# The report is due during the laboratory section next week and includes answers to analysis questions 1 to 8. Write answers to questions on sheets *separate* from the VERNIER (EXP 5) hand out. Hand write neatly and clearly; if you don't think you can write legibly, type it. Include a rendition of the table on page 53. Photocopying is fine but the boxes may be too small to write in all significant digits clearly. # GROUP REPORTS ARE ALLOWED; YOUR GRADE WILL BE COLLECTIVELY SHARED WITH GROUP MEMBERS , SO REMEMBER TO PARTICIPATE IN THE REPORT WRITING TO PREVENT CARELESS MISTAKES THAT WILL REDUCE YOUR GRADE. IN GENERAL, WHETHER OR NOT YOU OPT FOR AN OFFERED GROUP REPORT, write down your lab partners names on a cover sheet. You should be able to identify those with whom you worked. FOLLOWING IS A SURVEY OF THE REPORT'S MAIN PINTS AND THEN A MORE DETAILED QUESTION BY QUESTION TREATMENT: # We can address analysis questions 1 through 6 with a typical example using some of the ideas in the "ERROR ANALYSIS" handout. For background on sig. figs. visit http://library.thinkquest.org/10796/ch1/ch1.htm. (See other thinkquest chapters for basic physics and math summaries.) Suppose your data was: 9.784 +/ 0.004280 9.797 +/ 0.002524 9.791 +/ 0.001897 9.810 +/ 0.001820 9.810 +/ 0.002132 9.819 +/ 0.003080 +/ means plus or minus the RSME shown. The units are m/s^2 = meters per seconds squared. We will not use the RSME's directly calculations but they indicate the data points are precise to the 1/1000's placeone reason I urged you to write them down. The usual convention is rounding the RSME to one sig. figfor example 0.004280 = 0.004 after rounding. The sum of the data points is 58.811 which has 5 sig. figs. When you divide by 6, an exact number (i.e. 6 = 6.000.....), you get a 5 sig. fig. number 9.801833333 = 9.8018 after rounding. The handout suggests a method for getting the uncertainty or spread for small data sets: (max  min)/2 = (9.819  9.784)/2 = 0.0175 = 0.02 after rounding. You would report result as 9.8018+/0.02 = 9.80 +/ 0.02 after rounding. Many textbooks use the value of 9.80 m/s^2 for the accepted value of g as we will do in this lab. The acceleration of gravity depends on latitudewith a minimum value of 9.780 m/s^2 at the equator and 9.832 m/s^2 at the poles, a variation arising from the Earth's rotation and "equatorial bulge": http://en.wikipedia.org/wiki/Gravity_of_Earth . You can also express the uncertainty as a percentage of the acceleration: (0.0175/9.801833333)*100 % = 0.178538029 % = 0.2 % after rounding. With regard to question #6 , since the accepted value 9.80 is within the range of the 9.80 +/ 0.02 (average +/ uncertainty), the experimental result agrees with typical textbook values. (Note our textbook only uses two sig. figs. for the accepted value page 54) . It's coincidental the average above, rounded to the 1/100's place, is the same as the accepted value 9.80. Your average may differ from the accepted value. Finally, under #6, also compute the percent error. In this case we have (9.8018333  9.80)*100%/9.8 = 0 % since the difference between the two values is 0.0018333, suggesting a precision greater than that allowed by accepted value 9.80. Your percent error may not be zero. (See http://library.thinkquest.org/10796/ch1/ch1.htm ) Email me with questions. MORE DETAILS ARE PROVIDED BELOW ON THE LAB REPORT: DETAILED REPORT GUIDELINES Following is an explicit questionbyquestion outline of the work you must show under each question in the correct order so I can grade it easily. I want to grade without searching, sometimes in vain, for indications you did work. This process should not be an Easter egg hunt. If the report is disorganized with elements in the wrong place I will not grade it or give you zero on portions I cannot find easily. There are basically two types of questions, qualitative and quantitative, applied to each question . In all cases, list the questions as if the report was a homework assignmentwith the question number followed by the work you did and your answer. It's as simple as that. You must include the data table as a separate element with all your raw and derived numbers. But the derived numbers for the data table must be shown explicitly under the appropriate analysis questionjust like a homework problem in which you show work. You have two sections of the report: Preliminary Questions and Analysis Questions. Turn in the report in the following basic format. Under any question , do not say "See the data table ", without showing work. You must *show all the work* explicitly under the question leading to the number you entered in the table. Following the basic template below, I discuss how to answer each question. Please read this entire email message. REPORT FORMAT : Preliminary Questions 1. show work/reasoning 2. show work/reasoning 3. show work/reasoning Analysis Questions 1. show work/reasoning 2. show work/reasoning 3. show work/reasoning 4. show work/reasoning 5. show work/reasoning 6. show work/reasoning 7. show work/reasoning 8. show work/reasoning A COPY OF THE DATA TABLE MUST BE TURNED IN ON A SEPARATE SHEET; YOU CAN PHOTOCOPY YOUR DATA TABLE PAGE FROM THE HAND OUT. Following is what is required for each question: Preliminary Questions: 1. Aside from the 0.5 cm lengths , as the FENCE moves through the gate what additional info do you need to find the sequence of average speeds for your plots ? Explain. 