Part 2 - Determining the charge Q on a repelling balloon Consider the following experiment, which has already been performed. You do not need to set up the experiment yourself. Measurements for you to analyze will be given below. A. Blow up 2 balloons, tie them closed, and charge them by rubbing with fur. Try to get an even charge by rubbing all over each balloon, not just one part. The rubber of the balloon is an insulator so charge tends to stay in one place. B. Now tie the balloons to a pair of strings hanging down from the ceiling. They will most likely discharge during this process so once they're hung, charge them again. The balloons should separate from each other and make a 10- or 20-degree angle between the strings. C. Measure the vertical height h, and/or the diagonal distance L along the string, from the ceiling to the center of one of the balloons. D. We need to determine the angle between the strings, but use of a protractor at the ceiling is usually too difficult. Instead, measure the distance r between the centers of the balloons, to the nearest centimeter or two. Trigonometry can then be used to find the half-angle 0 (shown in the diagram below) based on the values of r and h (or r and L). Ceiling L h r Balloon Table 3 Experimental Measurements Separation between balloon centers Heighth from ceiling to balloon center Length L along string to balloon center Mass m of each balloon Angle as defined in diagram Charge q of each balloon 68 cm 190 cm 193 cm 3.65 g Now let's figure out the charge q on each of these balloons, based on the above measurements. We will assume that both balloons have the same mass m, and the same charge q. Think back to first- semester physics. How would you go about creating an equation that relates the forces and geometries of this situation, in order to solve for the variable q? The following steps will guide you through the process. 16. Draw a free-body diagram of the forces acting on just one of the balloons. Identify all forces acting on that one balloon, and label them with the appropriate force. 17. Use your free-body diagram to develop two Newton's 2nd Law equations, based on the condition of static equilibrium in the horizontal and vertical directions, respectively. It is strongly recommended that you are sure you can answer #16-17 before you leave lab. 18. Two of the force variables in your equations should be related to quantities listed in Table 3. Rewrite your equations in terms of those quantities, if you have not already done so. Your equations should still involve variables, not numerical values. 19. You should have two equations at this point, but each one only contains one remaining force variable, the value of which is unknown. Combine the two equations into one by eliminating this unknown force variable. 20. Solve the remaining equation for the unknown charge q in terms of all the other variables. Variables that should appear in your equation are: the separation r, the mass m, the angle 0, and the physical constants g and k. 21. Consult the diagram of the balloon experiment on the previous page. Use a right-triangle to calculate the numerical value of the angle 0, based on the other values in Table 3. Also, enter your result in Table 3 with the appropriate units. 22. Calculate the numerical value of the charge q on the balloon, and express it with the appropriate SI prefix and units. Also, enter your result in Table 3. 23. How many excess electrons were transferred onto the balloon during the charging process?