Pendulum Harmonic Motion Help Needed Asap ( work is shown)

AI Thread Summary
A bungee jumper with a mass of 66.0 kg oscillates after jumping from a bridge, hitting a low point eight times in 35.5 seconds and finally resting 28.0 meters below the bridge. The spring stiffness constant (k) of the bungee cord was calculated to be 132.3 N/m using the period of oscillation. To find the unstretched length of the bungee cord, the relationship between force, distance, and k was applied, leading to the equation M*g = -k*x. After solving for x, which represents the stretch of the cord, the unstretched length was determined to be 23.1 meters by adding the stretch to the final resting position. This approach effectively utilized the information provided in the problem statement.
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A bungee jumper with mass 66.0 kg jumps from a high bridge. After reaching his lowest point, he oscillates up and down, hitting a low point eight more times in 35.5 s. He finally comes to rest 28.0 m below the level of the bridge.

Calculate the spring stiffness constant of the bungee cord.
N/m


For this part i figured i could solve for period (T) which would be the 35.5 sec /8 whihc is 4.4375 s
and then i used T=2pi* (m/k)^1/2

and with that i thought i could solve for K

that comes out to be ...k=(4pi^2*mass) / T^2

so k=132.3 N/m



Calculate the unstretched length of the bungee cord

I could either use T= 2*PI*(L/G)^1/2


L=(4.4375 s^2 * 9.8)/4*pi^2-4.88 m ...but that's wrong

OR I COULD USE ---f= 1/2*pi *(g/l)^1/2 ...

L=(2.46*g)/f^2=477.69 m


and just solve for L ...rite?

but when i plug everything in i keep getting it wrong
 
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No no no no.

The first part (finding k) was correct. Exactly right. But then you start using other formula to find L simply becuase they have an L in them.

Here's a hint. You have just found the "k," and you are given a distance and a mass (from which you can find a force). What kind of relationship is there for stretchy things that relates force, distance and a "k" ?
 
ok i know that Force = - kx
could x=length of the bungee cord...

and which would lead me to believe that M*g=force also equals -Kx

so...should i be using 66kg (9.8)=-132.3(x) and solve for x?
 
Yes, you should solve for x, but realize that x is not the unstretched length of the cord.

The x in Hooke's law (F = -kx) refers to the amount by which the spring (or cord) is stretched from its unstretched position.
 
so how do i figure out the unstretched length...now I am confused
 
Make full use of the information provided in the problem statement, namely:
"He finally comes to rest 28.0 m below the level of the bridge."​
 
ok i think i got it...so ...66*9.8=-(132.3)x
X in this case is -4.8 ms.. so if i add that to the 28 meters the unstretched cord should be in length equal to 23.1 meters ...that should be rite
 
That's what I get.
 
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