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curator:Tim Erickson
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 Speed of a Cue Ball on a Ramp

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?).

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?

time mark
0.09910
0
0.08398
1
0.07410
2
0.06742
3
0.06243
4
0.05831
5
0.05505
6
0.05212
7
0.04940
8
0.04710
9
0.04514
10
0.04330
11
0.04172
12
0.04026
13
0.03893
14
0.03775
15
0.03660
16
0.03568
17
0.03474
18
0.03381
19
0.12914
-1
0.22187
-2

<text form of the data>

 ©2002 eeps media 866.341.3377 or Last updated February 14, 2007 supported by NSF award DMI-0216656