Dear Students, Please study the theoretical pre-lab materials, check the recommended educational website and You Tube videos given below, and try to follow the step-by-step instruction. If you still have any questions regarding this lab, I will also be available by Skype, Zoom.com video conference or email during our regular class time and beyond in order to provide all the necessary assistance and guidance. Please contact me at with any questions, but please keep in mind that it might take me some considerable time to respond, especially if I receive too many of your messages at the same time. 1 Theory Statics is the branch of mechanics that is concerned with the analysis of the physical systems that do not experience an acceleration (a = 0), but rather, are in static equilibrium with their environment. 1.1 Conditions of Equilibrium For an object to be in equilibrium, it must be experiencing no acceleration. This means that both the net force and the net torque on the object must be zero. The second condition necessary to achieve equilibrium involves avoiding accelerated rotation (main- taining a constant angular velocity). A rotating body or system can be in equilibrium if its rate of rotation is constant and remains unchanged by the forces acting on it. Force: Force is the action of one body on another. A force is either a push or a pull, and it tends to move a body in the direction of its action. The action of a force is characterized by its magnitude, by the direction of its action, and by its point of application. Torque: In addition to the tendency to move a body in the direction of its application, a force can also tend to rotate a body about an axis. The axis may be any line which neither intersects nor is parallel to the line of action of the force. This rotational tendency is known as torque which is also referred as moment of force. The magnitude of the torque at a point O is equal to the perpendicular distance from O to the line of action of F, multiplied by the magnitude of the force: T = Fd, where F is the applied force and d is the perpendicular distance from the axis to the line of action of the force. This perpendicular distance is called the moment arm, as shown in Fig. 1 d F Figure 1: Calculating the torque of a given force F. For the case of a balanced ruler (or a seesaw) in the vicinity to its horizontal equilibrium position, such as we see at Fig. 2, each torque due to the gravity force acting on each weight is calculated asDear Students, Please study the theoretical pre-lab materials, check the recommended educational website and You Tube videos given below, and try to follow the step-by-step instruction. If you still have any questions regarding this lab, I will also be available by Skype, Zoom.com video conference or email during our regular class time and beyond in order to provide all the necessary assistance and guidance. Please contact me at with any questions, but please keep in mind that it might take me some considerable time to respond, especially if I receive too many of your messages at the same time. 1 Theory Statics is the branch of mechanics that is concerned with the analysis of the physical systems that do not experience an acceleration (a = 0), but rather, are in static equilibrium with their environment. 1.1 Conditions of Equilibrium For an object to be in equilibrium, it must be experiencing no acceleration. This means that both the net force and the net torque on the object must be zero. The second condition necessary to achieve equilibrium involves avoiding accelerated rotation (main- taining a constant angular velocity). A rotating body or system can be in equilibrium if its rate of rotation is constant and remains unchanged by the forces acting on it. Force: Force is the action of one body on another. A force is either a push or a pull, and it tends to move a body in the direction of its action. The action of a force is characterized by its magnitude, by the direction of its action, and by its point of application. Torque: In addition to the tendency to move a body in the direction of its application, a force can also tend to rotate a body about an axis. The axis may be any line which neither intersects nor is parallel to the line of action of the force. This rotational tendency is known as torque which is also referred as moment of force. The magnitude of the torque at a point O is equal to the perpendicular distance from O to the line of action of F, multiplied by the magnitude of the force: T = Fd, where F is the applied force and d is the perpendicular distance from the axis to the line of action of the force. This perpendicular distance is called the moment arm, as