PHYSICS EXPERIMENTS --- 132 1-1
Experiment 1
PHYSICS EXPERIMENTS --- 132 1-1
The Simple Pendulum and Computer Data Analysis
PHYSICS EXPERIMENTS --- 132 1-1
In this experiment you investigate the behavior of a simple physical system called a pendulum, consisting of a mass swinging on string. Although mechanically simple, this system is important because it exhibits repetitive motion. The frequency of repetition depends on physical properties of the system; the mass and the string length. You experimentally determine how the motion is related to system properties by taking data and performing graphical analysis to obtain a mathematical “fit”. Comparison of this fit with theory results in a determination of the acceleration due to gravity.
Preliminaries.
Figure 1. A Simple Pendulum
A simple pendulum is a mass M swinging on the end of a string of length L whose other end is fixed, as shown in Figure 1. The mass swings back and forth with a period T. The period is the amount of time it takes for one complete back and forth swing. Theoretically, the period is related to the length of the string and to the acceleration due to gravity g according to
(eq. 1)
Squaring both sides of eq. 1 gives
(eq. 2)
The slope-intercept form for the equation of a straight line is “y” = slope• “x” + “y-int”. In the eq. 2 above, T2plays the role of “y” and L plays the roll of “x”. Therefore, the term 42/g, or everything between the equal sign and the L, is the slope of this straight line graph. (In this particular case the y-intercept is zero.)
The general plan of graphical analysis, which is a fundamental data processing technique and will be repeated many times in future experiments, is to (1) collect data, (2) graph the data so that the graph is a straight line, (3) determine the properties of the line (slope and intercept) and (4) calculate unknowns from the determined properties of the line.
In this particular experiment, you realize these steps by (1) measuring period for different string lengths, (2) graphing the data with period squared on the vertical axis and length on the horizontal, (3) determining the slope of the best straight line through the data points and (4) determining the acceleration due to gravity from the slope.
Procedure.
This experiment introduces the use of computer software tools for creating graphs and performing graphical analysis. You should have read, and should have available for reference, the document entitled Introduction to Graphical Analysis as you work through this experiment.
•Construct a pendulum by hanging a mass on a piece of string. Measure and record the string length from the pivot to the center of mass. As accurately as you can, determine and record the period, the time for one complete swing.
• Repeat the period measurement for at least five other string lengths. Make sure that your string lengths are quite different from each other and cover the complete range from the shortest to longest lengths which are practical (over the range 0.2 to 2 m).
•Enter the data points into the computer. Eventually you will need the squares of both the period and length in handling your data. Use the “simple math” or “transform” options on the appropriate pull down menu to have the computer determine these numbers for you.
●Use the computer to graph the data with the "period" on the vertical axis and "string length" on the horizontal axis. Make sure the data points are not connected by straight lines!
●Use the computer to graph the data with the "period squared" on the vertical axis and "string length" on the horizontal axis. Make sure the data points are not connected by straight lines!
•The points on the second graph (T2 vs L) should lie close to a straight line through the origin. Print out this graph so that it has the following features:
-full page
-descriptive title
-axis labels with units
-convenient numerical scale on axes
-visible graph origin (often it is useful to show both intercepts on the graph so you should learn how to select the max and min values on each axis)
-best straight line fit with equation of line visible
•Use the slope of the best fit line to determine the acceleration due to gravity, using eq. 2.
•Determine the percent difference between your value and the accepted value of g = 9.80 m/s2.
Questions (Answer clearly and completely).
1.Does your pendulum behave according to eq.1?
2. Why do you determine the acceleration due to gravity from the "period squared" vs. "string length" graph? What is "wrong” with using your plot of "period" vs. "string length" to determine the acceleration due to gravity?
3.How do you determine the pendulum period for achieving the greatest accuracy?
4.What value do you determine for the acceleration due to gravity? What is the percent difference from the accepted value of 9.8 m/s2?
5.Suppose you do an experiment where you measure pendulum period for the same length string using different swinging masses. What do you predict a graph of the data with period on the vertical axis and mass on the horizontal axis looks like (refer to eq. 1)?
rev. 8/13