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 Ramp: Time and Distance

Data from AP Physics students at Berkeley High School, Berkeley CA courtesy of Richard White.

Students rolled ball bearings down 3-meter steel tracks. They released them from specific positions (50 cm, 1 m, 1.5 m, etc.) and timed how long it took the bearings to get to the bottom. Timing was with stopwatches, generally three students timing per trial. They did about three trials at each height.

The purpose was to explore acceleration, and find the acceleration of the balls on the track.
Angle is the angle of the track in degrees (measured with a protractor).
distance is in meters, the distance from the ball release to the end of the track.
trial is the trial number, i.e., the three measurements for trial 1 were all the same roll.
time is the time in seconds
recorder is the initial of the person wielding the stopwatch for that measurement. Evidently this group got tired of recording that!

The data look more or less linear. How do you know that they are not?
What relationship do you expect between distance and time if there is uniform acceletarion?
In this experiment, which goes on the horizontal axis, distance or time? Why?
What was the largest and smallest acceleration at each angle that is consistent with the data?
How do you deal with the spread in the data?
What do you think -- are these data consistent with uniform acceleration?

Angle distance Trial Time Recorder
10 0.5 1 0.94 E
10 0.5 1 0.94 I
10 0.5 1 0.97 A
10 0.5 2 0.88 E
10 0.5 2 0.9 I
10 0.5 3 0.88 E
10 0.5 3 0.94 I
10 0.5 3 0.82 A
10 0.5 4 0.9 E
10 0.5 4 0.88 I
10 0.5 4 0.9 A
10 1 1 1.22 E
10 1 1 1.25 I
10 1 1 1.28 A
10 1 2 1.28 E
10 1 2 1.22 I
10 1 2 1.28 A
10 1 3 1.28
10 1 3 1.25
10 1 3 1.28
10 1.5 1 1.62
10 1.5 1 1.65
10 1.5 1 1.6
10 1.5 2 1.69
10 1.5 2 1.75
10 1.5 3 1.69
10 1.5 3 1.69
10 1.5 4 1.72
10 1.5 4 1.66
10 1.5 4 1.75
10 2 1 1.86
10 2 1 2
10 2 2 2.03
10 2 2 2.03
10 2 3 1.9
10 2 3 1.94
10 2 3 1.9
10 2.5 1 2.34
10 2.5 1 2.18
10 2.5 2 2.31
10 2.5 2 2.25
10 2.5 2 2.25
10 2.5 3 2.22
10 2.5 3 2.25
10 2.5 3 2.18
10 3 1 2.33
10 3 1 2.37
10 3 2 2.43
10 3 2 2.41
10 3 2 2.56
10 3 3 2.59
10 3 3 2.5
10 3 3 2.5
20 0.5 1 0.66
20 0.5 1 0.63
20 0.5 1 0.59
20 0.5 3 0.59
20 0.5 3 0.63
20 0.5 3 0.69
20 1 1 0.78
20 1 1 0.88
20 1 2 0.94
20 1 3 0.81
20 1 3 0.84
20 1 3 0.89
20 1.5 1 1.34
20 1.5 1 1.22
20 1.5 1 1.16
20 1.5 2 1.2
20 1.5 2 1.18
20 1.5 2 1.09
20 1.5 3 1.28
20 1.5 3 1.15
20 1.5 3 1.19
20 2 1 1.56
20 2 1 1.38
20 2 2 1.49
20 2 2 1.38
20 2 3 1.43
20 2 3 1.31
20 2 3 1.32
20 2.5 1 1.53
20 2.5 1 1.46
20 2.5 2 1.4
20 2.5 2 1.48
20 2.5 2 1.46
20 2.5 3 1.76
20 3 1 1.69
20 3 1 1.65
20 3 1 1.75
20 3 2 1.56
20 3 2 1.62

<text form of the data>

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