Although the best way to analyze the "falling mass pulling an air-track
glider" is to draw free body diagrams for the glider and also the falling
mass, and assume Newton's second law, and simultaneously solve the two
acceleration equations... I agree this might be too much for the typical
high school student. In fact, it gives quite a few college students
problems.
Since I do this experiment very early in my college course, I analyze it
both formally and simply. In high school I think you could use the simple
analysis by itself.
If m1 is the glider and m2 is the falling mass, then m2g is the force that
is causing the *system* to accelerate. But the total system mass is
(m1+m2), so the simple a=F/m analysis yields a=m2g/(m1+m2). I ask the
students to verify this with lab data. Note the emphasis on the word
"system," because m2g is not the force on m1.
I find that all students understand this simple analysis even though some of
them cannot see their way through an analysis of each mass separately
followed by a simultaneous solution.
The main point, of course, is to make sure they realize we want
a=m2g/(m1+m2) and not a=m2g/m1. I am embarrassed (for my high school
teacher) who had us do this experiment 30+ years ago with a Fletcher's
Trolley (no air tracks back then) and had us treat the acceleration as
m2g/m1; forgetting that m2 must also accelerate. The fact that all
accelerations were less than predicted was written off as friction.
Of course, with a good air track, and using the correct equation,
accelerations will still be less than predicted because of air friction,
pulley friction, and the rotational energy gained by the pulley. But the
"error" is a few percent less (depending on mass ratios) if you use the
correct equation. I have heard of some teachers slanting the track downhill
to counteract friction. I think this is okay if the amount of slant is
determined in a separate experiment. In other words, don't adjust the slant
until this acceleration experiment works correctly. That will be perceived
as fudging the experiment to make it come out correctly. Rather, slant the
track until a glider traveling by itself travels with constant velocity.
Then keep that slant, and do the acceleration experiment with the falling
mass attached. The slant counteracts the air friction on the glider, but
does not counteract the friction in the pulley nor the rotational energy
going into the pulley. With the good pulleys available today, the friction
there (and the rotational energy) is quite small.
Michael D. Edmiston, Ph.D. Phone/voice-mail: 419-358-3270
Professor of Chemistry & Physics FAX: 419-358-3323
Chairman, Science Department E-Mail edmiston@bluffton.edu
Bluffton College
280 West College Avenue
Bluffton, OH 45817
David Abineri said:
I am trying to come up with a good lab for high school students to do
that will clarify and test N2. I have air tracks available but have the
following experiences.
1. With a level air track, using a hanging mass as the constant force
pulling the mass on the track via a pulley seems very complicated for a
student seeing this kind of thing for the first time. The analysis of
such a system already requires a knowledge and acceptance of N2 in order
to figure the force being exerted on the horizontally moving mass so it
seems circular to the students. It is difficult to measure the force
directly since the air track can support limited weight.
2. Last year I tried tipping the air track and measuring the angle of
tip I could know the force acting down the incline and measured
acceleration with a motion detector (CBL). The results were not good
perhaps because it was difficult to measure the angle well.
Are there other ways I should consider having them check and appreciate
N2 or, how might I modify the above for a worthwhile lab. Any ideas are
welcome.