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Ernest Rutherford used statistical analysis and probability to help analyze the results of his gold foil experiment In this experiment, you will model the gold foil experiment using BBs and cups You will then analyze your results in terms of probability to estimate the size of an object that cannot be seen

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1 Use the centimeter ruler to measure the length and width of the inside of the shoe box Record the measurements in the data table 2 Use the centimeter ruler to measure the diameter of the top of one of the cups Record the measurement in the data table 3 Place the shoe box in the center of a folded towel, such that the towel extends at least 30 cm beyond each side of the shoe box 4 Randomly place the three paper cups in the bottom of the shoe box 5 Have your lab partner randomly drop 200 BBs into the shoe box Make sure he or she distributes the BBs evenly over the area of the shoe box Note that some of the BBs may miss the shoe box and land on the towel 6 Count the number of BBs in the cups and record the value in the data table

1 Calculate the area of the shoe box The area of a rectangular shape is given by the equation Area Length Width 2 Calculate the area of a cup using the diameter you measured The area of a circle is given by (Diameter)2 the equation Area

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3 Calculate the total area of the cups by multiplying the area per cup by the total number of cups 4 Calculate the percentage of shoe box that is occupied by the three cups by dividing the total area of the cups by the area of the shoe box and then multiplying by 100 5 Calculate the percentage of BBs that landed in the cups by dividing the number of BBs in the cups by the number of BBs dropped, and then multiplying by 100 766

Your Data Shoe box length (cm) Shoe box width (cm) Shoe box area (cm 2) Measured diameter of cup (cm) Calculated area of a cup (cm 2) Total number of cups Total calculated area of cups (cm 2) Percentage of shoe box occupied by cups (%) Number of BBs dropped Number of BBs in cups Percent of BBs in cups Percent of shoe box occupied by cups based on probability Total area of cups based on probability (cm 2) Number of cups Area of one cup based on probability (cm 2) 3 3 3 3 3 3 200 200 200 200 200 200 3 3 3 3 3 3 Data from Group 2 Data from Group 3 Data from Group 4 Data from Group 5 Class Average

6 Determine the percentage of the shoe box occupied by the cups based on probability Note that this percentage is (ideally) equal to the percentage of BBs that landed in cups 7 Calculate the total area of the cups based on probability To calculate this value, multiply the percentage of the shoe box occupied by the cups (based on probability) by the area of the shoe box 8 Calculate the area of each cup based on probability by dividing the total area of the cups based on probability by three 9 Record the experimental data from the other groups in the data table and then calculate classroom averages for all of the data 10 Error Analysis Compare your calculated value for the area of the cup based on probability (experimental value) with the area of the cup calculated from the measured diameter (accepted value) What is the percent error in your value based upon probability Calculate the percent error using the following equation: Percent error

1 Were you able to accurately determine the area of a cup based on probability Explain in terms of the percent error 2 List the error sources in this experiment and describe their effects on the results

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