Proving Galileo's Time-Squared Law

 The Italian Physicist Galileo proved that the distance an object falls in a medium is directly proportional to the time it takes the object to fall that distance squared.  I created an experiment with a ball and a ramp that proves this law.

8/8/11

McCallum High School AP Physics 3^rd Period

Galileo Galilei, born in 1564 and died in 1642, was an Italian astronomer, philosopher, physicist, and mathematician.  He was responsible for many breakthroughs in physics, mathematics, and astronomy that were central in the Scientific Revolution and foundational in science today.  He is considered “perhaps more than any other single person, responsible for the birth of modern science.”  Last week I devised an experiment that proves Galileo’s theory that the distance an object falls in a medium is directly proportional to the time it takes the object to fall that distance squared.  The experiment used a metal ball and a v-shaped ramp to replicate the object and distance fallen.

Materials:

1 V-Shaped Ramp

1 Metal Ball

1 Book or other flat object to incline the ramp

1 Meter-stick with centimeter increments

1 Stopwatch

Procedure:

1.    I placed the meter stick within the ramp and marked with a pencil every .1 m (10 cm) from one end of the ramp. 

2.    I situated the marked ramp on a significant point on top of the book (or other flat object) so that the angle of the ramp was exactly the same throughout the experiment.

3.    I placed the metal ball starting at the .1 m mark on the inclined ramp.  I let go at the precise time I started the stopwatch.  Then I stopped the watch when the ball hit the end of the ramp.  This gave me the time in seconds that the ball took to fall .1 m.  I recorded this time in a table.

4.    I repeated this procedure 5 – 10 times and averaged the results to get the mean time in seconds it took the ball to fall .1 m.

5.    I repeated these two steps for the rest of the increments (.2 m – .8 m)

6.    When I had gathered data for all the increments ( .1 m – .8 m).  I put them into the table. 

7.    I squared the average time in seconds for all the increments to get the average time in seconds squared (s^2).

8.    I put the time in seconds squared and the distance fallen in a table.  Then I used those numbers to create a graph. The distance fallen was the independent (x) variable while the time in seconds squared was the dependent (y) variable.

This gave me the proportion of Falling Distance to Time Squared.

The proportion is represented in this graph:

By making the increments proportional it allowed me to easily see if there was any correlation.  By repeating the timing process I was able to average many numbers to get a value that is closer to the true value.  This resulted in little experimental error, as seen in the graph above.  When I reviewed the graph, I saw the proportion had a positive and relatively direct correlation.  Given that experimental error is probable, the proximity to direct correlation was too close to regard as coincidence.  So I concluded that distance is directly proportional to time squared.