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Title: Equilibrium of Three Forces, Static equilibrium (Sum of forces equal zero)Post by: lookang on March 20, 2009, 03:57:31 pm
Equilibrium of Three Forces
good reference: EJS http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=171.msg782#msg782 http://www.walter-fendt.de/ph14e/equilibrium.htm A simple experiment concerning the equilibrium of three forces is simulated here: Weights are suspended from three tied cords. Two of the cords run over frictionless pulleys. The three forces acting on the knot (coloured arrows) are in equilibrium. You can write forces from 1 N to 10 N into the text fields (don't forget to press the "Enter" key!). Notice that each force must be smaller than the sum of the other two forces! It is possible to vary the positions of the two pulleys by dragging the mouse. The parallelogram of the forces which are directed to the top left and right (red respectively blue) will be drawn if you select the corresponding option. At the bottom right you can read the angles of these two forces with respect to the vertical. You will find that the sum of mg, T1 and T2 are always equal zero. Press play to find the vector of those three vectors. Title: Re: Eqilibrium of three forces Post by: lookang on March 20, 2009, 04:02:29 pm
learning journey to remix this for finer customization for my classroom teaching.
This is taken from my colleagues who modify from This activity is adapted from L.C. McDermott and the Physics Education Group, Physics by Inquiry (John Wiley & Sons, NY, 1996). There are also no pictures due to uncertainty concerns that i have about copyright infringement. TITLE OF ACTIVITY: Stay Ring, Stay! DURATION: 4 Periods (120 min) STATEMENTS OF LEARNING EXPECTATIONS 2 aaa Know, understand and apply scientific theories, principles and concepts in predicting and explaining outcomes. 2 ddd Infer from a set of observations and translate disparate facts and information into a general pattern. AIMS 1. To investigate the effect of balanced and unbalanced forces on a body. 2. To infer the method for adding two vectors to determine a resultant. ACTIVITY Obtain three 5N spring scales, some string, a small metal ring, 4-5 sheets of graph paper, a piece of softboard, some tape, a protractor and a pin. Label the spring scales 1, 2 and 3. Tape a graph paper onto the softboard. Place a pin so that it is in the centre of the graph paper. Attach three strings that are approximately 20-30cm in length to the ring so that they are free to slide along the ring. Attach the free ends of the three strings to the three spring scales. Centre the ring about the pin. 1. Set up scale 3 on one side of the ring and scales 1 and 2 on the opposite side as shown in the diagram. Spring scales 1 and 2 each exert a force of 2N. a) Predict the force that must be exerted by spring scale 3 in order for the ring to remain at rest. Explain. b) Check your prediction and account for any discrepancies. 2. Mark on your graph paper, angles of 0o, 10o, 20o, 30o, 40o, 50o, 60o and 70o on both sides of the axis through the pin as shown. Set up the scales so that spring scales 1 and 2 are each at an angle α = 30o on either side of the axis. Spring scales 1 and 2 each exert a force of 2N. Spring scale 3 pulls so that the ring remains at rest. a) Predict whether the force exerted by spring scale 3 is greater than, less than, or equal to that exerted by spring scale 3 in part (1). Explain. b) Check your prediction for α = 30o. Use the graph paper to check your angles throughout the experiment. c) Predict whether the force exerted by spring scale 3 for α = 90o is greater than, less than, or equal to that exerted by spring scale 3 when α = 30o. Explain. d) Check your prediction for α = 90o. 3. Set up the scales with spring scale 3 exerting a constant force of 3N. For values of α from 0o to 70o, record the forces that you must exert with spring scales 1 and 2 so that the ring remains at rest. a) How do the forces that must be exerted by spring scales 1 and 2 (individually) change as the angle α increases? b) Are there any angles for which spring scales 1 and 2 (individually) exert forces that are larger in magnitude than that exerted by spring scale 3? c) For any angle α, is it possible for spring scales 1 and 2 to exert forces of different magnitude and have the ring remain at rest? d) When spring scales 1 and 2 are exerting forces of equal magnitude, what is the smallest value of the force they can exert and have the ring remain at rest? What is the angle α corresponding to that force? e) When spring scale 3 exerts a force of 3N, are there any values of α (between 0o and 90o) for which it is not possible to use spring scales 1 and 2 in a manner such that the ring remains at rest? Explain. 4. On a new sheet of graph paper, draw a large dot to represent the ring you used in part (3). Draw an arrow to represent the 3N force exerted on the ring by spring scale 3. a) On the same diagram, draw arrows to represent the forces exerted on the ring by spring scales 1 and 2 for all eight values of α you examined in part (3). All forces should be drawn using the same scale. Use a protractor when constructing this diagram. b) How do the arrows representing the forces exerted by spring scale 1 (or spring scale 2) for various values of α differ from one another? How, if at all, are they similar to one another? c) Draw a best-fit line through the heads of the arrows representing the forces exerted on the ring by spring scales 1 and 2. d) Use your diagram to predict the magnitude of the forces exerted by spring scales 1 and 2 for α = 12o. Predict also for the spring scales when α = 53o. Check your predictions and account for any discrepancies. e) When α = 0o, how is the force exerted on the ring by spring scale 3 related to the forces exerted on the ring by spring scales 1 and 2? f) Is it possible to replace the forces exerted on the rings by spring scales 1 and 2 by a single force? If so, specify both the magnitude and the direction of that force. If not, explain why not. g) For other values of α, what relationship can you find between the forces exerted by spring scales 1 and 2 and the force exerted by spring scale 3? (Note: You need not express this relationship mathematically). h) Can you express this relationship diagrammatically? Explain i) Is it always possible to replace the forces exerted on the ring by spring scales 1 and 2 by a single force? Explain. 5. Set up the scales as for part (3). However, in this case, spring scales 1 and 2 make angles α1 = 30o and α2 = 60o, respectively, with the axis through the pin. Spring scale 3 exerts a constant force of 3N and spring scale 2 exerts a constant force of 1.5N. a) Predict the magnitude of the force that must be exerted by spring scale 1 so that the ring remains at rest. If you believe that it is not possible for the ring to remain at rest for this setup, state so explicitly. In either case, explain your reasoning. b) Check your prediction experimentally and account for any discrepancies. |