Introduction
The object of this experiment was to prove the third equation of
motion ,
The problem is as follows: If the angle of the
right track is increased and if the angle of the other track remains
constant, what is the relative pattern of where the collisions take place on
a level track? As the track angle increases on the right side, the cars will
continually collide closer to the left because the velocity of the right car
increases.
Procedure and Materials
The materials that were used in the experiment include three 225.80
cm tracks, eight books, a piece of foam, two low ‐friction cars, two
magnetic stoppers, and one stopwatch . The tracks were placed in a
straight formation and so that they were in contact with each other. There
was one track on either side of a level track. The tracks on the right and
left were angled, while the angle of the right track varied with the
experiment. We timed how long it took for the cars to travel down both
outside tracks, and then we measured how long and where the cars
collided on the level track. We then used the measurements to ultimately
find a theoretical value and percent error.
Constants and Equations
Data
Analysis
The data that was obtained from the experiment can be analyzed as to
come to several conclusions. A quadratic equation re presents the
measured data as y = ‐0.001x^2 + 0.128x ‐ 0.215 as a measured value. The R^2
value is 0.999, which is almost perfect . This tells us that our measured data
can be accurately described by the quadratic formula . The theoretical data
can be represented by y = ‐0.001x^2 + 0.117x ‐ 0.456, which is also
quadratic. The data that we had measured was precise because all of our
measured values per test were relatively the same. The data was accurate
in the sense that median percent error was 12.2%, but as the height
increased the percent error decreased, which shows that the higher the
velocity the less friction the car tires had on the track. The minimum
height that should work for the experiment should be 1.70 cm (measured)
or 4.03 (theoretical), and the maximum height should be 104.29 cm
(measured) or 160.04 cm (theoretical). The reason for this is that the level
tract is only 2.26 m long, so when the car moves at too fast a velocity or
too s low a velocity , the cars will collide on an angled tract, which would be
impossible to give a value for db. Therefore, the correct trend line should
fit the parameters 2.2580 ≥ x ≥ 0, as to model the experiment the best.
Conclusions
The object of the experiment was to de termine how the
height one end
of the right car track affected the collision distances to the right. As the
angle of the right track increased, the cars collided further to the right as
portrayed by the data. When the height of the right track was 8.60 cm, the
cars collided at 75.48 cm (from the right), while when the right track was
at 29.85 cm, the cars collided at 196.73 cm (from the right). Meaningful
sources of error lay in the fact that the wheels had friction on the grooves
in the tract when they were moving at a slow velocity, which altered our
data. Also, we had to as sume that the velocity stayed constant on the
lower track, which may have made our data less accurate. Lastly, the
angles between the outside tract and the level tract may have altered the
car velocities, and we did not account for those alte rations . The measured
values in the first five tests were at first higher than the theoretical values,
but in the last test the opposite occurred, and the percent errors account
for this. For future tests, I would first consider the sources of error, and
then I would continue the experiment by lengthening the level track,
lengthening the outside tracks, and adding mass to the cars. This test,
however, was complicated, but it brought good quality test results.
