Lab Balancing Act

Lab: Balancing Act PURPOSE In this experiment we will investigate the balancing of torques with regards to rotational equilibrium. THEORY A force’s tendency to produce the rotation of a rigid body is called the torque. It is equal to the product of the force and the moment arm, the perpendicular distance from the axis of rotation to the force’s line of action. This situation is illustrated below: The “fulcrum” of the seesaw is at the point of support. In this case it is located at the center of rotation. The 20 kg mass to the left is producing a torque that is trying to rotate the seesaw in a counter-clockwise direction. By the right hand rule, this is a positive torque. The 10 kg mass to the right is producing a torque that is trying to rotate the seesaw in a clockwise direction. This is a negative torque. The magnitude of the torque in either case is equal to the weight of the mass (m*g) times its moment arm (distance to the fulcrum, d). Hence these torque magnitudes are: τ left = F⋅ d τ (mg⋅ )d = (20 )(9.8 )() 1 right = F⋅ d = (mg⋅ )d = (10 )(9.8)() 2 = 196Nm = 196Nm In this case, the seesaw balances because the magnitudes of these torques are equal. Note that the normal force N is at the axis of rotation—hence this force has no moment arm and produces Page 1 no torque about that axis! In this example, the weight W of the seesaw is also acting at the axis of rotation and has no moment arm. (Note: This latter observation will be true only if the seesaw is balanced at its center of gravity! In this experiment we will only consider this case!) We already know that for translational equilibrium to exist, we must have no net force on a rigid body. For rotational equilibrium to exist—i.e. no rotation occurs--it must be true that the torques are equal in magnitude (but opposite in direction). Hence, we have no net torque. At rotational equilibrium, it should be true that: τ net =∑τ =τ left −τ right = 0 axis OBJECTIVES In this experiment, you will • 1. Investigate moment arms, torques and rotational equilibrium. • 2. Use torque equilibrium to solve for 8 unknown masses. • 3. Improve one’s torque equilibrium skills by mastering a “phun” game. SETUP Load the “Balancing Act” simulation by either clicking on the above link, or by clicking on the red JAVA file in the lab folder in Blackboard. Make the following selections: a. b. c. d. select “Mass Labels” select “Rulers” select “Forces from Objects” select “Level” Your initial screen should look like below: PART I: INITIAL INVESTIGATIONS Play around with the seesaw simulation. In all cases here, the moment arm will be the pure distance from the pivot (fulcrum) to the applied weight force. So to balance, the sum of the forces times moment arms on one side, should equal the sum of the forces times moment arms on the other side. 2. Try equal mass vs. equal mass, i.e. balance 5kg vs. 5 kg. Click “Remove the Supports” . See what happens when you vary the moment arm on either side of the fulcrum. You should find that, in order to balance, the moment arm distance must be the same on both sides of the fulcrum. 3. Now put 5kg on the left side, and 10 kg on the right side. Click “Remove the Supports” . Move the masses around until the seesaw balances. How does the moment arm for the 5 kg mass relate to the moment arm for the 10 kg mass? In order to balance, the 10 kg mass has to be closer to the fulcrum than the 5 kg mass. 4. Determine where the floating trashcan should be placed to ensure all objects are in equilibrium. 1.5 m on the right side 5. Determine where the floating trashcan should be placed to ensure all objects are in equilibrium. 0.25 m on the right side 6. Determine where the floating trashcan should be placed to ensure all objects are in equilibrium. 0.75 m on the left side Page 3 PART II: BALANCE LAB 1. Select the “Balance Lab” ! tab. Again select all of the “Show” boxes. Your initial screen should look like: 2. Place a 20 kg mass at the 2 meter position all the way on the left. Now add as many 5 kg masses as you need on the right side to make the seesaw balance. How many 5 kg masses did you need, and at what positions did you place them? Six 5 kg masses were placed on the right side of the seesaw, for a total of 30 kg. They were placed at 2, 1.75, 1.5, 1.25, 1, and 0.5 meters. Number of 5 kg masses needed to balance = 6 Positions of the 5 kg masses = 2.00 1.75 1.50 1.25 1.50 0.50 3. Keep the 20 kg mass at the left 2-meter position. Now fill all of the right side positions with 5 kg masses: 4. Decide where on the left side you need to put a 10kg mass in order to balance this configuration. Put the 10 kg mass there. Remove the supports. Did it balance? 