# Can the spring constant k be used for crumple? (not spring)

A question on my lab is find the amount of "stopping force" required to stop the egg, by determining the size of the "crumple zone"

A brief description of the lab:
Build a container that will keep an egg from breaking as it is dropped from the third floor of the school, your container must crumple on impact.

My container was crumpled 3.5cm, it was dropped from the third floor, I'm not sure of the height but i was thinking if i used conservation of energy of Eg from the top equal to Ee of the bottom ( ETotal top= ETotal after crumple, which is Eg = Ee) then finding k and subbing that into the equation of Fs=kx because the spring force is what absorbs the energy and causes the conatiner to stop.

I'm not quite sure if this is correct because the crumple zone isn't a spring.

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Simon Bridge
Homework Helper
Welcome to PF;
You need more experiments to make sure of the relatonship between the amount of crumple and the height of the drop.
The short answer is: no. Maybe you'll get away with it by accident.

haruspex
Homework Helper
Gold Member
I'm not quite sure if this is correct because the crumple zone isn't a spring.
One of the reasons crumpling is better at protecting cargo is that the force is more constant than for a spring. Instead of the force rising linearly with compression distance it rises very steeply to begin with then levels out. That allows more energy to be absorbed over a given distance for the same peak force. The exact profile will depend on the design of the crumple zone. If you assume it is very well designed, you can take the force as constant.

mfb
Mentor
One of the reasons crumpling is better at protecting cargo is that the force is more constant than for a spring. Instead of the force rising linearly with compression distance it rises very steeply to begin with then levels out. That allows more energy to be absorbed over a given distance for the same peak force. The exact profile will depend on the design of the crumple zone. If you assume it is very well designed, you can take the force as constant.
A steep rise in force can be dangerous on its own, especially if the egg does not start with a good contact to the crumpling material.

haruspex
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Gold Member
A steep rise in force can be dangerous on its own,
Why?

mfb
Mentor
The force might get transmitted locally at the point where the first hard contact to the egg happens. It is hard to crush an egg with a homogeneous force applied to one hemisphere, but a localized force can easily break it.
A smoother transition gives some crumple zone where the contact to the egg can be improved (by contracting those regions that are too thick).

haruspex
Homework Helper
Gold Member
The force might get transmitted locally at the point where the first hard contact to the egg happens. It is hard to crush an egg with a homogeneous force applied to one hemisphere, but a localized force can easily break it.
A smoother transition gives some crumple zone where the contact to the egg can be improved (by contracting those regions that are too thick).
Yes, but that's all to do with the peak force experienced by the egg, not the rate of increase of that force.
I understand you are saying that a rapid rise in force at the leading edge of the crumple zone might result in a high initial peak of force at the egg. Your argument appears to be that it could lead to a less homogeneous distribution of force than with a more gradual build up. Maybe, but it seems most unlikely to me. That said, I admit it's dubious to deal with this question intuitively. It's hard in the imagination to disentangle the condition of a rapid rise in force from that of a high peak force.

In the specific case of an egg, eggs have evolved to handle a force concentrated at the end of the egg. Distributing it too evenly over the leading half of the egg could prove counterproductive.

mfb
Mentor
Yes, but that's all to do with the peak force experienced by the egg, not the rate of increase of that force.
Well, we have the specific example of an egg.
For the more general case, a real-life example: curves for streets and trains are carefully designed to reduce jerk because it feels unpleasant. A constant acceleration on the other hand is easier to handle.

haruspex
Homework Helper
Gold Member
Well, we have the specific example of an egg.
For the more general case, a real-life example: curves for streets and trains are carefully designed to reduce jerk because it feels unpleasant. A constant acceleration on the other hand is fine for all reasonable acceleration values.
Yes, jerk is unpleasant, but not because it generates excessive forces. It is to do with human perception. I don't think the egg cares.

mfb
Mentor
Oh come on, you apply things I say about eggs to non-egg-situations and things I say about non-eggs to the egg example. That does not help.

Hitting the side of a car harder because this side suddenly started to accelerate with full acceleration is something not completely different between the two cases. Yes I'm sure you can find some setup where this model does not work.

haruspex