Date: Thu, 10 Dec 1998 11:18:40 -0800
Message-Id: <l03102803b294ae7ca404@[209.142.17.12]>
In-Reply-To: <199812080811.AAA08582@mail.inreach.com>
To: "Pinhole Listserv" <pinhole@exploratorium.edu>
From: Ronald Wong <ronwong@inreach.com>
Subject: Re: egg drop forces
Mish said:
>I'm doing an egg drop in Physics and am wondering if there is any way to
>calculate the force of impact the container makes on the ground. Any ideas?
You should get a lot of ideas on this one.
Here are two:
First, the Problem:
The problem in measuring the decelerating force on the container is that it
is NOT a constant force. So you have to ask yourself whether you want to
find the AVERAGE force during the time of the deceleration or the MAXIMUM
force that occurred during the deceleration.
Of course, you might want both.
The basic principle for getting the AVERAGE force is to equate the change
in momentum with the impulse that brought it about. By simply dividing the
change in momentum by the time needed to bring the container to rest you
will have the average force acting on the container while it comes to rest.
1. High Tech way to get the force (i.e. expensive):
Use a strain gauge. There are various kinds. They allow you to measure forces.
I'm familiar with the old wire-resistance type strain gauge but nowadays
you'd be better served buying a "force probe" - Pasco and Vernier carry
them (so do others). You'll need a computer and the appropriate software
for analyzing the data produced by the "force probe". The software usually
comes with the probe.
With the computer software, you will be able to get both the time required
to bring the container to rest AND the maximum force during that time
interval (a twofer!).
One setup that might work as far as getting this force involves using a
large, level platform that is supported along its edges by 3 force probes
hooked up to their respective computers - a three-legged table so to speak.
Drop the container so that it lands on the platform and read out the
results. The maximum force would be the sum of the maximum forces recorded
by each of the probes (if you can only afford one force probe,... Well,
I'll leave that one for you to figure out. It's almost the same but
constraints come into play).
If you all you want is the MAXIMUM force acting during the collision, than
we're through.
2. The low tech way to getting the force:
Go and buy one of those balls that have an accelerometer built into them (I
forgot what they are called but someone at the Exploratorium can probably
come up with the name).
Zero it out.
Place it in the container.
Determine the total mass.
Drop the container (with the ball inside).
Retrieve the ball and read the acceleration (should be negative).
Knowing the total mass and the acceleration you can, by simply
multiplication, get the average resultant force on the container upon
impact - good old Newton's Second Law.
Keeping in mind that this is NOT the decelerating force, you apply the
necessary correction and ... voila! The AVERAGE decelerating force.
Unfortunately, you won't be able to get the MAXIMUM force that was acting
on the container when it was coming to rest using this approach but, for
the price, how can you complain?
Of course you will never know whether eggs survive even though, for a very
brief time, extremely large forces were coming into play while other eggs
broke even though the maximum forces were well below those that survived.
An important issue could be lost because of this lack of knowledge.
Nonetheless, you do have the AVERAGE retarding force and, if you can live
with that you're through.
If you went the High Tech route, all you have is the maximum force and the
time it took to come to rest. If you want the average force you'll have to
get the change in the momentum. Since the final momentum is zero, the
change in momentum is simply equal in size to the initial momentum just
before impact. All you have to do is get the speed just before impact and
multiply it by the mass.
There are two ways to get the speed.
One is the high tech way: Photo gates or sonic rangefinders hooked up to
computers that will determine the speed just before impact.
The other is the low tech way: Treat the event as a free fall problem.
With the speed and mass you have the change in momentum. With the time, you
have the AVERAGE force and you are finished.
Actually, there is a third way to get the average force. I call it "The
sophisticated/black box" way. This only applies if you used the "force
probe" approach to this problem.
Since the computer software used with the "force probe" gives you both
force and time (usually in the form of a graph of force vs time) you can
use the concepts of calculus to determine the change in momentum WITHOUT
measuring either the mass of the container or its speed just before the
collision (actually, the software will give you the change in momentum on a
silver platter if you ask it to). This third approach is no fun at all (so
the computer software is really a threefer - it gives you the maximum
force, time duration of collision, and change in momentum).
Divide the change in momentum by the time and you have the average
retarding force. What could be easier (shows what you can do if you have
the money)?
I like the low tech approach myself. When things go wrong we seem to learn
a lot more useful stuff.
ron