SOTM LAB: P14R I. TEACHER NOTES & GUIDELINES TITLE OF LAB: Force Table Exploration DEVELOPERS OF LAB: Ron McDermott, JD566 Lee Cabe, JD863 OVERVIEW OF LAB DESCRIPTION In this lab students will experiment with the Pasco force table to determine the principles involved in the addition of force vectors. A modification of the traditional use of this force table will be the use of a force probe to observe real-time changes in the resultant of vectors. The laboratory exercise is intended as an introduction to force vectors, but can be used for students with some prior knowledge as well. CURRICULUM CONSIDERATIONS This laboratory exercise is designed to assist students in predicting resultant changes, which occur when adjustments are made in the angle between two vectors. The addition of vector quantities is part of the regent s curriculum for regent s physics in New York State. It is assumed that students already have a vague understanding of forces and their directional nature. They do NOT require an understanding of the vector nature of forces; in some ways it may be preferable if they do NOT possess this knowledge. The introduction of the term magnitude is assumed. SAFETY CONSIDERATIONS Students should be cautioned in handling the force probe carefully to avoid dropping it. BACKGROUND INFORMATION A. SCIENTIFIC VIEWPOINT The fundamental concept here is that the resultant (sum) of two vectors is angle dependent. B. COMMON MISCONCEPTIONS 1. The sum of TWO forces is always more than ONE of the forces. 2. To add vectors, you simply add them numerically (direction doesn t matter). 3. The angle between two vectors, which point in the same direction, is 0 degrees. 4. The angle between two, oppositely directed vectors, is 0 degrees. 5. Any change in the angle between two vectors is directly proportional to the change in the resultant (simple ratio theory ).
OBJECTIVES After completion of the laboratory exercise, students will be able to: 1. Accurately predict the effect of angle changes on the resultant of two vectors. 2. Indicate the angle, between two vectors, which produces a minimum resultant. 3. Indicate the angle, between two vectors, which produces a maximum resultant. 4. Relate the force exerted by a hanging mass to the magnitude of its mass. EQUIPMENT/MATERIALS PROVIDED BY SOTM 1. 10 - Force tables 2. 10 - Pasco force probes 3. 10 - Laptop computers with Pasco 500 or 750 interfaces 4. 10 - Mass sets with hangers 5. 10 - Surge protectors 6. 10 - Ringstands ADVANCE PREPARATION II. PRE-LAB Gather sufficient ringstands for all groups and assemble the force tables. PRE-LAB EXERCISE TO ELICIT STUDENTS PRIOR KNOWLEDGE AND MISCONCEPTIONS The teacher will set up the force table with three masses on hangers set up in equilibrium prior to the beginning of class (if possible). Care should be taken to use approximately equal masses; to avoid prejudicing the students opinion of the principles involved. Students should complete a pre-lab questionaire and hand it in. A list of recommended questions follows; feel free to add or delete questions as needed: 1. What forces act on the center ring? 2. What are the directions in which those forces act? 3. What relationship exists between the three forces being exerted on the center ring? 4. What would you expect would happen if you moved two of the masses farther apart? 5. Closer together? 6. What would happen if you moved one of the masses? 7. What would happen if you changed one of the masses? 8. If the equilibrium were disturbed in 2-4 above, what changes would have to be made to restore the equilibrium (for each case in which a disturbance occurs)? DISCUSSION OF PRECONCEPTIONS The teacher should moderate a class discussion of the ideas, which developed from the questions above. In the process of this discussion, the teacher may pose questions to elicit the common misconceptions listed previously (as well as any others, which might arise).
Important points: 1. The masses exert forces, which are proportional to the masses. 2. The forces being exerted are outward from the center ring. 3. An equilibrium exists when all forces cancel out (their sum is zero). III. EXPLORATION OF SCIENTIFIC PRINCIPLE & INTRODUCTION OF EXPERIMENTAL PROTOCOL PROBLEM: Set up the laptop, interface, and force probe, and determine the relationship between mass applied and force probe reading. EXPERIMENT AND TECHNICAL OPERATION OF EQUIPMENT If the students are familiar with Science Workshop, force tables, and calibration of the force probes, or if you have previously set up equipment, skip to step 7. Otherwise proceed with step 1 below: 1. Connect Pasco 500 interface to laptop, plug in power cord, and turn on interface. 2. Plug in, open, and turn on laptop. 3. Set up force table for one hanging mass and a second string to a force probe anchored to a ringstand. 4. Connect force probe to the Pasco 500 interface analog channel A. 5. Open Science Workshop by double-clicking icon. 6. Click on FILE, OPEN, on arrow next to DRIVES, select a:, and finally on the file FORCETBL.SWS to load experimental setup. 7. Starting with no mass attached (just the hanger), double-click on the force probe icon (immediately below channel A on setup page). 8. Press the TARE button on the force probe.
