Falling Objects and Bouncing
Location: Outside U.S.
Date: April 2008
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.
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
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
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
Hope this helps,
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.
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.
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Update: June 2012