Calculating Bungee Length and Extension using Hooke's Law

In summary: From this, you can calculate the value for x.In summary, the person is asking for help with an assignment involving determining the length of extension for a bungee cord by using Hooke's law and energy conservation principles. The problem can be solved by breaking it into two parts: estimating the velocity when the bungee line is straight but not stretched, and calculating the stretch phase using the elastic energy and gravitational loss in potential energy.
  • #1
frisy4
3
0
Hi I am new to this forum I am currently doing year 11 physics at school nothing to complicated. now i have an assignment which i need to determine the length of the extension for a bungee and I am going to drop it from a certain height now i have the spring constant of my bungee and can figure out the equilibrium point using Hooke's law F=kx how do i figure out the rest that includes being able to drop the weight from a point and figure out how far it will stretch?
 
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  • #2
Welcome to PF, frisy4!

Now, it is simplest to split the problem in two parts:

1. Estimation of velocity when the bungee line has become straight, but NOT stretched.
In this phase, we have FREE FALL:

Here, use energy conservation, in that the potential energy associated with the height drop becomes converted into kinetic energy.

(That height drop has a very simple relationship with the length of the bungee line..!)
2. Stretch phase:

Here, the kinetic energy gained at 1. is converted into elastic energy.
Take care to include the effect that you in this time period also lose more potential energy due to falling from a higher to a lower place.

Specifically, use energy conservation principles to solve the problem.
 
  • #3
ok so well velocity i will just get a stop watch and do an approximate time of where it passes the point then times by 9.8 after that i sub in KE=1/2mv^2 after that my KE=EPE right? from there were do i go?
 
  • #4
You do not NEED time explicitly; only think energy conservation!

In the second phase:
a) What is the expression for the elastic energy stored in the line when stretched a distanced x?

b) What is the gravitatitonal loss in potential energy associated with a fall over a distance x?
 
  • #5
well the rule for EPE is 1/2kx^2. I am not exactly sure about the gravitational loss in PE over a distance.
 
  • #6
Oops, stupid formulation on my part, sorry about that.

It should be -mgx.

Thus, if v is the velocity when the bungee line is straight but not stretched, and "x" is used as the distance fallen when the velocity has become 0, energy conservation says:
[tex]\frac{1}{2}mv^{2}=\frac{1}{2}kx^{2}-mgx[/tex]
 

Related to Calculating Bungee Length and Extension using Hooke's Law

1. What is Hooke's Law?

Hooke's Law is a principle of physics that states the relationship between the force applied to an elastic material and the resulting deformation or change in length of that material. It states that the force applied is directly proportional to the change in length of the material, as long as the material remains in its elastic limit.

2. How does Hooke's Law apply to bungee jumping?

In bungee jumping, Hooke's Law applies to the bungee cord or rope that is used to secure the jumper. As the jumper falls, the bungee cord stretches, and according to Hooke's Law, the force applied to the cord is directly proportional to the amount of stretch. This allows for a controlled descent and prevents the jumper from hitting the ground too hard.

3. Why is Hooke's Law important in bungee jumping?

Hooke's Law is important in bungee jumping because it ensures that the bungee cord will stretch and absorb the energy of the falling jumper, preventing them from hitting the ground with a potentially dangerous force. It also allows for a controlled and safe descent.

4. Is Hooke's Law the only factor to consider in bungee jumping?

No, there are other important factors to consider in bungee jumping such as the weight and height of the jumper, the length and elasticity of the bungee cord, and the location of the jump. These factors can affect the amount of force applied to the bungee cord and the overall safety of the jump.

5. Can Hooke's Law be applied to other activities besides bungee jumping?

Yes, Hooke's Law can be applied to many other activities involving elastic materials, such as trampolining, rock climbing, and even everyday activities like stretching a rubber band. It is a fundamental principle of physics and can be seen in many different scenarios.

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