Ph101: Fundamentals of Physics Laboratory 1
Instructor: Tony Zable
Laboratory #3: Galileo’s Experiment
Purpose:
1. To study the motion of a uniformly accelerating object.
2. To compare the motion of 2 different balls
Introduction: The Greek period of science flourished from 300 B.C. to A.D. 300. This early knowledge formed the foundation for the work of Galileo Galilei (1564-1642). He stands out as perhaps the dominant figure to lead the world of physics into the modern era. In 1609, he became the first to make astronomical observations with a telescope. He observed mountains on the moon, the larger satellites of Jupiter the rings of Saturn, and spots on the sun. His observations convinced him of the correctness of the Copernican theory that the planets circled the sun. Galileo’s work on motion was particularly well known, and because of his leadership, experimentation has become an important and essential part of our search for knowledge. In this lab experience, we shall endeavor to explore this study of motion using balls rolling down a gently inclined plane. However, Galileo would be completely amazed at the tools we will use, like the digital stopwatches and graphing computers, to mimic his study.
Preliminary Questions:
1) A physicist performing a similar experiment sets up an incline and rolls a small ball down the ramp. In this particular experiment, the ball traveled 2.5 meters down the incline during each measurement while the experimenter recorded the time of each ball roll. The time data were collected by the physicist are shown on the right.
a) What is the average time the ball travels down the 2.5 m incline? (To calculate an average, add up all of the measured times and divide this value by the number of data points)
b) Determine the distance/(average time)2 , or d/t2, ratio for this set of data.
c) What are the units of the d/t2 value? Do these units remind you of particular physical quantity we have studied?
File Name: \ph101\Ph101_Lab03-Galileo.doc
Ph101: Fundamentals of Physics Laboratory 4
Instructor: Tony Zable
Apparatus:
File Name: \ph101\Ph101_Lab03-Galileo-nograph.doc
Ph101: Fundamentals of Physics Laboratory 4
Instructor: Tony Zable
· 2-3 meter sticks
· 1 small metal ball
· 1 medium rubber ball
· a stopwatch
· Logger Pro Software (optional)
· 2 photogate sensors (optional)
File Name: \ph101\Ph101_Lab03-Galileo-nograph.doc
Ph101: Fundamentals of Physics Laboratory 4
Instructor: Tony Zable
Procedure:
A) Galileo determined that the distance was directly proportional to the square of time for a uniformly accelerated body by taking measurements of distance and time for a ball rolling down a slightly inclined plane. Build such a plane out of two meter sticks and wooden blocks, with a small gap between the sticks for the ball to roll inside. To reduce friction as much as possible, the gap should be as small as possible. Use a stop watch to measure the passage of time as the ball rolls various distances down the inclined plane. Repeat 10 times for each distance. Enter your data in the table below. Using a calculator, determine the average times and calculate the distance-time squared ratios. Repeat your measurements using a different ball. Warning: Be sure not to move the inclined plane.
Galileo proved the above underlined theory by calculating the following ratios:
d1/t12 = d2/t22 = d3/t32 = etc.
He did not use a calculator or computer, but you can!
Alternative Measurement Procedure: Performing short time measurements with a stopwatch can be potentially sloppy, due to human error and response time. A more precise way to measure the time is to use 2 photogates, placing one at the top and the other at a lower position on the ramp. The first photogate should be positioned just in front of the starting position of the ball so that as the ball just begins its roll it triggers the sensor.
Obtain 2 photogates and connect them to DG1 and DG2 respectively. Turn-on the ULI interface then start-up the computer. Open the software program by selecting Start®Program Files®Vernier Software®LoggerPro.
Now, open the appropriate experiment file, “PHY101-Exp03” from the PHY101 experiment files for LoggerPro.
The photogates can be positioned using ring stands and clamps, and the distance between them can be measured directly, thus eliminating “human judgement” when ball reaches the desired distance down the incline.
Ball #1:
Distance / #1 / #2 / #3 / #4 / #5 / #6 / #7 / #8 / #9 / #10 / average
time / d/t2
Average
d/t2
Ball #2:
Time (trial #)Distance / #1 / #2 / #3 / #4 / #5 / #6 / #7 / #8 / #9 / #10 / average
time / d/t2
Average
d/t2
Question: Observe the d/t2 values above, do your d/t2 calculations agree with the underlined theory? Explain why or why not?
Final Analysis
1) What is the average value of your d/t2 calculations for: Ball 1? Ball 2?
2) What is the minimum d/t2 value for: Ball 1? Ball 2?
3) What is the maximum d/t2 value for: Ball 1? Ball 2?
4) One way to observe how close data points are to one another is to calculate the % Range for the data set. To calculate % Range:
Calculate the % Range for each of your d/t2 data sets.
5) What do your % Range values say about the d/t2 values in each data set? Do your values support Galileo’s conclusion? Why or why not?
6) Is this the best way to test the theory? Why or why not? If not, how might you propose to better test it?
File Name: \ph101\Ph101_Lab03-Galileo-nograph.doc