These data are from the curator.
We set up a ramp at a fairly shallow angle. The ramp had numbered
marks on it every 10 cm. We released a cue ball from various marks.
It rolled down the ramp and through a photogate set up at the position
mark = –2.5, i.e., 25 cm downhill from the
zero of the "mark" measuring system.
The purpose was to see if the acceleration of the cue ball on the
ramp was uniform (and to see if the data were better than with the
tennis ball).
time is in seconds  the time it took the cue
ball to pass through the photogate.
mark is the position (described above) from which
the ball was released.
In doing the analysis, there are many things you do not know, for
example, the angle of the track and the diameter of the ball. That
might matter if we were more ambitious, but we're only setting out
to see if this setup produces uniform acceleration; we are not,
for example, trying to determine the acceleration of gravity. So
you will not be able to use customary units for speed, say, unless
you measure a cue ball.
Before you begin analysis: Think about this—the
father up the ramp the ball starts, mark will be
larger. The larger the value of mark, the (faster
or slower?) the ball will be going at the bottom of the ramp. The
faster (or slower) the ball is rolling, the (longer or shorter?)
the time it will take to go through the photogate.
Therefore, the graph of time as a function of mark
will be (increasing? decreasing?).
Questions and tasks
Does the graph of the raw data match your prediction?
Make a new variable, speed, to represent the speed
of the ball as is goes through the photogate. Figure out how to
calculate it.
Make another new variable, distance, that is the
distance in centimeters between the place where the ball was released
and the photogate.
Make a graph of speed as a function of distance.
Use physics to figure out how speed behaves as
a function of distance under some uniform acceleration
a.
Find a value for a that best fits the data.
(In Fathom, make a a slider and use Plot
Function to put your function on the data graph.)
Do the data look as if they fit the model? That is, are the data
consistent with uniform acceleration?
What assumptions did you make in your calculations?
Compare these data with data for a tennis ball rolled down the
same ramp.
>> Tennis Ball data
Extra. Make a residual plot of how the data deviate
from the model. It should not look like random scatter, which we
usually associate with a good model. Yet the residuals are quite
small. What do you conclude?
