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Name: Sam
Status: Student
Grade: 9-12
Location: Outside U.S.
Country: Belgium
Date: April 2008


Question:
I am looking to compare different masses, objects, shapes and compare these to dents made in a specific plate (e.g. polystyrene). For this experiment I would need not only to be able to work out the velocity of the object but also how much air resistance is effecting the object plus the amount of air is jammed between the object and the plate.

If possible, I would also be looking for a way to measure how much, for instance, an object would bounce back, or how much weight and height will get me the best results, but I also need to find a formula to see wether any of my results make any sense. I was thinking of letting an object dimensions around 5 x 5 (base) by 5-10 (height) depending on object otherwise for sphere a 3 cm radius object drop from around 3 meters object mass around 250g to 1kg. I do not know if pressure, humidity or temperature matters.



Replies:
Hi Sam,

It sounds like you're asking for someone to 1. validate your methodology, and 2. suggest any other factors you need to consider. Is that right? (if not, reply and let me know what else).

First, the methodology. It sounds like you have an ambitious approach, but I think some organization up front will really help you get good value from your efforts. There is a method known as 'design of experiments' that might help. I am going to walk you through some basic steps, and hopefully it will help.

Step one is to have a hypothesis. What are you trying to prove? It sounds like you are testing something about elastic collisions (such as the relationship between objects and the mark they leave on a plate), but I am not clear what.

Step two is to organize and categorize your variables. You have two kinds of variables: independent and dependent. An independent variable is something you can set yourself (such as how high to drop the object, which object with which properties, etc.). A dependent variable, often called a response variable, is one that is determined by independent variables. The mark left on the plate or the height the object bounces might be response variables. A third type of "variable" is a factor that you do not intentionally change (I put "variable" in quotes because sometimes they change and sometimes they do not). There are lots of these factors, some of which you can control and some you cannot. You might always choose to use the same target plate -- that is a factor that you hold constant. You might work outside, and have to deal with wind or temperature changes -- these affect your results, but you cannot control them. It is a good idea to record variables and factors that affect your results -- they may be helpful later in interpreting your results.

Step three is to revisit your hypothesis -- restate your idea in terms of the variables that you can measure. Saying "I want to see what happens....". is not as powerful as saying something like "A change of independent variable A will lead to a change in dependent variable B in this way C."

Step four is to set up your equipment to actually test your hypothesis. Keep it simple -- pick materials and equipment that fit what you are trying to test. Remove things that will introduce uncontrollable variables. The more variables you try to change, the harder the experiment will be to run and the harder the results will be to analyze. Sometimes you have to have a lot of variables, but it is often a good idea to start simple first, and then work your way up to more complicated experiments.

I strongly recommend you read about 'design of experiments' to help you understand the approach I am suggesting here. The Internet has a ton of information, as would a library too.

Now for your specific situation.

It sounds like you are trying to do experiments involving colliding objects. Have you studied 'kinetic energy' in physics yet? I would start there. You can get all the equations you need. I would specifically study elastic and inelastic collisions. Usually collisions are not purely one or the other. With a rubber ball, the ball deforms as it strikes a hard object. Some energy is dissipated in the deformation, and some is returned elastically. If you are hitting an expanded Polystyrene ('Styrofoam') target, the energy of the falling object will be partially/mostly absorbed by the Styrofoam. For your objects and distances (~1kg, ~10m), I think you can safely neglect air/wind effects. If you consider objects of different shapes, now you have a very difficult-to-control factor as now the orientation of the object affects how it bounces (I would avoid this variable, to be honest -- stick with spheres). As for weights and masses, it probably does not matter that much unless you use very light, low-density objects (they will be affected by air). Ball bearings, rocks, and other similar 'heavy' objects should all behave similarly.

Hope this helps,
Burr Zimmerman


Hi Sam,

That is a massively difficult and computationally intensive endeavor you want to undertake! I am afraid that the best answer I can give, is to say that with without a supercomputer running extremely complex Finite Element Analysis software, and a lot of very expensive computer time, there is no way to do what you are suggesting. It is amazing how complex it is to accurately describe something as seemingly simple as dropping a block though air! Further, before you can even think of attempting to see how far an object would bounce off your polystyrene plate, you would need to mathematically characterize the detailed physical characteristics of both the plate and the falling object.

So, I am sorry, but to do what you want to do is simply impossible with the resources available to someone like you or even me.

Regards,

Bob Wilson


You have a pretty complicated project. For a "dropping" distance of ~ 3 meters, air pressure, humidity and temperature will probably be negligible. For a sphere, Stokes' Law says that the shear viscosity is F=6 x pi x a x nu x v (for Reynolds numbers 1 (true for air)). For heavy objects of radius 'a' the velocity 'v' falling through air with a viscosity 'nu' will not be significant I don't think. How bodies of different shape fall is a complicated problem because they tend to tumble, so you should probably stick to spheres. Relating the indentation of the base to the mechanical parameters may be very tricky too. Not all polystyrene, for example, has the same elasticity, which determines how much of the energy of the falling object is absorbed compared to how much is retained by the falling object.

Vince Calder



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