Determining Deformation in Bouncing Balls

Name: Andrew
Status: student
Grade: 9-12
Location: IL

Question: I am conducting an experiment for my physics class in
which I plan to compare how bouncy various balls are by measuring
and comparing how much they deform when dropped from a constant
height. Originally I planned to place a piece of carbon paper over
notebook paper on a hard surface, measure the diameter of the ball
mark, compare it to the balls diameter. However, this proves to have
some problems. When I drop a tennis ball it leave no mark, and when
I drop a baseball only the seams leave a mark. I was wondering if
you could think of a more pressure sensitive substance I could use
to obtain a mark left from the ball's bounce. I was thinking perhaps
a thin layer of sand or talcum powder over a hard surface might
work. Please offer me any advice you have on this issue.
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Not sure sand or talc would work, as the air dragged with the ball with blow
it around. Since you are trying to measure deformation, not momentum/impulse,
I am not sure measuring the impact area is a good idea. You need to separate
the two variables -- by measuring impact zone width, momentum and
deformation are coupled (and likely momentum will far outweigh the
deformation). To measure deformation directly, I would suggest high speed
photography, if your school has a suitable camera.

Assuming you do not have a high speed camera, I would try to measure it
indirectly. However, using things like your eyes and your hands may not be
precise enough to get good data. I am just thinking out loud here, so perhaps
you can refine the experimental procedure based on the equipment you have. I
would put the balls into a vice or some kind of press where you can measure
the force applied to the ball. Measure the deformation of the ball as a
function of pressure. Then, based on the velocity of the ball falling and
the elasticity of the surface it is hitting, calculate the impulse (the
change in momentum) and the time over which it occurs -- from which you can
get the force applied to the ball. The greatest force will occur at the
point of the greatest rate of change in momentum, which is a function of the
object it is hitting. If you assume instantaneous change in momentum, you
get infinite force, though, so you will need to take care to figure out the
change in momentum over very short periods of time (tricky indeed!). I am not
sure the best way for you to measure that amount of time (depends on the
equipment you have), but you can take measurements of how long the ball
takes to go from the top of one bounce to the top of the next (along with
the height) to get an estimate -- I am just not sure you will be able to do it
precisely enough by to get meaningful data, but many physics labs have laser
timers, which would be fantastic. Then, from the table of force vs.
deformation you developed, you can estimate the deformation of the ball.

Hope this helps,
Burr Zimmerman
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Interesting project. To generalize your problem -- you are looking for a 
material(s) that transfer a detectable amount of some agent that can be 
identified. The "softness of the ball" will be proportional to the contact 
area. The "problem" is to find a substance that will transfer from the hard
surface to various balls as a function of ball-type and height -- now this 
next statement is critical -- on a time scale of the order of the "contact" 
time of the transfer substance.

Carbon paper did not work because its designed to not transfer. Otherwise you 
will get what is call "set off" or "off set", which is the transfer of the 
carbon paper ink to hands, fingers, etc. One way carbon paper ink designers 
achieve this is to formulate some wax into the ink formulation, giving the 
carbon paper the proper "release" properties -- which are just the opposite 
of what you want.

You need an identifiable substance that transfers on a short time scale -- I 
would guess a few milliseconds. A suggestion: use a hard polished surface -- 
I am thinking a small slab of polished marble, "shatter proof" glass (not too 
thin to avoid shattering), Plexiglas(@ trademark), or a piece of polished 
stainless steel. If you choose glass you can obtain that from a window glass 
store -- they will cut to size and have the right kind of "shatter-proof" 
glass.

Method 1: Formulate a transfer substance using water, uncolored dish soap 
(a few %), and food coloring (or fluorescent dye -- you will need a UV light 
to 'see' the impact mark, but the sensitivity may be much greater than food 
coloring). The dish soap is simply to reduce the surface tension which in turn 
increases the "wetting" of the surface and the ease of transfer to the ball. 
You can also experiment with small amounts of a polymeric wetting agent. This 
increases the "tackiness" of the transfer substance.
   
Vince Calder
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Cover the surface of the ball with chalk. You should be able to see the area
of contact between the ball and the surface by the mark left by the chalk, 
particularly if impacting black paper.
You might also want to try covering the ball with talcum power, flour,
baking powder, or charcoal.

Scott Smith
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Yep, carbon paper is very pressure-dependent and needs a high pressure,
which you get only from bounces with smaller footprints.

Powder is the right idea.
A dark powder on the ball, if you want to put a mark on a white surface.
Fingerprint power, carbon black, or perhaps graphite powder.
Laser-printer toner powder would probably work well, but it is aggressively messy,
watch out and wear junk clothes and disposable gloves.

If you are using talc, that is white, so you need a gloss black surface.
For photographing it, the gloss is like a partial mirror,
and you want to keep the reflection of your light-source out of your picture.
Either photograph straight-on with side-lighting and no flash and a dark space behind you,
or use flash but photograph at a 45-degree off angle so the flash cannot be in the picture.

If you include two rulers in the picture, at right angles to each other,
the picture contains all you need to measure the spot.

In principle, fainter white-mark-on-dark might make visible fainter dust-smudges
than dark-mark-on-white.
In practice, if you do not perfect the lighting, it might be the other way around.

Alternatively you could make the ball oily or greasy,
bounce it on clean white paper, then slide dark graphite dust over it.
It will stick where the grease wets onto the paper.
That would probably work too.
I wonder if vegetable oil works well.   Hair gel?
Slob it all over the ball, wipe it off for 20 seconds with one dry paper towel,
and then the grease or oil coat will be a pretty uniform and thin.
That way the footprint will have the same intensity for all balls,
and the grease will not take much bounce out of the best-bouncing balls.
Water might work, or it might wipe off too well when thin
and damp the bounce too much when thick.

I think it would be OK to use your mind
to help complete the circular outline of the ball's footprint.
The diameter of that outline is what you really want to measure.
Any three small patches of visible edge can define a circle.
If you make a big X of grease across the bottom of the ball,
that will print 4 line-ends on the paper,
and if they all fit on the same circle,
you can be pretty sure all 4 were accurate.
This uses less gunk and damps the ball's bouncing less, if that matters.
But you would have to drop the ball carefully with no rotation,
or randomly multiple times.

Jim Swenson
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