shown in Fig. 1 d F Figure 1: Calculating the torque of a given force F. For the case of a balanced ruler (or a seesaw) in the vicinity to its horizontal equilibrium position, such as we see at Fig. 2, each torque due to the gravity force acting on each weight is calculated asTmg = Force x distance = mgr, (1) where r is the distance from the pivot to the point where the mass m is attached. Figure 2: A seesaw in balance equilibrium. When an object is balanced on a pivot the turning effect of the forces on one side of the pivot must balance the turning effect of the forces on the other side as shown in Fig. 3 +Distance 1 -4 Distance 2 Force 1 Force 2 Figure 3: Balancing a ruler on a pivot with two weights attached to its sides. In summary, when an object is balanced in equilibrium the sum of the clockwise torques from the weight located to the right of the pivot is equal to the sum of the anticlockwise moments from the weights hanging on the left side of the ruler. Ta = Tad , (2) Td = M1, right g d1, right + M2, right g d2, right + m3, right g d3, right + ..., Tad = mi, left g d1, left + ma, left g d2, left + M3, left g d3, left + ..., or, after simplification, the equilibrium equation is obtained as M1, right d1, right + M2, right d2, right + ... = mi, left d1, left + m2, left d2, left + ... (3)Tmg = Force x distance = mgr, (1) where r is the distance from the pivot to the point where the mass m is attached. Figure 2: A seesaw in balance equilibrium. When an object is balanced on a pivot the turning effect of the forces on one side of the pivot must balance the turning effect of the forces on the other side as shown in Fig. 3 +Distance 1 -4 Distance 2 Force 1 Force 2 Figure 3: Balancing a ruler on a pivot with two weights attached to its sides. In summary, when an object is balanced in equilibrium the sum of the clockwise torques from the weight located to the right of the pivot is equal to the sum of the anticlockwise moments from the weights hanging on the left side of the ruler. Ta = Tad , (2) Td = M1, right g d1, right + M2, right g d2, right + m3, right g d3, right + ..., Tad = mi, left g d1, left + ma, left g d2, left + M3, left g d3, left + ..., or, after simplification, the equilibrium equation is obtained as M1, right d1, right + M2, right d2, right + ... = mi, left d1, left + m2, left d2, left + ... (3). d. d2 d3 Figure 4: Balancing a ruler on a pivot with several weights attached to its sides. There could be only one force on each side of the pivot, as we see in Fig. 3, or a few, as shown in Fig. 4. 2 Useful resources 2.1 Educational websites . http://www. schoolphysics. co. uk/age11-14/Mechanics/Statics/text/Balancing_/index . html . https://courses . lumenlearning. com/boundless-physics/chapter/conditions-for-equilibrium . https://en . wikipedia. org/wiki/Statics#cite_note-6 2.2 YouTube videos . https://www. youtube. com/watch?v=jg4e8W44_E4 . https://www. youtube. com/watch?v=xM_oklMF7uI . https://www. youtube. com/watch?v=0BIgFKVnlBU and many-many others available online. 3 Procedure 1. Open our present online lab by clicking on the following link: https://phet . colorado . edu/en/simulation/balancing-act 2. Select Balance Lab window at the center of your initial menu screen. 3.1 Two or more known masses As the first part of this experiment, we are going to test the location of an additional known mass which would bring the whole system to equilibrium. 3. Place two masses - m1 = 15 kg 15k and m2 = 10 kg 10 kg in the positions shown at Fig. 5. d. d2 d3 Figure 4: Balancing a ruler on a pivot with several weights attached to its sides. There could be only one force on each side of the pivot, as we see in Fig. 3, or a few, as shown in Fig. 4. 2 Useful resources 2.1 Educational websites . http://www. schoolphysics. co. uk/age11-14/Mechanics/Statics/text/Balancing_/index . html . https://courses . lumenlearning. com/boundless-physics/chapter/conditions-for-equilibrium . https://en . wikipedia. org/wiki/Statics#cite_note-6 2.2 YouTube videos . https://www. youtube. com/watch?v=jg4e8W44_E4 . https://www. youtube. com/watch?v=xM_oklMF7uI . https://www. youtube. com/watch?v=0BIgFKVnlBU and many-many others available online. 3 Procedure 1. Open our present online lab by clicking on the following link: https://phet . colorado . edu/en/simulation/balancing-act 2. Select Balance Lab window at the center of your initial menu screen. 3.1 Two or more known masses As the first part of this experiment, we are going to test the location of an additional known mass which would bring the whole system to equilibrium. 