(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 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 using as height references), a list of equipment, and how you made your measurements. Describe how you Will determine the uncertainty in your measurements and how many measurements of time you will make for each height. The tables below suggest several heights to use and the fact that you should make several time measurements for each height. If you think you need to make more time measurements for a given height then feel free to create your own table. The more data the better! THEVWHTEUP As you work through this lab activity you should be building your lab report or writeup. The rst page must be a cover page with the lab title, date, your name and the names of any classmates who contributed. The second page should be a description of your procedures for making your measurements, photographs of your setup and any information on technique that you found lead to better results. The next few pages should be the data tables, plots, and answers to questions asked within the procedures section below. And nally, the last page should be a thorough conclusion summarizing the results of this experiment and including reflection on your data including interpretations and conclusions that argue for whether the acceleration due to gravity depends on height or mass. Your conclusion should also discuss things that you would have done differently if you had different equipment and what that different equipment might be. PROCEDURES Some of the procedures below ask you to do something then explain something. Write your explanations in the space provided below the question and include the data tables along with the questions and answers as part of your writeup. 1) Measure the time it takes for the metal ball to fall through the suggested heights shown in Data Table i. For each height be sure to do at least 4 time measurements and then calculate the average time. Be careful how you measure the height, for example make sure to measure the distance that only the bottom of the ball moves rather than comparing the top of the ball with the bottom of the ball; reference only one point on the ball. DATA TABLE 1 Displacement (meters) Time (seconds Trial 1 (1.5 m suggested m Average Time = 3 Trial 2 (1.25 m suggested m Average Time =(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. 3) 4) 5) 6) 8) Use the Curve Fit Function in Logger Pro to try to nd the curve that is the closest t for the graph. \\Which of the following curve types gives the best t? Try each to nd out. Remember to edit the function to include only the terms and parameters that you want to use. (See Lab 1 for practice in plotting and tting using a sample set of data.) a) linear t? b) quadratic (power 2.)? c) exponential? The curve with the smallest root mean square error (RMSE) is the better t (but is not necessarily the most correct mathematical model for the physical phenomena being studied, as you learned in lab 1). Print your plot (or take a screenshot) showing the various ts. Be sure your graph includes the equation for your ts. Knowing the correct relationship between height and time, can you determine the experimental acceleration of gravity from your graph's best fit equation? Explain how and show your work. If a linear function is not the best t of your plot above, how would you plot your height and time data so that the resulting plot 15 linear? Explain. (You should be making a new plot using your data but changed in some way. You won't be manipulating or using the equation(s) from your original plot.) Print the graph (or a screenshot) showing a linear t to your data and include properly labeled axes. Can you determine the experimental acceleration due to gravity from this linear graph's best t equation? Explain how and show your work. 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