Egg drop experiment with a twist

In summary, the bungee cord needs to be a certain length in order to not touch the ground when dropped from a certain height. The success of the lab is determined by how close the experiment can get to the ground without touching.
  • #1
trgoostrey
3
0
Hello,
My physics class is doing the classic egg drop experiment, but with a different twist.
We are asked to find the length of the bungee cord needed given a mass and a height to drop it from. The success of the lab is determined by how close we can get to the ground without touching.
We are using a single bungee cord, and not multiple bungees.
This is a common question here, but I haven't been able to determine the equations to use to determine what I need.

I have tried using U1 + K1 = U2 + K2 +Uspring
Where U1 is the initial potential energy (mgh1)
K1 is the initial kinetic energy (K1 = 0)
U2 is the final kinetic energy (mgh2 with h2 being the closest distance off the ground)
K2 is the final kinetic energy (K2 = 0)
And Uspring is the integral of Force with respect to distance F(x) from 0 to the unstretched bungee length - h2

Our F(x) function is 2.823 - 6.696x + 31.64x^2 - 110.9x^3 + 177.3x^4 - 103.3x^5
This is the characteristic that our bungee follows.

Using this, I get the correct value, if the egg wasn't dropped, but rather if the egg was just hanging there.

My question is, what am I doing wrong? and what equations/principles could I use to determine the length of the string that I need?
 
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  • #2
Are your limits in your integral correct? Think about how you have defined x.
 
  • #3
Zatman said:
Are your limits in your integral correct? Think about how you have defined x.

Should I define it from the unstretched length to the height off the ground? I know that the integral gives me the work done by the bungee, so it would make sense, but I am out of the lab now, and have no way of testing this.
 
  • #4
I would imagine you have x defined as the extension of the string, but I don't really know where your equation for F(x) has come from so I can't tell if this is the case or not.

Do you know the modulus of elasticity, [itex]\lambda[/itex], of the string? If yes then you can just use

[itex]E.P.E = \frac{\lambda e^2}{2l}[/itex]

where e is the extension. This would be a lot easier and you woudn't need to use an integral.

If you don't know [itex]\lambda[/itex] then assuming your equation for F(x) is correct with x as the extension, you would want to integrate over the entire extension, i.e. x=0 to the distance from where the string first goes taut to the bottom, [itex]h_1 - h_2 - l[/itex], where l is the natural (unstretched) length of the string. Draw a diagram to help you see this. :)
 
  • #5
Thank you. I will try this and see if it works. Unfortunately I don't know the modulus of elasticity, but I will try integrating it :)
 

1. What is the purpose of adding a twist to the traditional egg drop experiment?

The purpose of adding a twist to the traditional egg drop experiment is to introduce variables and factors that will challenge the students to think creatively and problem-solve in a more complex and realistic scenario.

2. How does the twist affect the outcome of the egg drop experiment?

The twist can affect the outcome of the egg drop experiment by changing the conditions and requirements for a successful drop, such as adding weight or changing the landing surface, which can make it more difficult for the students to protect the egg.

3. How can the egg drop experiment with a twist be used to teach scientific concepts?

The egg drop experiment with a twist can be used to teach scientific concepts such as gravity, force, and energy. Students can observe and analyze how their design choices and materials affect the egg's protection and apply these concepts to real-life scenarios.

4. What materials and equipment are needed for an egg drop experiment with a twist?

The materials and equipment needed for an egg drop experiment with a twist may vary depending on the specific twist chosen, but typically include an egg, various materials for building a protective device, and a designated drop zone (e.g. a balcony or staircase).

5. How can the egg drop experiment with a twist be adapted for different age groups?

The egg drop experiment with a twist can be adapted for different age groups by adjusting the complexity of the twist and the materials used. For younger students, simpler twists and materials can be used, while older students can be challenged with more complex twists and materials.

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