should be one of the phases I suggested above.
b) assuming it´s really the conserved total energy that´s meant the question is trivial and only depends on where you set x=0. Chose any phase that seems appropriate to you.
c) I really don´t know what your teacher wants to hear there but "maximum velocity" really doesn´t sound like "equilibrium" to me. Equilibrium between what, btw?
d) If you know the point where the maximum velocity is attained then calculating it out is easy.

 

[Doc Al]

mgh= 1/2kx² height= x+5 where x is the stretch of the bungee cord
mg(x+5)=1/2kx²
√(2mg(x+5))/x= x
as you can see I am going nowhere... what i got lead to a quadratique equation... I don't know if I need to use one or not

Don't give up so easily. You are on the right track. Now solve the quadratic equation to find the maximum extension (x) of the cord.