\fGENERAL PHYSICS 1 Vector Addition/First Condition for Equilibrium Experiment 1 (FORCE TABLE) I. Introduction In this experiment, the force table is used to determine the resultant of two forces by measuring the equilibrant directly. The resultant is the vector sum of all forces and is equal in magnitude and opposite in direction to the equilibrant of that system of forces. This experiment will compare the analytical method and the graphical method. II. Apparatus 1. Force table 2. Pulleys 3. Clamps 4. Mass hangers 5. Mass set 6. Strings III. Procedure 1. Set up the force table and make sure that it is horizontal. 2. Hang a 65 g mass at the end of a string and align it at angle zero. Measure the mass of the hanger and add it to the 65 g mass. 3. Hang a 40 g mass from another string and align it at angle 120 degrees. 4. Again, measure the mass of the hanger and add it to the 40 g mass. 5. By trial and error, find the angle for the third pulley and the mass that needs to be suspended from it to balance the two other forces. 6. The forces are balanced when the ring is centered. 7. Toggle the ring slightly to one side and let it go. The system is in equilibrium if the ring returns to the center. 8. Record the magnitude and the angle of the equilibrant and that of the two other forces. 9. The resultant force is equal to the magnitude of the equilibrant but opposite in direction. 10. Compare the magnitude and direction of the resultant vector using the graphical method and analytical method. IV. Calculations A. Graphical Method 1. Adopt an appropriate scale to represent forces. Indicate this scale on the graphing paper. 2. Draw and add the corresponding vectors using the scale and the angle used in the force table.3. On a graphing paper, draw the magnitudes and directions using a ruler and protractor. 4. Determine the resultant vectors magnitude and direction. B. Analytical Method 1. Using components, calculate the resultant of the following forces: A = 65 g + mass of hanger; 0 B = 40 g + mass of hanger; 120 2. Calculate the magnitude and direction of the resultant vector R. V. Analysis Result of Graphical Method Magnitude of Resultant Direction of Resultant