Galileo’s Lab
Abstract:
Mr. Wright’s AP physics classes were asked to test Galileo’s method of proving that distance equals the square of time.
Introduction & Purpose:
Galileo, a sixteenth century Italian physicist tested his presumption that distance is proportional to the square of time in a falling object by rolling balls down an inclined plane. By using that method he did not have to include gravity in his calculations and it did not change the outcomes of his testing. The purpose of the experiment that the 7th period AP Physics class was assigned was to copy Galileo’s method of testing to prove or disprove that his presumption was correct. The controlled variable in this experiment is distance and the uncontrolled variable is time.
Hypothesis:
I predict that Galileo’s presumption is correct by observing everyday motion and the knowledge gained about kinematics and motion in my previous year of physics.
Background Information:
Galileo was a brilliant physicist that scientifically discovered many equations and true facts of motion. He set up experiments that proved our current understanding of motion and physics to be true. Much of his work was with kinematics and some of the things we are taught during Pre-Ap physics come from the works of Galileo and his experimentation. He also really evolved the common people’s knowledge of astronomy in his time with his heliocentric theory, which was not accepted to be true in the 16th century. Scientists all over the world should appreciate the works of Galileo because without his accomplishments modern science would not be where it is right now.
Materials:
- 1 Steel ball
- 1 aluminum ramp .885 m long
- Stop watch (used to measure time)
- Meter stick (used to measure distance)
- Notebook & Pen (for recording data)
Method:
- Find materials and find an empty area on a flat surface such as the ground or a table.
- Set up aluminum ramp on the table.
- Measure the length of the ramp and each time going down by about 15 cm when repeating procedure. Each time start the ball at the place marked so the independent variable is changed.
- Then have on person at the end of the ramp say stop to signal the person with the stopwatch to stop the time.
- After the time is recorded repeat the experiment but make sure that you complete 3 trials of every distance so you have the most accurate data by taking the average of the 3 trials measurement of time.
This shows a graph of how Distance effects Time squared based on data:
Average Time Squared (s^2) | Distance (m) |
12.04 | .89 |
11.35 | .74 |
9.42 | .59 |
7.45 | .44 |
5.43 | .29 |
3.24 | .14 |
This shows the basic relationship between time and distance & the data we actually recorded:
Time (s) | Distance (m) |
3.47 | 0.89 |
3.37 | 0.74 |
3.07 | 0.59 |
2.73 | 0.44 |
2.33 | 0.29 |
1.8 | 0.14 |
Conclusion:
Based on the data that was collected my group and I concluded that distance is proportional to the square of time. Our graph of the time squared vs. distance is almost perfectly linear meaning that distance is very close to time squared. The straight forward relationship between time and distance showed that as time increases distance increases so that means they are proportional to one another. But by graphing the time squared vs. distance it shows the direct relationship that is a closer estimate of their proportionality. The distance is the factor that we controlled during the expirement and the time is the factor that got changed based on the different distance measurements the steel ball was placed. Galileo was right that distance and time squared are proportional and we were able to prove it using his methods of eliminating gravity and using a ramp but they are not truly equal.
Appendix:
www.uwc.utexas.edu/node/145