Galileo's Water Clock

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During our lab, Galileo's Water Clock, we created our lab to describe the motion of a ball on a plane using the water clock as an alternative method for measuring time. Our main purpose in this lab was to determine if the displacement of the ball is determined by the time or the time squared.

Once the water clock was set up, a ball was let go from the ramp at various distances for three trials each. Once the ball was let go, the water clamp was opened and then immediately shut once the ball reached the bottom. The amount of water released into the test tube (ml) and centimeters from which the ball was released were used together to find the average time, and average time squared.

Data, Observations, Sample Calculations and/or Graphs:
By looking at our collected data, when the displacement decreases, the average time and average time squared decrease with it. The formula used to come up with the average time and average time squared is as follows:

-see data tables on separate page
-see graphs on separate pages

Analysis of Data:
After measuring the data, graphical analysis suggests that the ball is proportional to the time squared rather than time. That is because the displacement vs. time squared is a straight line, which means they are directly proportional. The graph of displacement vs. time is curved, which means they are still proportional, but the rate of change varies depending on the displacement. The increase of displacement for each unit of time changes as the graph progresses. The displacement can always be matched to the time squared because it has a slope, and that tells us that the displacement always depends on time squared.

From this lab I have concluded that when a ball' displacement is more centimeters then the time in milliliters will also be higher. As the displacement goes down so does the time in milliliters. The graph proves that displacement is determined by time squared, because they are...
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