The Resolution and Addition of Vectors: The Vector Force Table 1 Objective To experimentally verify vector addition. 2 Overview The main idea is to set up two to four vectors quantities and compute their vector sum (resultant) using vector components. Then, using the computed resultant as a guide, exper imentally determine the actual resultant and compare it to the computed resultant. 3 Apparatus 1. Force Table (FT): A horizontal disk with degree markings on it. 2. Small ring that serves as a particle. 3. Level, pulleys, string, protractor, ruler. 4. Various slotted masses with hangers. 4 Experimental set up and Procedure Figure 1 shows the experimental set up. 1. Place a circular or linear level on the FT. Adjust it's feet till it is horizontal. If you use a linear level, pick two perpendicular directions to test for horizontality. 2. Position the ring in the center of the FT by inserting a peg/ pin in the central hole. 3. Tie the desired number of strings to the ring. Clamp pulleys at the desired angular positions at the edge of the FT. For use by the physics department, Ohlone College, Fremont, CA. Figure 1: Experimental Setup 4. Run the strings over the pulleys and attach the weight hangers. Place the desired weights in the hangers. We have not yet studied this, but the pull (tension) on each string is a vector, with the magnitude of the vector proportional to the mass (hanger + slotted mass), and direction along the string. 5. Make sure that the strings are stretched and radial. Use a ruler to check that the strings would extend to pass through the center of the ring. You might have to slide the string knots on the ring to make the strings radial. Also, make sure the strings and the pulley pointer are lined up. Check the alignment often throughout the experiment. 6. Make sure that the strings are taut and do not touch the FT and are parallel to it, and that the masses hang freely and do not rest the lab table or oor, etc. 10. 11. Treat the total mass (hanger plus slotted mass) in gmms to represent the magnitude of the vector in arbitrary units. For example, a total mass of 200 g represents a vector of magnitude 200 units. . Pick a set of coordinate axis. For instance, E-aXiS at 20 and then, yaxis at 90 +200 2 110. . For each case suggested in the next Section or a slight variation of your choice, compute the 3:, 3; components of each vector. Pay attention to the signs. Then, compute the vector sum (resultant) in component form. Finet : 2 F: Fnet,m : Z FEB: FREE?! : 2 Ray Then, convert ne, to magnitudeangle form. Now, construct a balancing vector that is antiparallel (180 opposite) to the computed resultant by a new string, pulley, hanger and slotted mass arrangement. Absent any experimental errors, what would you expect? Adjust the angle and magnitude slightly For use by the physics department, Ohlone College, Fremont, CA. 12. till you achieve exact balancethe ring achieves equilibrium and rests with its center aligned with the center of the FT. Remove the pin/ peg or make sure that the ring does not touch the pin / peg. Because of the pulley friction, there is a (small) range of masses and angles that will achieve equilibrium, instead of a theoretically unique vector. As a result the ring remains at rest when released from slightly different offcenter positions. After completing each experimental case, weight each mass and each hanger and record these measured values in the data table. Use these values in all your calculations instead of the printed values. Record the components and, the magnitude and angle of the calculated resultant in the data table. Also, record the magnitude and angle of the experimental vector in the data table. Experimental data, calculations and analysis 5. 1 Experimental data Table 1 lists various vector addition cases to experiment With. Note: the angles specied are measures counter clockwise form the Litaxis. Table 1: Data Fable Theory Fmt Case Vectors Experim. Fm; % Error F1 2 2009, 91 = 20 F2 2 1509, 92 = 80 F1 : 2009, 61 : 30 F2 2 3509, 92 2 120 F = 300 ,9 250 1:; = 4103, 9; = 160 F3 : 2309, 93 : 240 F4 2 3509, 94 2 270 5.2 Calculations 1. For each case, draw a Figure that shows all vectors, with magnitude and angles labeled. 2. Show all your calculations: components of individual vectors, the components and magnitude-angle of the resultant, etc. 3. When calculating the angle, be careful in interpreting the answer from your calculator, and then correctly identify the quadrant in Which the resultant lies. 4. Box key quantities. For use by the physics department, Ohlone College, Fremont, CA. 5 . 3 Error analysis 1. Calculate the percentage error between theoretical and experimental values: Fne em _ Fne cor 6Fnet : t' 1" W 1' x 100 Fnet,theory 66 : Hemp _ etheory X 100 9theory 2. Record the computed errors in the table. 3. Discuss possible sources of error. 4. How did you estimate the experimental uncertainty in the value of the magnitude and angle of the resultant force? What was the uncertainty? 6 Conclusion Briey summarize your ndings