Galileo's Lab

Abstract

This lab covers the relationship between distanced traveled and time squared, an association Galileo first discovered centuries ago.

 

History

Probably Galileo’s most famous experiment was when he dropped objects off the Leaning Tower of Pisa to prove that mass did not influence the time it took for an object to reach the ground. While many historians believe that this was a thought experiment instead of an actual one, the results became a cornerstone of kinematic motion. His ideas proved Aristotle incorrect in his theory that heavy objects fall faster than lighter ones. The results of Galileo’s experiment demonstrated that the distance an object would fall was proportional to the square of time. This theory became a law of kinematics, later being transcribed into an algebraic equation by others. 

Materials

• An aluminum channel that can be used as a ramp
• A steel ball
• A stopwatch

Procedure

Step One: prop the channel up so it forms an angle with the table or floor. The angle is not important, but it should be steep enough to allow the ball to move freely.

Step Two: Mark off different lengths on the channel to the bottom of the ramp, creating enough distances for a suitably large sample.

Step Three: Roll the ball down the channel at each distance three times, measuring the time it takes for the ball to reach the bottom.

Step Four: Average the time it took for the ball to reach the bottom at each individual distance.

Step Five: Create a graph displaying the relationship between distance traveled and the average time squared that it took to travel it.

Conclusion

The results from our experiment show a direct correlation between distance traveled and the square of time. Our results agree with Galileo’s, demonstrating a direct relationship between these two quantities.

This graph clearly demonstrates this association. Time squared, shown on the y-axis, is plotted against distance traveled, shown on the x-axis. The trend line plotted on the graph displays a link between the two variables. This clear pattern among the data points toward the direct proportionality that Galileo discovered.