2. Draw a qualitative sketch of v vs t 3. Answer the question by drawing a qualitative sketch of v vs t if you threw the fence down instead of dropping it. Analysis Questions: 1. From the six drops, identify the maximum and minimum from your six values of the acceleration . DERIVE THE AVERAGE EXPLICITLY by adding up the six numbers and dividing by 6. This work must be shown as if it was a homework problem. Use correct sig. figs. See previous emails and handouts on how to correctly compute the average with correct sig. figs. SHOW WORK ! For example from the string of numbers below, identify the min and max entered in your your data table. Then add the six numbers and divide by six to get the average with correct sig figs. For sig. figs. review, visit: http://library.thinkquest.org/10796/ch1/ch1.htm. SHOW WORK ! 9.784 9.797 9.791 9.810 9.810 9.819 2. Describe in words the shape of D vs t for the free fall experiment. You should also draw a qualitative sketch. SHOW WORK! 3. Describe in words the shape of v vs t for the free fall experiment. You should also draw a qualitative sketch. Relate this to the D vs t graph. Recall the instantaneous slope of D (position) equals the velocity. 4. Derive the uncertainty by computing (min  max)/2 , where the min and max are among your six drops. Round the uncertainty to one sig. fig. Round the average to the same decimal place. For example, drawing from the info in emails and handouts, if your uncertainty was (10.185  9.214)/2 = 0.4855, you would round to 0.5. Suppose your average was 9.7870. Then you would report you answer as 9.8 +/ 0.5. As another example, suppose your uncertainty was (9.819  9.784)/2 = 0.0175 rounded to 0.02. Then if your average was 9.8018, you'd report 9.80 +/ 0.02. SHOW WORK ! See example in the lab hand out under Analysis Question 4. 5. Find the precision from your data, defined to be (uncertainty)*100%/average. For example, from the the examples in the previous questions, the precisions would be (0.4855/9.784)*100 % = 4.9607 % = 5 % and (0.0175/9.8018)*100 % = 0.1785 % = 0.2 % after rounding to one sig . fig. See example in the lab hand out under Analysis Question 5. 6. Compare your average with the accepted value 9.80 m/s^2 in two ways; (i) using the range as discussed in the lab hand out under #5 (ii) using the percent error as suggested by me. (i) To see if the accepted value falls within your range you must compute that range. Here's how: Using the first example in question 4 above, the upper limit is 9.7870 + 0.4855 = 10.2725 = 10.3 after rounding to the 1/10's place. The lower limit is 9.7870  0.4855 = 9.3 after rounding to the 1/10's place. Thus the range is [9.3, 10.3]. The accepted value 9.80 does fall within the range. (ii) To find the percent error (PE), use definition PE = your average  accepted value*100%/accepted value. In the case of the first example in question 4 above, we get 9.7870  9.80*100%/9.80 = 0.013*100%/9.80. Note that from sig.fig. rules, 0.013 would be rounded to one sig . fig. i.e. to 0.01 since 9.80 is precise to the 1/100 's place. But do not round off until the end of the computation. You get PE = 0.013*100%/9.80 = 0.1327 % = 0.1 % after rounding to one sig. fig. 7. This is a qualitative prediction. Sketch your prediction for the acceleration from the straight line behavior of v. You then changed the upper "D vs t" graph to "acceleration vs t" to compare your prediction with the experiment. Comment on the differences between your prediction and the actual plot on the screen. You had to change your scale of the "a vs t" plot since acceleration was about 10 m/s^2. 8. Using the acceleration vs t graph on the screen, click the STAT BUTTON and copy down the mean, min and max. The mean is what you are most interested in. Compute the percent error (PE) between the that mean and the accepted value 9.80. Please REREAD THE LAB HAND OUT QUESTIONS and do not rely only on the comments in this email. Below is pasted an earlier email message on this lab.  Regarding graphs, one representative picture is sufficient for trials 1 to 6 corresponding to analysis questions 1 6, only one image for analysis q 7/8. Also below replace "RSME"by "RMSE," the rootmeansquareerror of the leastsquaresfit slope computation if it was was ever misspelled that way. # The report is due during the laboratory section next week and includes answers to analysis questions 1 to 8. Also answer the three Preliminary Questions. Write answers to questions on sheets *separate* from the VERNIER (EXP 5) hand out. Hand write neatly and clearly; if you don't think you can write legibly, type it. Include a rendition of the table on page 53. Photocopying is fine but the boxes may be too small to write in all significant digits clearly. # Try to write down your lab partners names on a cover sheet. During Monday's discussion section, if not before, you should be able to identify those with whom you worked.
