Lab 11: Equilibrium of a body with torque For this lab we will be constructing a system to measure how torque will affect the balance of a balanced stick. For this lab we will need some materials to set up and a ruler will work best as a stick to balance because it has measurements directly on it, but other items can be used to balance like a coat hangeL We want to set up 5 different scenarios where we use the paper as weights and hang them on the ruler at different distances from the center to measure the torque. Constructing the experiment at home. 1. Collect the materials a. 6 pieces of paper b. String 0. Pin or hoid puncher d. Ruler/meter stick, or straight stick Figure 1: All the materials 2. Tie a piece of string around the center of mass of the ruler and hang it so that it is balanced and level Figure 2: Here the ruler is balanced and the string is being held on top of a desk with a physics textbook (It's more useful than you probably give it credit for!) " ' - .. 'W/ztw' . _..._ .. (a 3. Attached the string to the paper. In order to have different masses we will use 1 sheet of paper tied to a string as mass '1, 2 pieces of paper as mass 2, and 3 pieces of paper as mass 3. a. Make sure to cut the string into equal lengths so their masses will be the same and do not affect the torque measurement. Figure 3: The string has been tied to a single sheet of paper and a loop (large enough to slide the ruler into) has been tied on the other end of the string. 4. Use the paper as weights and place them at different distances on the ruler and try to get them to balance out. Figure 4: Here the number of sheets of paper is labeled in marker to make it easier to distinguish in the picture. We see that the center of mass of the ruler is approximately at 6 inches. Mass 1 is around 5 inches away from the center, mass 2 is 1 inch away, and mass 3 is about 2.25 inches away from the center. Here we see that the torque on the left side of the ruler (positive, counterclockwise) is equal to the torque on the tight side of the ruler (negative, clockwise). Collecting Data Part 1: After you have constructed the lab, you will go through a few trials of finding the equilibrium position of the ruler. M1 distance (cm) M2 distance (cm) M3 Distance (cm The goal is for you to use trial and error to nd the equilibrium distance that is left blank for each of the 5 trials. Then calculate the torque on the left side of the ruler (counterclockwise, positive) and see if it is equal in magnitude and opposite in sign to the torque on the right side of the ruler (clockwise, negative) Part 2: Now that you have tried 5 different scenarios, nd 2 completely new scenarios where you decide where the first two masses go, calculator where the third mass goes and test to see if you were right. Make sure to include pictures of your 2 original scenarios. Quick refresher on calculating torgue 1: = r x F (1) When we see the cross product we know that we have to use the sine of the angle between the moment art (the ruler in this cass) and the direction we are applying the force (the force the paper is applying on the ruler) t= ||r||*llF||*Sin 9 (2) In this case we know that the force applied from the paper is perpendicular to the ruler, which means they are at a 90 degree angle, and the sine of 90 degrees equals 1. After you calculate the torques please calculate the percent difference between the counterclockwise torque and the clockwise torque to include in the analysis of your report