Galileo Lab

History/Background

During the 16th century, a physicist by the name of Galileo Galilei proposed that a falling body with negligible air resistance has a uniform acceleration.  Galileo also was able to test, not discover, the relationship between the distance an object falls and time:  d∝t^2.  There was one obstacle that Galileo faced when attempting to test this theory:  he had no accurate way to measure the time it would take a ball to fall.  But Galileo, being and intelligent, problem-solving physicist, was able to make measuring easier by using an inclined plane to roll balls instead of a straight down drop.

Materials

• Stopwatch
• 2 Pens/Pencils (one of them could break so have two!)
• Clipboard (Optional)
• One partner (two if needed)
• Aluminum ramp (for inclined plane)
• One ball of appropriate size
• Meter stick
• Book or something of the like that allows you to hold up the ramp
• Calculator (unless you are a SUPER GENIUS)

Procedure 

1. Use a book or something to make it so that the aluminum ramp is at a fixed angle
2. Mark out spots 30 cm, 40 cm, 50 cm, 60 cm, 70 cm,  and 80 cm from the base of the ramp
3. Create a table that has 30 cm, 40 cm, 50 cm, 60 cm, 70 cm,  and 80 cm as independent variables in one column and a dependent variable column for the corresponding times
4. Have one person drop the ball from the first distance in the table 3 times and record each time.
5. Record the average time
6. repeat steps 3,4, and 5 for the rest of the distances.

Hypothesis

I hypothesize that Galileo’s testing of the theory that d∝t^2 is correct.  No matter what distance the ball rolls, the distance divided by the time squared will equal the same number.

Data Table

Distance (cm)      Average Time  Time squared d/t^2
80                              2.38            5.66                 14.12
70                              2.19            4.80                 14.60
60                              2.01            4.04                 14.85
50                              1.84            3.39                 14.77
40                              1.68            2.82                 14.17
30                              1.44            2.07                 14.47

Scatter Plot

Conclusion

To conclude, the theory that Galileo tested was in fact correct.  The theory’s validity is most evidently seen in the data table above.  Each distance divided by the corresponding time squared was equal to around 14.6 or so.  Thus, distance is proportional to time squared.  The results are not perfectly exact because of the human error that occurs when operating the stop watch.  It is rather difficult to stop the stopwatch EXACTLY when the ball reaches the ground.  No human could possibly do it.  But the results are still close enough to prove the relationship.  Next time it would be in the best interest of the experimenter to us scientific equipment to clock the ball’s roll time.

Sources

Sharratt, Michael (1994). Galileo: Decisive Innovator. Cambridge: Cambridge University Press.