Physics laboratory project - bumpers/crash tests

[Pole]

Hello everybody,
It'd be very helpful if you could propose some ideas, suggestions to what we've already made.
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So, we had a test rig consisting of an inclined board, connected with floor using a curved steel plate. The model of a car, after gaining some acceleration, then hit a wall. On the front of the car we attached different materials such as: aluminum foil, cardboard, plastic (from disposable cups), gum (from toys), sponge.

We were using an accelerometer (Vernier WDSS) to record plots of acceleration in time for different bumper materials. We've also made two short films using a high speed camera showing the details of collision.

Besides we measured the mass of a car, the length of a car path, the angle of incline.

From all this data we wanted to create plots of momentum in time (using LoggerPro) and discuss the "safety" of each of those materials for a potential passengers.

I thought that we would obtain: (see attachments)
Where the left plot would be obtained for not flexible materials, and the right one for flexible ones (better safety).
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However, integrate function from LoggerPro gives us only the value of velocity on a selected region, whereas I wanted to obtain a set of points every t period so that after multiplying it by the mass we would obtain momentum in time, as said before.

What are your other ideas for the theoretical analysis of such an experiment? What could we present as well?
Regarding of course the topic of elastic/inelastic collisions; safety; gravity overload.

 

[Cadaei]

Considering it's a lab on momentum, you're probably expected to employ the impulse-momentum theorem, for which your graphs are perfect candidates. If you can't get the program to integrate it for this purpose, then there are a couple of ways to do it:

-Fit a curve to it and integrate that by hand
-Do a riemann sum approximation to both of the areas.

It is discouraged on these forums for us to give you detailed solutions, but the following questions would be helpful for you to ask.

What is the impulse-momentum theorem? How does it relate to safety in a collision?
What is impulse and how does it relate to momentum?

Good luck.

 

[Pole]

Considering it's a lab on momentum (...)

Actually it's not, it's a bigger project lab, where we are supposed to extend our knowledge in a chosen topic. No theory (as a manual or sth) is provided.

Do a riemann sum approximation to both of the areas.

Any advice how to do that in MATLAB ? Because wikipedia theory on that subject is quite...hard to understand and use

What is the impulse-momentum theorem? How does it relate to safety in a collision?

I've read about it, but I can't find any link to safety other than extending collision time. Are there any formulas/other info?

Because I can't find any difference in time between gum and sponge, but their graphs are very different from each other, so the "safety" as well [sponge has almost no acceleration after collision, whereas gum is quite opposite]

What is impulse and how does it relate to momentum?

I can't find any common factor, the first is Force x time, and the second mass x velocity

 

[afreiden]

Your accelerometer data probably has some high frequency 'noise.'
I would recommend you download the trial version of DPlot.
Save your data as a .csv file using MS Excel.
Use one of DPlot's built in low-pass filters (watch your units) to figure out the real peak acceleration. Compare this to the accelerations that a human can withstand.

If you like, you can also multiply the acceleration-time history by the mass (watch your units) of the car to obtain force. Then, perhaps you can integrate this (using DPlot) to obtain impulse (watch your units).

 

[Pole]

Your accelerometer data probably has some high frequency 'noise.'
I would recommend you download the trial version of DPlot.
Save your data as a .csv file using MS Excel.
Use one of DPlot's built in low-pass filters (watch your units) to figure out the real peak acceleration. Compare this to the accelerations that a human can withstand.

If you like, you can also multiply the acceleration-time history by the mass (watch your units) of the car to obtain force. Then, perhaps you can integrate this (using DPlot) to obtain impulse (watch your units).

Thanks for suggestion but unfortunately I don't have access to the accelerometer anymore, I have to stick to results obtained.
Can DPlot somehow use values recorded by LoggerPro?

 

[Cadaei]

I don't know if you have a textbook or not, but simply put, impulse is equal to the change in momentum, and this is probably what it would tell you. Thus if you know initial momentum and final momentum, or how to find them, you can calculate the impulse that acted on an object.

Another way of looking at this, which can be shown through some basic integration, is that the impulse an object experiences is equal to the area under the force-versus-time curve.

If you don't know what a Riemann sum approximation is then your class probably isn't calculus based, which is also probably the reason that the impulse-momentum theorem is giving you trouble. So simply put, you would approximate the area under the curve by using rectangles of equal width (the equal width is often called Δx), and varying height (the height is f(x) at that point). The more rectangles you use, the better the approximation.

If this is not calculus based, then I'm fairly certain that this approximation would more than suffice, especially if you use a decent number of rectangles.

 

[Pole]

My apologies, I must have misspelled that in google and searched for sth different.
My course is calculus based, I didn't know that method has such a name.
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Now I have another problem: transforming such plots (see attached images) into a plot a bit similar to that I've attached in the 1st post.

How to implement trapezoidal formula for calculating integral into MATLAB/Excel so that I can get a decent resulting plot?
I know that the first step should be "Fit curve" tool so that the plots I provided in attachments are smoothened.