MadSci Network: Physics
Query:

Re: Is there a formula for Inelastic Collisions where the objects do not stick?

Date: Thu Mar 8 02:55:53 2001
Posted By: Duje Bonacci, Grad student,
Area of science: Physics
ID: 983733267.Ph
Message:

Hallo, Jeremy, and thanks for the question!

I will split this answer in two parts. First part will be the (more or
less)
straight answer to the question, along with some comments on how to obtain
that answer. The second part will be a comment of rather philosophical
nature, but I believe that you will find it more helpful than the first
part.

So, the beehive hangs suspended from the isolated old oak-tree on a lovely
meadow carpeted with flowers... (this rustic setting is just to help you
understand that physics is not just some weird science done exclusively in
sealed and heavily guarded underground labs, but is rather a way of looking
at the real world around you, and as such can be applied even to the trees
and meadows!) A young lad passes by, resting a while from his study (he's
got a physics exam in two days and is just studying collisions), and he
wonders what would happen to the beehive if he hit it with a stone (he'd
like to see some physics in action, because seeing it just in the books can
bore you to death). SO he runs back home, picks up a paper and a pencil,
and dashes off back to the meadow and sits himself in the shadow of the old
oak.

First he has to model the process, so he needs to make some assumptions
about the quantities he can and needs to measure in order to calculate the
ones he can't directly measure. He picks the 'known' quantities to be the
masses of the stone and beehive. He also simplifies the whole process of
hitting-the-bee-hive-with-a-stone by just considering a beehive to be a
pendulum, i.e. a mass suspended on a string. Also he considers a stone to
be the point-mass object. Further he assumes that he knows the speed the
stone attains when he throws it and finally, he assumes that when the stone
hits the beehive, it penetrates it from one side and doesn't pass through,
but instead gets stuck in it. 

This is just a sort of process you have inquired about. It is called
TOTALLY INELASTIC COLLISION, and there certainly IS a way on how to
calculate the speed of the compound object (beehive with a stone in it)
that resulted from the collision. I will not solve it for you, but instead
give you the hint on how to do it yourself (an old Chinese proverb says 'do
not give the fish you have caught to the hungry - teach them how to catch
the fish themselves instead'). Two physical quantities you can consider are
the total energy and the total linear momentum at moments just before and
just after the collision. Since beehive and the stone constitute the
closed physical system, both these quantities are conserved throughout the
collision process. 

But alas, the main characteristic of the inelastic collision, as opposed to
the elastic one, is that the part of the initial kinetic energy (due to the
motion of the stone before the collision) is transformed to heat. This
transformation comes about due to the friction between the stone and the
inside of the beehive which acts as to halt the stone's motion with
respect to the beehive. Effectively, when considering just the kinetic
energies in the system, their sum is not conserved. So conservation of
energy cannot help us much... (unless we can somehow accurately measure
all the energies that are transformed, such as heat and sound)

Hence we turn to the conservation of (linear) momentum. Before the
collision, the total momentum of the system is contained in the motion of
the stone (you should know that the expression for the linear momentum of a
point mass m moving with the known velocity v is m*v). After the collision
the total momentum is equal to the (M+m)*v', where M is the mass of the
beehive and v' is the unknown velocity of the compound object, a beehive
with a stone stuck in it. Now what you get when you use the conservation of
momentum principle is one equation (momentum before equals momentum after
the collision) with one unknown (velocity of the compound object) that you
can solve. Hence the unknown velocity...  

Now to the philosophy... PLEASE, DO NOT THINK OF PHYSICS IN TERMS OF
FORMULAE. Formulae are just algerbra, number-letter juggling. Think of it
rather as the multitude of processes that go on around you (and within
you). Do not ask for a formula - that is something you can work out
yourself. Ask for the description of the process - what you can measure,
what you can't measure, which quantities are relevant for the given
process, which are obsolete. I'm saying this because I know that just
memorizing formulae makes physics dull and gray, and the final result is
not that you actually learn something new but instead you become unable to
think of the phenomena without your formula-booklet in your hand. 

Hope you are satisfied with the answer, and hope you'll enjoy your future
journeys into the world of physics.





Current Queue | Current Queue for Physics | Physics archives

Try the links in the MadSci Library for more information on Physics.



MadSci Home | Information | Search | Random Knowledge Generator | MadSci Archives | Mad Library | MAD Labs | MAD FAQs | Ask a ? | Join Us! | Help Support MadSci


MadSci Network, webadmin@www.madsci.org
© 1995-2001. All rights reserved.