3. Place two masses - m1 = 15 kg 15k and m2 = 10 kg 10 kg in the positions shown at Fig. 5Show Mass Labels Forces from Objects Level Position None OR Marks Bricks 5 kg 15 10 kg 10 15 Kg 20 kg INTO Balancing Act PhET. = Figure 5: Schematics for Step 3. 4. Using Eq. (3), calculate the position of the third unknown mass m3 = 20 kg which would keep the whole plank in stable equilibrium. On which side of the ruler should mass m3 be positioned? 5. Add mass m3 = 20 kg to the position which you obtained in the previous Step 4 and verify your theoretical result. Remove the support In and check whether the level signs turn green (the equilibrium is achieved). 6. For the same experimental arrangement, as presented at Fig.5, can you achieve the equilibrium with the additional mass m3 = m1 = 15 kg? 7. Repeat the exercise with the people with larger masses . For a couple with the masses mdad = 80 kg and mmom = 60kg(see Fig. 6) find the position of a child with mass mboy = 20 kg which leads to the equilibrium. As we normally do, please calculate the position of the boy first using the balance equation (3) and then verify your findings experimentally? Can you solve this problem putting the boy on the other side of the ruler? Is it possible that the father with the largest mass maad = 80 kg could be seated further from the pivot than any other family member?Show Mass Labels Forces from Objects Level Position None OR Marks Bricks 5 kg 15 10 kg 10 15 Kg 20 kg INTO Balancing Act PhET. = Figure 5: Schematics for Step 3. 4. Using Eq. (3), calculate the position of the third unknown mass m3 = 20 kg which would keep the whole plank in stable equilibrium. On which side of the ruler should mass m3 be positioned? 5. Add mass m3 = 20 kg to the position which you obtained in the previous Step 4 and verify your theoretical result. Remove the support In and check whether the level signs turn green (the equilibrium is achieved). 6. For the same experimental arrangement, as presented at Fig.5, can you achieve the equilibrium with the additional mass m3 = m1 = 15 kg? 7. Repeat the exercise with the people with larger masses . For a couple with the masses mdad = 80 kg and mmom = 60kg(see Fig. 6) find the position of a child with mass mboy = 20 kg which leads to the equilibrium. As we normally do, please calculate the position of the boy first using the balance equation (3) and then verify your findings experimentally? Can you solve this problem putting the boy on the other side of the ruler? Is it possible that the father with the largest mass maad = 80 kg could be seated further from the pivot than any other family member?Show Mass Labels Forces from Objects Level Position None O Rulers Marks 60 kg 80 kg People D 30 kg 9 60 kg A Balancing Act PhET = Figure 6: Schematics for Step 7. 3.2 Finding one unknown "mystery" mass In this part of our experiment, we will need to find an unknown mass based on its equilibrium position. 8. Place any " mystery mass" me-? o at x = 1.25m on the right side of the ruler, as shown at Fig. 7. Show Mass Labels Forces from Objects Level Position ONone Rulers Marks Bricks 5 kg 10 kg 2 275 1.9 125 1 0.75 0.5 025 2 25 0.5 0.75 1 15 kg 20 kg Meters Meters Balancing Act PHET = Figure 7: Schematics for Step 8. 9. Take one or a few known masses and place then on the left side of the plank. Remove the support and find the position for your known masses which would bring the system into equilibrium. Using the balance equation (3), find the unknown mass mr.Show Mass Labels Forces from Objects Level Position None O Rulers Marks 60 kg 80 kg People D 30 kg 9 60 kg A Balancing Act PhET = Figure 6: Schematics for Step 7. 3.2 Finding one unknown "mystery" mass In this part of our experiment, we will need to find an unknown mass based on its equilibrium position. 8. Place any " mystery mass" me-? o at x = 1.25m on the right side of the ruler, as shown at Fig. 7. Show Mass Labels Forces from Objects Level Position ONone Rulers Marks Bricks 5 kg 10 kg 2 275 1.9 125 1 0.75 0.5 025 2 25 0.5 0.75 1 15 kg 20 kg Meters Meters Balancing Act PHET = Figure 7: Schematics for Step 8. 9. Take one or a few known masses and place then on the left side of the plank. Remove the support and find the position for your known masses which would bring the system into equilibrium. Using the balance equation (3), find the unknown mass mr.10. Remove the previously used known masses from the plank and replace them with another non- equivalent set of bricks (one or a few, you can use some of them again). Find the new equilibrium position of the system and verify the value of unknown mass m, which you found in the previous Step 9. Are the two results the same, close to each other or completely different? 