What is the correct spring constant for the bungee cord?

In summary, the natural length of the bungee cord is 10m and Sam comes to a rest when the cord is stretched to 18m. The height of the tower is calculated to be 19.6m. To find the spring constant of the bungee cord, the total potential energy at the top of the tower must be equal to the total potential energy at the bottom of the fall. Taking into account the negative gravitational potential at the fully stretched point, the correct spring constant is 210N/m.
  • #1
TyErd
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Homework Statement


The natural length of the bungee cord is 10m
Sam stops falling and first comes to rest momentarily when the length of the bungee cord is 18metres. Height of the tower was calculated to be 19.6metres

What is the spring constant of the bungee cord?


Homework Equations


mgh
0.5kx^2


The Attempt at a Solution


after free falling 10metres the gravitational potential would be 70*10*9.6=6720. then equate that to 0.5kx^2, so 6720=0.5k*8^2, thus k=210N/m.
I was absolutely confident my solution was correct but turns out it isnt.
 

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  • #2
Hey there, I'm not sure if I'm qualified to help you, but I'll try my best.

It seems you are trying to equate the potential elastic energy of the bungee cord when it is fully stretched with Sam's potential gravitational energy from when he is at the top of the tower with respect to when the cord starts stretching. I believe your answer is wrong because Sam is still converting gravitational potential to elastic potential as the cord is stretching. If you add that little bit you should get the right answer. Just remember:

When equating...
Eg = Ee

You are actually equating...
Etotal1 = Etotal2
Eg1 + Ee1 = Eg2 + Ee2

But at the very top of the tower, Ee1 = 0, and at Sam's lowest point Eg2 = 0 so...
Eg1 = Ee2

Bear in mind that this only holds true if you set your "zero" (Point of reference for gravitational potential) at Sam's lowest point on his jump. Since you set your point of reference at the point where the cord begins stretching, you need to account for the "negative" gravitational potential that Sam owes to your point of reference when the cord is fully stretched because he has gone past that point.

Hope this helps!
 

What is a spring constant?

A spring constant is a measure of the stiffness of a spring. It is represented by the letter k and is measured in units of force per unit length.

How is the spring constant calculated?

The spring constant can be calculated by measuring the force applied to the spring and the resulting displacement. The formula for calculating spring constant is k = F/x, where F is the force applied and x is the displacement.

What factors affect the spring constant?

The spring constant is affected by the material and shape of the spring, as well as the number of coils and the diameter of the wire. It can also be affected by external factors such as temperature and applied force.

What is Hooke's law and how does it relate to the spring constant?

Hooke's law states that the force applied to a spring is directly proportional to the resulting displacement. This means that as the force increases, the displacement also increases. The spring constant is a measure of this proportionality and is used to calculate the force required to produce a certain displacement.

How is the spring constant used in real-world applications?

The spring constant is used in a variety of fields, such as engineering, physics, and medicine. It is used to design and test springs for various purposes, such as in suspension systems, mechanical devices, and medical devices. It is also used in calculations for measuring the elasticity of materials and for determining the force needed for different types of movements.

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