Vectors!! A PBI INVESTIGATION LESSON. Vector lab. Functions and Modeling (course handout). Retrieved from UTeach at UT.

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1 Red River Catastrophe Project Vectors!! A PBI INVESTIGATION LESSON Author(s): Title of Lesson: Vector Force Table Date of Lesson: Week 1 Length of Lesson: 50 min Name/Level of Course: Physics Source of the Lesson: Vector lab. Functions and Modeling (course handout). Retrieved from UTeach at UT. Concepts The students should be able to: Use force vectors to create equilibrium Differentiate between theoretical and actual results Performance Objectives Students will be able to: Balance force tables Create systems of force that are in equilibrium TEKS Addressed Physics (c) Knowledge and skills. (4) Science concepts. The student knows and applies the laws governing motion in a variety of situations. The student is expected to: (D) Calculate the effect of forces on objects, including the law of inertia, the relationship between force and acceleration, and the nature of force pairs between objects; CCRS Addressed II. Foundation Skills: Scientific Applications of Mathematics C. Understand relationships among geometry, algebra, and trigonometry 1. Understand simple vectors, vector notations, and vector diagrams, and carry out simple calculations involving vectors.

2 Red River Catastrophe Project 3. Understand basic trigonometric principles, including definitions of terms such as sine, cosine, tangent, cotangent, and their relationship to triangles. Materials List and Advance Preparations Force Table system- 1 per group Varying weights- set for each group Protractor- 1 per group Student Handout (Lab Paper) Safety Students should not be tossing around weights. Students must adhere to all lab rules. In the beginning of the semester students should have completed the lab safety online modulo. In this modulo, they learned about all safety requirements when working in a Physics Lab. Supplementary Materials, Handouts Worksheet, pre-assessment, and quiz

3 Engagement What the Teacher Will Do Exploration What the Teacher Will Do Each group of students will have a force table and set of different weights. They will be shown how to move around the clips on the force table to make them into equilibrium. The worksheet will be passed out for students to work through. Probing Questions By a show of hands, how many of you have been on a see-saw before? Now when we have another person on the other side, we use the middle point as leverage to push one side up and the other down. What if we were to try to make it so that both people were in the air for at least 5 seconds? How would go about trying to do this? We are going to explore the concept of equilibrium today with a force vector lab, but first we are going to make sure we have our basic trig properties down. (We need trig properties to resolve vectors into their x and y components.) Probing Questions How are you moving the clips around to create equilibrium? Do you need different weights on each to create equilibrium? See additional questions on student handout. Vector Force Table Page 3 of 11 Time: 3 minutes Student Responses and Potential Misconceptions [Get people of the same weight, move the fulcrum of the see saw to balance the weight] [Misconception: have the heavier person push up slowly when they are leaving the ground.] Time: 25 Student Responses and Potential Misconceptions

4 Explanation What the Teacher Will Do Have the students present their results to the class. Probing Questions What do we think of when we hear the word equilibrium now? What are your actual results? What are your theoretical results? How do the theoretical and actual results compare? Vector Force Table Page 4 of 11 Time: 7 Student Responses and Potential Misconceptions [The forces work of the x and y component work together and balance one another out.] [Answers will vary by group] [Answers may vary by group] [They are close, but there are more factors to think about when actually performing the experiment. The friction where the string touches the table is a force that acts upon the system. The accuracy of the instruments is also not incredibly precise.] Elaborate What the Teacher Will Do Go back to the initial problem of the see-saw. Discuss how this ties into the bridge project. Probing Questions Looking back at our first problem with the see-saw, what are some other ways you can think about in order to balance the forces of the people? Time: 5 Student Responses and Potential Misconceptions [Giving weights to one person to balance the weight, having one person move up or down the see-saw to change the position of the weight acting downward. Moving the actual board the see-saw is made of.]

5 Vector Force Table Page 5 of 11 Evaluate What the Teacher Will Do Give students post-assessment if time permits. Also, student will write a conclusion to the lab with students applying it to bridge design. Probing Questions Time: 10 Student Responses and Potential Misconceptions

6 Vector Lab Pre-assessment 1) Define vector: 2) Define scalar: Use the triangle to answer questions 3, 4, and 5: 3) a = 12, b = 13, c =? 4) Find the two angles if a = 3, b = 4, c = 5 5) a =?, b = 14, c = 42

7 Vector Force Lab Purpose: In this lab we explore Newton s 1 st Law: at equilibrium and Newton s 2 nd Law: F = ma using vector forces on a force table. For the first half of the experiment, equilibrium for three vectors will be investigated by resolving each force into its vector components. In the second part of the lab, vector addition will be explored by finding a resultant between two added vectors and verifying your result using a third vector. Method: A force table system is used underspecified conditions to simulate the addition and subtraction of vectors. The vectors are created by hanging various gram masses from strings that are draped over pulleys and connected to a moveable ring near the center of the force table. The ring, when suspended off the table and centered, represents equilibrium in the system. For our purposes we will ignore friction at the pulleys.

8 Vector Force Lab Procedure and Analysis, Part 1 1. Set up your vector table as shown above making sure that the middle ring is in equilibrium (i.e. the ring is not touching the center post on the vector table. Be sure to use various masses at each pulley to create your vectors at different angles. 2. For each of the vector string forces, the magnitude of the force can be found by using F=ma where m is the mass of the gram masses measured in kilograms, and a is the acceleration due to gravity: 9.8. Show your calculations for finding the magnitude of each of the three vector forces v 1, v 2, and v Using a protractor, draw your vectors precisely onto the coordinate system provided below. The angles of the vectors from the horizontal should be correctly shown and the magnitudes of the vectors should be proportionately represented.

9 Vector Force Lab 4. Now resolve all three vectors into and. If you truly have equilibrium, what should each of these two sums equal? Show calculations to support your answer. Procedure and Analysis, Part 2 5. For this part of the lab you will use the same set of three vectors from Part I. a) Now resolve any two of the vectors into and to find the resultant vector. Show your calculations. b) Once again, using a protractor, draw your vectors exactly onto the coordinate system provided below AND include your drawing of the resultant vector associated with the addition of the two vectors you chose to add in a) above.

10 Vector Force Lab 6. What should the relationship be between the resultant vector found in step 5 and the third vector in your system? Did you find the conjectured relationship to be true for your system? Support your answer. Conclusion 7. Was there error present in your system? If so, what are some of the sources of error? 8. What conclusions are you able to make concerning your results keeping in mind the purpose of the lab from above? Additionally, write a short paragraph applying this lab to the bridge design.

11 Vector Force Quiz Balance the following force tables: 1) , ) , ) ,