! Equlpmen! Force table Ruler Strings Weight hangers Assorted weights Bubble level 4 Experimental Setup Given two force vectors you will determine the third force that will produce equilibrium in the system. This third force is known as the equilibrant and it will be equal and opposite to the resultant of the two known forces. You will use a force table as shown in Figure 8. and work with force vectors. The force table is a circular platform mounted on a tripod stand. The three legs of the tripod have adjustable screws that can be used to level the circular platform. The circular platform has angle markings, in degrees, on its surface. Two or more pulleys can be clamped at any location along the edge of the platform. In this lab we will use three pulleys. Three strings are attached to a central ring and then each string is passed over a pulley. Masses are added to the other end of the strings. The hanging masses will produce a tension force in each string. The masses are directly proportional to the gravitational force. The tension force in each string is equal to the gravitational force. For example, doubling the mass doubles the force. etc. When the forces are balanced. the ring will be positioned at the exact center of the table. When the forces are not balanced, the ring will rest against one side of the central post. (Note: The force due to each hanging mass will be mg where g is the acceleration due to gravity.) To U1 Figure 9: The force table with axes make it easier to read the angles, assume the x-axis to be from the 180 degree mark to the 0 degree mark, with 0 degrees being the positive x direction, and the y-axis to be from the 270 degree mark to the 90 degree mark with 90 degrees being the positive y direction. See Figure 9. 5 Procedure: Finding the equilibrant of two known forces 0 Use the bubble level to check if the circular platform is horizontal. Use the leveling screws, if necessary, to make the necessary adjustments. 0 You are given two 150 g masses that are to be placed at 60 degrees and 300 degrees 0 Remember that the weight. hangers have a mass of 50 g each and this needs to be included as part of the hanging mass. You will determine the magnitude (in newtons) and angle of the third force needed to balance the forces due to these two masses. 0 Represent these forces as vectors on a diagram on a clean sheet of paper. Be sure to include the axes. a Each vector in the diagram should be drawn so that the larger the vector the bigger the force it represents 0 Calculate the x and y components (to the nearest thousandth of a Newton) and write these numbers down. 0 Find the x and y components of the resultant of the two vectors. 0 Now calculate the x and y components of the equilibrant of these two vectors. 0 Calculate the magnitude and angle of the equilibrant. These are the calculated value of the third force. 0 Add this vector to your diagram to represent. the third force. 0 Position the third string at the angle you determined for the equilibrant and hang the mass (includ ing the hanger mass) corresponding to the calculated third force to represent the third force. Make adjustments (if needed) to the mass and the angle until the ring is at the center. Record this value. 0 You will do the above procedure in groups with your TA several times for dierent combinations of angles and masses. Each (large) group should do this at least 3 times. 6 Data analysis Compare the calculated and experimental values for the third force by computing the percent difference between the two values. Do this for the angle and magnitude of the third, for each of the iterations of the force table. Include your diagrams with axes and vectors drawn to scale in your lab report. 7 Discussion Discuss what. could have caused the differences between the calculated and experimentally measured values in the previous section. 2 Objective The objective of this experiment is to find the equilibrant of one or more known forces using a force table and compare the results to that obtained by analytical method. 4 Central Pulleys ring Hanging masses Leveling screws Figure 8: The force table