0.50 meters, yes Page 4 5. If it didn’t balance, move the 10 kg mass to a new position until the seesaw balances. Calculate the magnitude of the torque (force times moment arm) on each side of the seesaw. Left side total torque = 441 Nm Right side total torque = 441 Nm 6. How do these two torque values compare? They are of equal values. 7. Click the right arrow to investigate new objects to balance. Stop when you get to “People 1.” On the left side of the seesaw, place the man at the 1.5-meter position, and place the boy at the 0.75-meter position. 8. Now click the right arrow ! again to get to “People 2.” Position the woman and the girl on the right-hand side of the seesaw in such a way as to make the seesaw balance. 9. Write your positions for the woman and the girl here: Position of the woman = 1.75 m Position of the girl = 1.00 m Page 5 PART III: FIND THE MYSTERY OBJECTS 1. Under “Balance Lab” ! , select Reset All . Select all of the “Show” boxes again. Click the right arrow ! to investigate new objects to balance. Stop when you get to “Mystery Objects 1.”Pull out object “A” and place it on the right-hand side of the seesaw. Now click the left arrow ! to go back to “Bricks.” Mystery Objects Left Side Object Left-Side Mass (Brick) Left Moment Arm Left-Side MassTorque (M*d) Right Side (Mystery Object) Right Moment Arm Right-Side Mass A 15 2.0 30 1.5 20 B 10 0.75 7.5 1.5 5 C 10 0.75 7.5 0.5 15 D 10 0.75 7.5 0.75 10 E 10 0.25 2.5 1.0 2.5 F 15 1.75 26.25 0.5 52.5 G 15 1.25 18.75 0.75 25 H 10 0.75 7.5 1.0 7.5 Page 6 2. Choose a brick and position it on the left-hand side to balance the see-saw against the mystery object “A.” Write down the mass you used, its moment arm, and the left side “masstorque,” which is the mass times the moment arm. (Normally we would use force as weight, but the acceleration of gravity g will be the same for both sides—so we cancel it out). 3. Since the seesaw balances, the right-side “mass-torque” is the same in magnitude. So divide the left-side “mass-torque” by the right-side moment arm to get the value of the mass for mystery object “A.” 4. Repeat steps 1 through 3 for all of the Mystery Objects “B” through “H.” Fill out the table.! Page 7 PART IV: THE GAME 1. This section is worth 3 of your lab points…plus. Click on the “Game” tab. You should see the following screen: 2. Each game has a maximum point score of 12 points. The level you select will be a multiplier for your final score. In other words, your final score for this section will be computed as the following: core = Level ( ⋅ )(Po ints ÷) 10 3. For example, if you scored 10 points on Level 3, your final score would be 3. However if you scored 12 points on Level 4 (the maximum possible!), your final score would be 4.8. So you can actually make an “extra credit” of 1.8 points on this section. 4. You may play this game as often as you like, but your final time for any particular game must be 3 minutes or less. When you are finished, record your final score and time here: score = time = 4.8 2:00 Page 8 5. Do a “screen save” of your final tally and paste it here: QUESTIONS 1. What two conditions are needed to establish equilibrium for a rigid body? The moment arm and the mass of the objects. 2. Why isn’t the normal force “N” considered when balancing the torques on the seesaw? Normal force isn’t considered because gravity is the same on both sides of the seesaw so it cancels out. Page 9 CONCLUSION Write a conclusion summarizing the results of this experiment. Be sure to 1. Restate the purpose, 2. State the main data values that pertain to the purpose, 3. State the % error on these main data values (if applicable), and 4. State at least three sources of error in the experiment. The purpose of this lab was to identify the relationship between moment arms, torques, mass, and how to find the unknowns for moment arms, and mass. In part I, initial investigations, the relationship between different masses and their moment arms were observed by placing different masses at different moment arms and observing what happened to the seesaw. In part II, balance lab, different amounts of mass were tested for balance at different moment arms. In part III, find the mystery objects, unknown masses were identified by calculating the torque of the opposing side. In part IV, the game, calculating torque, moment arms, and masses were summarized. Overall, there was little error throughout the course of the experiment. There were some errors in identifying the unknown masses in part III but they were solved by continuing the calculation process. Page 10