(revised 7/6/221) REQUIRED SUPPLIES AND ANALYSIS TOOLS 0 Steel ball and plastic ball; smart phone or other device to measure time to at least tenths of a second; meter stick or tape measure; spring scale to measure mass of balls; anything else as needed to make better measurements. Logger Pro for plotting and curve tting. Calculator for doing what calculators do. Information from Lab 1 on using Logger Pro. Information on measurement errors and uncertainty from the Measurement Handout included with this lab. LAB GOALS By the end of this lab students 0 Conduct an experiment to condently evaluate whether the acceleration due to gravity is constant and to determine its value. Identify Sources of statistical uncertainty, instrumental precision, and systematic errors. Decide what and how much data are to be gathered to produce reliable measurements. Dene and calculate the mean (average) and mean absolute deviation of a set of data. Compare measurements with differing uncertainties and with the expected value of What is being measured. Propose and carry out follow-up investigations or revisions in light of the data and model, particularly to improve the reliability of the data. 0 Write a summary of all the decisions made during the experiment including justications of those decisions. 0 Present data and calculations in a well-organized fashion including labeled tables and results that are referenced in the summary and / or conclusion. 0 Write a detailed conclusion that discusses the outcomes of the investigation specically detailing results of revisions and iterations. INTRODUCTION The goal of this investigation is to determine whether or not the acceleration due to gravity, g, depends on the height from which a ball is released and to determine a value for g. If we take the downward direction to be negative and the landing position of the ball to be zero, then the initial height, h, would be a positive number and the acceleration would be negative. Further, if we drop the ball from rest and use one of the constant acceleration equations we have: 1 0 = h Egtz Solving for ggives us: 2h 9 = tz Now, of course, this is valid only if g is constant. And thus if we measure the time of fall from different heights we should get the same value for g from this equation if g is indeed constant. If we get statistically different values for g then g is not constant and the value we calculate for g will be more like an average value acceleration over the distance considered. Discuss with your group a plan for a high-precision measurement of the acceleration due to gravity for drop heights between 1.5 m and 0.5 m. Write down a clear description of your plan including a sketch of your setup (perhaps include a photograph that shows your setup and any household objects like doors, counters, dressers, that you are (imamm 2) Plot height as a function of the average time using Logger Pro. (Does height or time go on the \"vertical\" (or y) axis?) Make sure that you label the axes of your graph properly and give the graph a descriptive title. 9) How do your two experimental values of "g" compare with the accepted value (g = 9.80 m/s?) for the acceleration of gravity? Give a mathematical comparison using what you learned about measurements previously. (Show work)QUESTION AND FURTHER PROCEDURES 1. What is the greatest source of error in performing the experiment? 15 this error a random error or a systematic error? Explain how you know. 2. Can you think of another way to determine your experimental value for the acceleration due to gravity besides plotting your data? (See the Measurement Handout for a hint.) Do the appropriate calculations and give your answer for g in the form: g = average experimental value +/ average deviation 3. At this point you should have calculated g in three different ways (A quadratic graph, a linear graph, and your method from question 2) above. Which technique do you think is best? Do all three techniques give the same answer? If not, which technique do you think has the most error and Why? Viewing 4. How might you modify your procedures to determine Whether or not g depends on the mass of the falling object? Do the experiment and calculate g using your favorite technique. Report your results here