11: Torque & Equilibrium Lab Objective To understand torque and rotational equilibrium. Materials · Meter stick • Support stand • Center clamp 3 clamps with mass hooks Hanging mass set Lab balance Procedure 1. Using the lab balance, measure the mass of the meter stick without any clamps attached and the mass of one of the clamps with a hook. Do not measure the mass of the center clamp. Record the values in Data Table 1. 2. Place the center clamp on the meter stick and clamp it so that it is located close the to center of gravity of the meter stick. Place the meter stick on the support stand using the side protrusions of the clamp. You will be balancing the meter stick several times in this lab. Balancing will be much easier if the clamp is upside-down. 3. Determine the center of gravity of the meter stick by adjusting the location of the clamp until the stick is balanced. Record the value of the center of gravity in Data Table 2. Experiment 1: With the meter stick balanced, place 300 g on a hooked clamp and slide the clamp to the 40 cm mark. Using trial and error, place a 100 g mass on another clamp and find where it should be located to balance the system. Record its location in Experiment 1 Data Table. Experiment 2: Remove the masses above and replace them with 200 g at the 10 cm mark, and 500 g at the 70 cm mark. Determine where a 100 g mass should be located to balance the system. Record its location in Experiment 2 Data Table. Data Experiment 3: Remove the masses used in the step above. Place the center clamp at the 30 cm mark. Add a 200 g mass on the meter stick and determine where it should be placed to balance the system. Record its location in Experiment 3 Data Table. Experiment 4: Remove the masses used in the step above. Keep the center clamp at the 30 cm mark. Add a 300 g mass at the 40 cm mark, and determine where a 500 g mass must be placed to balance the system. Record that value in Experiment 4 Data Table. Data Table 1 Object Mass Meter stick 101.49 Clamp 19.99 Data Table 2 Meter Stick Center of Gravity 50cm Experiment 1 Data Table Mass Mass of clamp (g) Total Mass (kg) Location 300 g 100 g 23.39 23. 0.3233kg 0.1233k 40 cm 76.5cm Experiment 2 Data Table Mass Mass of clamp (g) Total Mass (kg) Location 200 g 23.3 0.2233k 10 cm 500 g 23.79 0.5233g 70 cm 100 g 23.3 0.1233 36cm Experiment 3 Data Table Mass Mass of clamp (g) Total Mass (kg) Location 200 g 23.3 0.2233g 20.6cm 56 Experiment 4 Data Table Mass of clamp (g) Total Mass (kg) Location Mass 300 g 23.3g 23.3g 500 g 0.3233 0.5233 40 cm 19.8en Calculations For useful formulas, see Appendix A. 1. For each of the data tables above, insert the mass of the clamp and calculate the total mass of the hanging mass plus clamp in kilograms. 2. For each mass, calculate the lever arm as the distance of the weight from the point of rotation. Record the value in meters in the Calculation tables below. Experiment 1: (Determination of the 100 g lever arm) a. Calculate the experimental lever arm by finding the distance of the 100 g mass from the axis of rotation as found in your experiment. b. Calculate the theoretical lever arm by performing a sum of torques equation. All weights on one side of the axis of rotation are clockwise torques, and all weights on the opposite side of the axis are counterclockwise torques. The sum of all torques should be zero. For this case, consider the lever arm of the 100 g mass as the unknown. Write the sum of torques equation and show your work in the space provided. Note: Remember to include the mass of the clamp when necessary and use weights in your calculation (not masses). c. Calculate the percent error between the experimentally determined lever arm and your calculated value. Experiment 2: (Determination of the 100 g lever arm) a. Calculate the experimental lever arm by finding the distance of the 100 g mass from the axis of rotation as found in your experiment. b. Calculate the theoretical lever arm by performing a sum of torques equation. All weights on one side of the axis of rotation are clockwise torques, and all weights on the opposite side of the axis are counterclockwise torques. The sum of all torques should be zero. For this case, consider the lever arm of the 100 g mass as the unknown. Write the sum of torques equation and show your work in the space provided. Note: Remember to include the mass of the clamp when necessary and use weights in your calculation (not masses). c. Calculate the percent error between the experimentally determined lever arm and your calculated value. Note: Remember to include the mass of the clamp when necessary and use weights in your calculation (not masses). Experiment 3: (Determination of the 200 g lever arm) a. Calculate the experimental lever arm by finding the distance of the 200 g mass from the axis of rotation as found in your experiment. b. Calculate the theoretical lever arm by performing a sum of torques equation. In this case, remember to consider the weight of the meter stick. We can consider the weight to be concentrated at the center of mass. c. Calculate the percent error between the experimentally determined lever arm and your calculated value. Experiment 4: (Determination of the 500 g lever arm) a. Calculate the experimental lever arm by finding the distance of the 500 g mass from the axis of rotation as found in your experiment. b. Calculate the theoretical lever arm by performing a sum of torques equation. Again, remember to consider the weight of the meter stick. c. Calculate the percent error between the experimentally determined lever arm and your calculated value. .50m J Experiment 1 Calculation Table Sum of Torques Equation M₂-01233 que (2) Force & lever an (2018-03 X=0.262206002 >=(+1) Text = T-Ty=0 (0.3233)()() 42-(424) = 0.316824-1.20834X Peams of 7626-74.5 725 Experiment 2 Calculation Table M=0.227 626 Mas 0.5233 P100% P-1.065373772 Theoretical Lever Arm Experimental Lever Arm Percent Error 0.262206002 0.265- -1.065873779 Sum of Torques Equation Tag (7) = For Lon The T-T-40 y= 0.1233 Tu migh-h (82) (2) - (0.12.13)(+0)x Top (0.875306)-(0)-(1.2034)x Per E (0,1244 (2)-(&) ( 0.2014) (0.878336-|-(1-025668) Row X=-0.124412 002m. Theoretical Lever Arm Experimental Lever Arm 0.124412003 0.1400 Percent Error 12.5293353% 59 09 60 Experiment 3 Calculation Table M₁-0.2221 -9300- 40206 0.078 Experiment 4 Calculation Table Sum of Torques Equation Theoretical Lever Arm Experimental Lever Arm Percent Error Sum of Torques Equation Theoretical Lever Arm Experimental Lever Arm Percent Error Questions Answer the following post-lab questions. See "Good Lab Practices" on page 1. 1. What are the requirements for an object to be in static equilibrium? ⑦ 2. If an object is in equilibrium, describe its motion. 3. You did not measure the mass of the center clamp. Why is this information not needed to compute the torque values? 4. For the first experiment, determine the force with which the support pushes up. 5. Discuss the accuracy of each experiment using your percent error values. Give reasons for your error. 61