9. Go to LOW VALUE and click on READ. 10. Click on the box next to the LOW VALUE label and type in 0.0. 11. Put a known mass on the hanger and calculate its weight. 12. Go to HIGH VALUE and click on READ. 13. Click on the box next to the HIGH VALUE label and enter the actual weight you calculated (see diagram following).
14. Click on OK (lower right corner). 15. Click on MON to observe the force acting on the force probe. 16. Vary the mass on the hanger and observe the effect on the force probe. IV. ELABORATION OF SCIENTIFIC PRINCIPLE: INQUIRY-BASED STUDENT INVESTIGATION PROBLEM: Is there a relationship between the magnitude of forces in equilibrium and their relative orientations? HYPOTHESIS OR PREDICTION There is a relationship between the orientations of forces in equilibrium and their respective magnitudes. EXPERIMENTAL DESIGN 1. A force probe allows you to measure a single force (which will be your dependent variable. What are the things that you can vary (the independent variables)? 2. Once you have identified the independent variables, you want to vary only one of them at a time, so you may be performing more than one set of experimental processes in your lab. 3. Design an experiment(s) which will allow you to test the effects of the independent variables you have identified above, and call me when you have it written out in draft form. Checkpoint: Students should identify the mass (force) and the angles as the independent variables and arrange to vary one at a time. PLAN FOR DATA COLLECTION & ANALYSIS 1. In your data you will be keeping track of your independent and dependent variable values for EACH process you have identified above. What is the best way to arrange that data? 2. What would be the best choice of units to work with? 3. What is the best way to display your data to support your conclusion(s)? 4. When you have formalized a plan for the management and arrangement of your data, call me for evaluation. Checkpoint: Students should identify a table format as the best way to organize their data, and newtons and degrees as the best units to use. CONDUCTING THE EXPERIMENT Students should take note of any changes in their procedure which become necessary, and why those changes were required. Students should pay careful attention to the recording of data; ask them about how they are organizing the recording and if they believe they will be able to understand the data when it comes time to write their lab report.
Checkpoint: Independent and dependent variable data should be associated to facilitate organization into table form. ANALYSIS OF DATA 1. Are calculations required? 2. Does your data indicate any kind of a pattern between changes in your independent variables and your dependent variable? 3. Are there any adjustments you could make in the display of your data, which would make conclusions more obvious? 4. Would a graph help you to illustrate your conclusion? Checkpoint: It is important for students to understand that the way data is presented may aid in, or detract from, the formation of conclusions. DISCUSSION OF RESULTS COMPARE PERSUADE RELATE 1. Did you find that some of what you thought was true in the pre-lab exercise turned out NOT to be true? 2. Did your lab observations support your lab hypothesis? 3. If not, did your observations lead you to a different conclusion? 4. Did you have to make adjustments in your data arrangment scheme in order to detect a pattern? 5. Assuming you found some relationships between your independent and dependent variables, are you able to express them mathematically (as proportions, perhaps)? 6. Does a numerical comparison between the sum (total force) exerted by the two independent forces in relation to the third dependent force exist? 7. If so, is the relationship what you would have expected? If not, how are they different? 1. What have you concluded (there may be more than one)? 2. What evidence do you have for your conclusion? 3. Does your conclusion allow you to make predictions? 4. Did you test your ability to make predictions? 5. Is your conclusion consistent with your pre-lab observations? How might your conclusions be applied in the real world? (Note: hanging signs, cranes, clotheslines)
V. EVALUATION POST-LAB SURVEY OF STUDENTS CONCEPTIONS Have students retake the Pre-Lab Exercise. Compare pre-lab and post-lab responses. Alternatively, the teacher may take three ropes, connected at a point, and ask three students to arrange themselves so that one of them experiences a zero force and, later, a maximum force. They may follow this by predicting of the effect of angle changes by two students on the third student. TRADITIONAL 1. The angle between two forces, which results in the maximum total force would be? 2. The angle between two forces resulting an the minimum total force would be? 3. As the angle between two forces increases, their total force..? 4. As the angle between two forces changes from 180 degrees to 110 degrees, the total force..? 5. If a 3.0 newton force and a 2.0 newton force act on the same point (unknown angle between them), their maximum possible total force would be..? 6. In the problem above, what would be their minimum possible total force? 7. For the problem above, if the angle between the two forces was 90 degrees, what magnitude do you think the total force would have? Why? ALTERNATIVE Define several geometrical arrangements of three forces and provide the students with two of the forces. Have them find their sum by predicting the magnitude of the third force required to place the combination in equilibrium. This material is based upon work supported by the National Science Foundation under Grant No. ESI 9618936. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.