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Purpose: to determine the relationship between the circumference and the diameter of cylindrical objects; to determine the accuracy of measurement; to compare accuracy and precision Materials: five cylindrical objects, i.e. metal tubing, salt containers, etc string (non-elastic) metric ruler graph paper or graphing program Lab TIME ! Procedure 1. Obtain at least five cylindrical objects for measurement. 2. Construct a data table that lists the name of the object, the circumference (C) (cm), the diameter (d) (cm), and a column that shows the result of dividing C by d. C and d MUST be measured…not calculated. 3. Make measurements using an estimated digit with the school metric ruler (Each measurement should have one decimal place in cm.) 4. Carefully measure the diameter and the circumference of each object and record. Questions/Analysis: 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. For each object, divide the circumference by the diameter. Place this value in the appropriate column in your data table. Do you notice any pattern or similarities between the resulting numbers? What unit does the resulting number have? Construct a graph, by placing the circumference on the y-axis and the diameter on the x-axis. To determine the scale for the axis, follow this procedure: For the y-axis, first count the number of boxes on the y-axis; then divide the highest circumference value in the data table by the number of boxes. Round UP to the nearest workable value. For example, if when divided the answer is 0.033…round to 0.05. If the value is 1.7…round to 2. Usually multiples of 1, 2 and 5 work best for counting. This is the number that EACH BOX will represent. But, label the lines, not the box. DO NOT label every line since it will look crowded; instead label ~every 5th line. To construct the x-axis (diameter), count the number of boxes on the x-axis and then divide the highest diameter by the number of boxes. Finish as in Step 3. Using the method above will allow use of nearly all of the axis. Graphs do not look good if they are scrunched in one corner or if the data points go off the page. Plot the five points from the data table on the graph paper. Make a best-fit line by taking a ruler and drawing the BEST AVERAGE line through the points. You DO NOT have to start at zero, although for this graph the line should end up going through (0,0). End the line near the last data point. THE LINE DOES NOT HAVE TO TOUCH ANY POINT YOU HAVE COLLECTED! This is called a REGRESSION line, which is an average of all data points. Some points should lie above and some below the line. Give the graph a title; usually the format Y vs. X, in this case Circumference vs. Diameter. Line graphs in science are generally titled this way. Make sure that each axis is properly labeled and contains units: Circumference (cm) and Diameter (cm) Find the slope of the line on the graph by using the formula y/x or Rise/Run. Calculate a percentage error using the following formula: |EXP – THEO| x 100 THEO In this case, the EXPerimental value is the slope you found. The THEOretical value is 3.14. Absolute value is used so that all percentage errors are positive. 11. Why is the theoretical value for this lab 3.14? 12. 13. The percentage error you found is called the ACCURACY…how close the experimental value is to the standard or theoretical value. PRECISION is the reproducibility of the measurements. When you divided C by d in question #1, were the values close to each other? If they were close, precision was good; if they were random, precision was poor. Describe your precision. Using a dartboard as an example, describe how a dart thrower, using three throws, could have the following: (A) good accuracy and good precision (B) poor accuracy and good precision (C) poor precision and poor accuracy 14. In this lab, your accuracy could be good with the precision being poor. Explain using your graph to support your argument. Data Table: Object Circumference Diameter C/d = slope