How much money do you want to spend? How many complete set-ups do you
need?
I think the Pasco 2.0-meter air track is exceptionally good. We have 6
of them. They cost $559 each. The air supply is excellent and fairly
quiet. It cost $349, but adequately powers two tracks if you have the
right work space to get two tracks positioned to use the same air
supply. So for one setup you need $908, and for two setups you need
$1467. Each track include two gliders and an accessory kit (weights,
pulley, bumpers, etc.)
I consider the electric launcher a necessity. That's $79 for one end of
one track. If you want to do head-on collisions you need one on each
end. You also need some power supplies to run the launchers, but you
may already have those (about 5V, 2). You need photogate timers or
other electronic timing systems that can time to at least the nearest
tenth-millisecond (0.0001 s). For making near instantaneous velocity
measurements you should use "double-flag timing." For details on this
please see my on-line paper at
www.bluffton.edu/~edmistonm/double.flag.timing.pdf
Okay... if you do all that, what kind of results can you get?
(1) Horizontal Atwood's Machine: The glider (m1) is pulled by a falling
mass (m2) that is connected to the glider by a thin string passed over
the low-mass ball-bearing pulley. N2L-predicted acceleration is a =
m2g/(m1+m2). If students are careful to level the track, determine gate
positions to nearest quarter-millimeter [ for determining acceleration
from a = ((vfinal)^2-(vinitial)^2)/(2deltax) ], the percent disagreement
between theory and experiment runs about 1 percent. Experimental-a is
less than theory-a because of residual friction.
(2) Same setup as (1) but look at conservation of energy. delta-GPE of
falling mass equals delta-KE of (glider and falling mass and pulley).
Note, rotational energy of pulley is really small and can be omitted
from the calculation if you want. Again, the percent error is about 1%.
The KE is about 1% lower than the GPE.
(3) Collisions: Elastic collisions using the rubber-band bumpers
supplied with the accessories show about 95% retention of KE. Momentum
conservation for elastic collisions yields error of about 2 to 3%, but
you have to watch out how you calculate this. For a head-on collision
with equal-mass gliders with roughly equal-opposite velocities the
initial momentum is about zero. If you figure percent-error the normal
way you might be dividing the difference by a near-zero number. There
are other ways such as dividing the difference of the two numbers by the
average of the two numbers.
For inelastic collisions using the coupler provided (a small nail on one
glider sticks into modeling clay on the other glider) the conservation
of momentum is a bit worse (about 5% error) because when the gliders
stick together they may not retain perfect collinear alignment, and that
can create a slight interaction with the track either at the time of
collision, or extending beyond the actual collision time. However, in
this regard, I find the Pasco coupling system quite better than sticky
tape or Velcro systems. The nail/clay system is the best I have used.
I also have a Pasco 2.2-meter track (non-air) with wheeled carts. We
tried this to see if we could get results anywhere near the air-track
results. We cannot. However, I sometimes transport it to class to show
a demonstration (without measurements) so students can get a general
idea of something. Not needing to transport (and listen to) an air
supply makes this a good in-class demo tool, but for acquiring data it's
difficult to get even 10% results. At $449 for the track and
accessories we got, that's about 50% of the cost of one air track, and
two systems would be 61% of the cost of two air tracks sharing one air
supply. So there is some savings, but you pay for it with
much-lower-quality data.
That's enough for now. If you have more questions about my experience
with these systems, ask away.
Michael D. Edmiston, Ph.D.
Professor of Physics and Chemistry
Bluffton University
Bluffton, OH 45817
(419)-358-3270
edmiston@bluffton.edu