4 Lab Report I am not going to demand any specific format or presentation style of your lab reports. This is completely up to you: you can type it in MS Word, Latex, online Google documents, you can just scan the handwritten notes or even take the pictures on your phone. However, it is crucial that you: 1. Do and properly explain all Steps which are printed in bold font in the Procedure section. Each such Step or a task (printed in Bold in you manual) should be properly addressed in your lab report in all detail. 2. Provide sample calculations which include all the equations, numbers and units for every calculation which you have performed for your lab experiment. Sample calculations means that you don't need to repeat it in all detail if the same calculation is performed multiple times, such as filling a table for different values of a parameter. However, you will still need to do the calculation each time and put in the results into the table. 3. Conclusions, or main physics learning points from this experiment. Here, you should briefly discuss which laws of physics you have learned and experimentally tested, what kind(s) of phenomena you have dealt with, as well as your calculations and mathematical equations. Is this experiment helpful for your science education in general and why? Discuss the precision of your results and the percent errors, make any other comments you might think of (no one will be penalized for making critical comments regarding our course). This section should not exceed 15 lines. Here, I will specifically value its originality, your own words and thoughts which are not copied from a textbook or someone else's report. Also, there are no specific requirements regarding the size of your lab report and, in fact, you cannot find a professor who wants to receive and grade 30-page reports but all the questions need to be answered completely and in a lot of cases your score depends directly on the amount of relevant and original information which you provide within a specific response. The report should be submitted to Blackboard as an Assignment on or before the posted date or (as an exception, if the Blackboard submission system failed) sent by email to10. Remove the previously used known masses from the plank and replace them with another non- equivalent set of bricks (one or a few, you can use some of them again). Find the new equilibrium position of the system and verify the value of unknown mass m, which you found in the previous Step 9. Are the two results the same, close to each other or completely different? 4 Lab Report I am not going to demand any specific format or presentation style of your lab reports. This is completely up to you: you can type it in MS Word, Latex, online Google documents, you can just scan the handwritten notes or even take the pictures on your phone. However, it is crucial that you: 1. Do and properly explain all Steps which are printed in bold font in the Procedure section. Each such Step or a task (printed in Bold in you manual) should be properly addressed in your lab report in all detail. 2. Provide sample calculations which include all the equations, numbers and units for every calculation which you have performed for your lab experiment. Sample calculations means that you don't need to repeat it in all detail if the same calculation is performed multiple times, such as filling a table for different values of a parameter. However, you will still need to do the calculation each time and put in the results into the table. 3. Conclusions, or main physics learning points from this experiment. Here, you should briefly discuss which laws of physics you have learned and experimentally tested, what kind(s) of phenomena you have dealt with, as well as your calculations and mathematical equations. Is this experiment helpful for your science education in general and why? Discuss the precision of your results and the percent errors, make any other comments you might think of (no one will be penalized for making critical comments regarding our course). This section should not exceed 15 lines. Here, I will specifically value its originality, your own words and thoughts which are not copied from a textbook or someone else's report. Also, there are no specific requirements regarding the size of your lab report and, in fact, you cannot find a professor who wants to receive and grade 30-page reports but all the questions need to be answered completely and in a lot of cases your score depends directly on the amount of relevant and original information which you provide within a specific response. The report should be submitted to Blackboard as an Assignment on or before the posted date or (as an exception, if the Blackboard submission system failed) sent by email to