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NAME: Rotational Motion Objectives • • • Apply the torque concept to explain the position of handle on doors. Apply the torque concept to explain the safest way to lift heavy objects. Apply the center of mass concept to decide if an object’s mass is uniformly distributed within the object’s volume. Equipment • • • • ruler (tape measure) in meters cell phone camera an object (i.e. a bag of flour/sugar, water container) for which you know the mass access to a door Part I. Explaining the Position of Doors’ Handles When one opens a door, a rotational motion takes place – the door rotates about the hinge. In this part of the lab, you will use the concept of torque to determine the optimal position of the handle on a door (i.e. the position of the handle that will make the door easiest to rotate). We learned that Torque = rꓕ * F (1) Part I. Procedure The physical situation depicted in Fig.1 takes place when you open a door. You apply a force at point A and the pivot point is at P. 1. Get access to a door. 2. Measure the door width. This is approximately the lever arm (moment arm) r ꓕ of the torque you exert when you open the door. Record it in Table 1. 3. To a good approximation, the force that you exert when you slowly open the door is about F = 10N. 4. Use the eq (1) to calculate the torque you apply on the door when you open it using its knob. Record it in Table 1. 1 A = The point where the force is applied perpendicular to the door and to rꓕ P = The pivot point Rotation Axis rꓕ 11 1 A P Lever/Moment Arm FIGURE 1 (Picture from https://www.wayfair.com.) Imagine now that the doorknob is not at the usual position, but instead it is in the middle of the door. The new physical situation is depicted in Fig.2. A = The point where the force is applied perpendicular to the door and to rꓕ P = The pivot point Rotation Axis A rꓕ 11 1 P Lever/Moment Arm FIGURE 2 2 5. Work with the same door as before. 6. Calculate the new lever arm (moment arm) of the torque you exert when you open the door using a doorknob placed in the middle of the door. Now rꓕ is about half of the value you measured at point 2. Record it in Table 1. 7. To a good approximation, the force that you exert when you slowly open the door is about F = 10N. 8. Use the eq (1) to calculate the torque you apply on the door when you open it using a doorknob positioned in the middle of the door. Record it in Table 1. Table 1. Determining the Optimal Position for a Doorknob rꓕ (m) F(N) Torque (N*m) when opening the door like in Fig 1 (the traditional way) when opening the door like in Fig 1 (the traditional way) rꓕ (m) F(N) 10 Torque (N*m) when opening the door like in Fig 2 (using a doorknob positioned in the middle of the door) when opening the door like in Fig 2 (using a doorknob positioned in the middle of the door) 10 A larger torque applied to the door makes it easier to open. Based on your calculations, where should the doorknob be positioned on the door to make it easier to open? Why? Push a door according to the two configurations presented above. Try to use the same force. Explain what you experience. When is the door easier to push? 3 Part II. Explaining the Safest Way to Lift Heavy Objects When a person lifts heavy objects is engaged in a rotational motion about the hip joints. In this part of the lab, you will use the concept of torque to determine the optimal way to lift heavy objects (i.e. the way that will hurt the back the least). Part IIa. Lifting Objects while Keeping the Knees Straight Find an object for which you know the mass (i.e. a bag of flour or sugar, a water container, etc.) and place it on the floor. Lift the object without bending your knees like the person from Fig 1. You will calculate the net torque exerted on your hip joints (pivot point at P) when you do the lifting motion. r1 P W1 r2 111 111 W2 Figure 1 111 111 https://twitter.com/HospitalPolaris/status/1077796732862386176/photo/1 W1 = your body weight (in N), assume that it acts in the middle of your chest W2 = the weight of the object you lift (in N), assume that it acts along your arms r1 = lever arm for W1 (m) = the distance between your hip joint and the middle of your chest r2 = lever arm for W2 (m) = the distance between your hip joint and your shoulders 4 Part IIa. Procedure 1. Record your weight W1 in Table 2. 