Re: pinhole Baseball Experiment Ideas

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From: Marc Kossover (zeke_kossover@yahoo.com)
Date: Tue Dec 14 2004 - 14:01:50 PST 

Message-ID: <20041214220150.62474.qmail@web53404.mail.yahoo.com>
Date: Tue, 14 Dec 2004 14:01:50 -0800 (PST)
From: Marc Kossover <zeke_kossover@yahoo.com>
Subject: Re: pinhole Baseball Experiment Ideas

Howdy-

--- Anita Roberts <anitaqr@yahoo.com> wrote:

> An 8th grade student of mine is interested in doing
> a project that compares the distance a cheaper
> baseball travels with the distance a more expensive
> "professional" baseball travels when hit. The one
> variable that I am having a hard time helping him
> with is the swing. He is planning on hitting the
> baseballs with a bat to see how far they travel. Any
> ideas on how to test this using a more consistent
> method?

I wouldn't try hitting the ball. As you suggest, it is
rife with unrepeatability and hidden variables.
Instead, I would start by dropping the ball from
different heights to measure the coefficient of
resitution.

For an object hit (or dropped) onto an immoveable
surface, the coefficient of restitution is equal to
the ratio of the speed of the object after the
collision divided by the speed of the object before
the collision. (See note below.)

So, a ball that bounces off at the same speed in which
it hits has a coefficient of one and a ball that hits
and splats has a coefficient of zero.

By comparing the coefficients of restitution between
the cheap ball and the expensive ball, the
"bounciness" of the ball can be determined.

I can hear your students saying that this isn't the
same thing as hitting it. True, but it is close. One
of science's most important features is the ability to
generalize from one experiment to another.

Actually, this is exactly how tennis balls, golf
balls, and baseballs are tested. Major League Baseball
(as do the governing bodies of nearly every sport) has
rules governing the range of acceptable coefficients
for their ball. I believe that it is from about 0.52
to 0.56, but I don't know for sure offhand.

Or course, COR isn't the only factoring determining
distance. The height of the laces is important and the
quality of the wrapping matter to the air resistance.

A more important issue though is the placement of the
center of mass of the ball. Since the ball will rotate
around its center of mass as it moves thorugh the air,
any displacement of the center of mass away from the
geometric center of the ball will cause significant
air resistance. Coupled with an initial rotation of
the ball, all sorts of weird flying is possible.

-----

The coefficien to resitution's formula is

co_resitution (v_1_before - v_2_before) = -(v_1_after
- v_2_after)

This formula measures how elastic the collision is,
with perfectly elastic collisions having coefficients
of restitution equal to one and totally inelastic
collisions equal to zero.

This simplifies to the equation above when one object
is immoveable and only the magnitudes of the velocity
are used.

Marc "Zeke" Kossover

                
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