Ball on Incline Lab Report

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```					                                                                   Andrew J. Kartsounes
November 2nd, 2005
The Ball Rolling Down an Incline Lab
PURPOSE
To create graphical and mathematical representations of the relationship
between the position and the time for a ball rolling down an incline.

APPARATUS
Photogates

Meter Stick                                   x
Ball
Incline ramp

PROCEDURE
Choose a position by placing the photogates at a particular separation. Measure
the time it takes for the ball to roll to the chosen position by starting the ball as close
as possible to the top photogate and letting it roll down the incline. Repeat three
times for each position and record the trials. Repeat for a total of six different
positions.

DATA

Position                                        Time (s)
(m)                    Trial 1                 Trial 2                 Trial 3
0                       0                       0                       0
0.1168                  0.3632                  0.3717                  0.3639
0.2571                  0.6129                  0.6021                  0.6043
0.3761                  0.7222                  0.7284                  0.7271
0.5561                  0.8716                  0.8794                  0.8961
0.5871                  0.9434                  0.9360                  0.9336
0.8095                  1.1017                  1.0832                  1.0801
The Ball Rolling Down an Incline Lab                                                page 2

EVALUATION OF DATA

Average Time Time2
(s)      (s2)
0           0
0.37        0.14
0.61        0.37
0.726       0.53
0.88        0.77
0.94        0.88
1.1        1.2

The position vs. time was graphed resulting in a top–opening parabola. The
position vs. the time2 was then graphed resulting in a straight line of correlation
coefficient 0.9985 containing the point (0, 0). Therefore, the position is directly
proportional to the time2.
The Ball Rolling Down an Incline Lab                                                 page 3

CONCLUSION

As stated in the EVALUATION OF DATA section, the position ( x ) is directly
proportional to the time2 ( t 2 ).

x  t2
Since the y-intercept found from the graph is less than 5% of the maximum position,
the y-intercept is negligible. This means that when the time is 0 s, the initial position
of the ball is 0 m. The slope of the graph is 0.6636 m 2 which as shown in class is ½
s
of the acceleration. Therefore, our math model is

x  (0.6636 m 2 )t 2 .
s
Any error in this experiment may have been caused by not releasing the ball as
close as possible to the top photogate or incorrect measurements of the position of
the photogates.

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