2. Assume that your center of mass is in the middle of your chest. Assume that your pivot point is where your hip joint is. Measure r1 = lever arm for W1 (m) = the distance between your hip joint and the middle of your chest and record it in Table 2. 3. Use eq (1) to calculate the torque exerted by W1 on the hip joints. Record it in Table 2. 4. Record the weight of the object you lift W2 in Table 2. 5. Measure r2 = lever arm for W2 (m) = the distance between your hip joint and your shoulders. Record it in Table 2. 6. Use eq (1) to calculate the torque exerted by W2 on the hip joints. Record it in Table 2. 7. Calculate the net torque exerted on the hip joints. The net torque is the sum of the torque you calculated at points 3 and 6. Record it in Table 2. Table 2. The net torque exerted on your hip joints when you lift objects with your knees straight (like in Fig. 1) W(N) rꓕ(m) Torque (N*m) 1 2 Net Torque on Your Hip Joints Part IIb. Lifting Objects while Keeping the Knees Bent Now bend your knees, keep your back straight, try to bring the object as close to your body as you can and then lift it (like the person from Fig 2). You will calculate the net torque exerted on your hip joints (pivot point at P) when you do the lifting motion. 5 Figure 2 https://myhealth.alberta.ca/ Part IIb. Procedure 1. Record your weight W1 in Table 3. 2. Assume that your center of mass is in the middle of your chest. Assume that your pivot point is where your hip joint is. When you bend your knees, keep your back straight, try to bring the object as close to your body as you can and then lift it, you make r1 (the lever arm for W1) almost zero. This is the value recorded in Table 3. 3. Use eq (1) to calculate the torque exerted by W1 on the hip joints. Record it in Table 3. 4. Record the weight of the object you lift W2 in Table 3. 5. Measure r2 = lever arm for W2 (m) = the distance between your hip joint and the object you lift. Make sure the object is as close to your body as possible. 6. Use eq (1) to calculate the torque exerted by W2 on the hip joints. 7. Calculate the net torque exerted on the hip joints. The net torque is the sum of the torque you calculated at points 3 and 6. Record the net torque in Table 3. Table 3. The net torque exerted on your hip joints when you lift objects with your knees bent (like in Fig. 2) W(N) rꓕ(m) Torque (N*m) 1 0 2 Net Torque on Your Hip Joints 6 Based on your calculations, which way do you think is the safest way to lift heavy objects (i.e. which way creates the smallest torque on your hip joints)? Why? Besides the physical details featured above, when lifting objects, there are also medical details that need to be taken into account. Watch this video to learn how to lift heavy objects https://www.youtube.com/watch?v=_YoOL3HipvA Insert a picture of all your calculations below. (Instructions on how to insert pictures in Word documents are here https://www.youtube.com/watch?v=uL-gEtDkmWY). Part III. Applying the Center of Mass Concept a) Watch this video https://www.youtube.com/watch?v=CNH0lXKqP9I to learn about the most inclined building in the world. Explain why this tower is safe despite its tilted orientation. b) Choose an extended object (e.g. stick, ruler) for which you will determine the position of its center of mass. c) To determine the position of the object’s center of mass, place the object on the top of a chair back support; move the object back and forth until you find a point about which it balances. That is the location of object’s center of mass. d) Measure the distance from the left end of your object to the center of mass that you established. Write it below. CM Position _____________(m) e) Object that have the CM coinciding with their geometrical center have their mass uniformly distributed within their volume. Is the mass of your extended object uniformly distributed? Explain. 7 f) Include a picture of your balanced object below. (Instructions on how to insert pictures in Word documents are here https://www.youtube.com/watch?v=uLgEtDkmWY). A physics teacher won an honorable mention by making a dog a good support point. See what the teacher did and the physics explanation here https://www.aapt.org/Programs/contests/winnersfull.cfm?id=9702&theyear=2019 . What problems done in lectures and homework involve scenarios identical to the one studied in this lab. 8

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