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Back and Forth Motion (Motion Detector) Back and Forth Motion (Motion Detector)   Graphical Analysis 2 Back and Forth Motion (Motion Detector) Lots of objects go back and forth; that is, they move along a path first in one direction, then move back the other way. An oscillating pendulum or a ball tossed vertically into the air are examples of things that go back and forth. Graphs of the position vs. time and velocity vs. time for such objects share several features. When an object changes speed or direction, it accelerates. By examining the graphs, you will be able to tell if an object is accelerating. In this experiment, you will observe several objects that change speed and direction as they go back and forth: · Oscillating pendulum · Dynamics cart rolling up and down an incline · Student jumping into the air · Mass oscillating at the end of a spring · Ball tossed into the air Analyzing and comparing graphs of the motion of these objects will help you to apply ideas of kinematics more clearly. objectives · Qualitatively analyze the motion of objects that move back and forth. · Analyze and interpret back and forth motion in kinematics graphs. · Use kinematic graphs to catalog objects that exhibit similar motion. Materials Chromebook, computer, or mobile device Graphical Analysis 4 app Go Direct Motion pendulum with large bob spring with hanging mass Vernier Dynamics Track Vernier Dynamics Cart Motion Detector Bracket Adjustable End Stop rubber ball (15 cm diameter or more) protective wire basket for motion detector protractor meter stick Preliminary questions 1. Do any of the five objects listed in the Introduction move in similar ways? If so, which ones? What do they have in common? 2. Below are four velocity vs. time graphs. Which graph represents the motion of an object that has a constant positive acceleration? Explain why you chose that graph. 3. Do any of the five objects from Preliminary Question 1 have a constant acceleration? If so, which one(s)? 4. Consider a ball thrown straight upward. It moves up, changes direction, and falls back down. a. Examine the graphs below. Which graph represents the position vs. time for the ball? Which graph represents the velocity vs. time for the ball? b. What is the acceleration of the ball on the way up? What is the acceleration when it reaches its top point? What is the acceleration on the way down? Procedure These five activities ask you to predict the appearance of graphs of position vs. time and velocity vs. time for various motions, and then collect the corresponding data. The motion detector defines the origin of a coordinate system extending perpendicularly from the front of the motion detector. Use this coordinate system in making your sketches. Part I  Oscillating Pendulum 1. Launch Graphical Analysis. Connect the motion detector to your Chromebook, computer, or mobile device. 2. Place the motion detector near a pendulum with a length of 1 to 2 m as shown in Figure 1. The motion detector should be level with, and about 1 m away from, the pendulum bob when it hangs at rest. The bob should never be closer to the detector than 25 cm. 3. Sketch your prediction of the position vs. time and velocity vs. time graphs of a pendulum bob swinging back and forth. Ignore the small vertical motion of the bob and measure distance along a horizontal line in the plane of the bob’s motion. Based on the shape of your velocity graph, do you expect the acceleration to be constant or changing? Why? Will it change direction? Will there be a point where the acceleration is zero? Figure 1    4. Pull the pendulum about 15 cm toward the motion detector and release it to start the pendulum swinging. 5. Click or tap Collect to start data collection. 6. When data collection is complete, a graph of position vs. time is displayed. If you do not see a smooth graph, the pendulum was most likely not in the beam of the motion detector. Make adjustments and repeat Steps 4–5 until you get a smooth graph. 7. Answer the Analysis questions for Part I before proceeding to Part II. Part II  Dynamics Cart on an Incline 1. Adjust the equipment for Part II. a. Confirm that your Dynamics Track, Adjustable End Stop, and Motion Detector Bracket are assembled as shown in Figure 2. The angle of the incline should be between 5° and 10°. b. To set the motion detector to detect a cart on a ramp, click or tap Device Manager,, and then click or tap Sensor Channels. c. Select the check box for Motion (cart). Click or tap Done. Figure 2    2. Sketch your prediction of the position vs. time and velocity vs. time graphs for a Dynamics Cart rolling freely up an incline and then back down. The cart will be rolling up the incline and toward the motion detector initially. Will the acceleration be constant? Will it change direction? Will there be a point where the acceleration is zero? 3. Place the cart on the track near the end stop. Click or tap Collect to start data collection and then give the cart a push up the incline. Let the cart roll freely up nearly to the top, and then back down. Keep your hands away from the track as the cart rolls, then catch the cart as it nears the end stop. The cart should not get closer than 0.15 m to the motion detector. If you do not see a smooth graph, the cart was most likely not in the beam of the motion detector. Make adjustments and repeat data collection until you get a smooth graph. 4. Answer the Analysis questions for Part II before proceeding to Part III. Part III Student Jumping in the Air 1. Adjust the equipment for Part III. a. Secure the motion detector about 3 m above the floor, pointing down. b. To change the motion detector channel, click or tap Device Manager,, and click or tap Sensor Channels. c. Select the check box for Motion. Click or tap Done. 2. Sketch your predictions for the position vs. time and velocity vs. time graphs for a student jumping straight up and falling back down. Will the acceleration be constant? Will it change direction? Will there be a point where the acceleration is zero? 3. Stand directly under the motion detector. 4. Click or tap Collect to start data collection, then bend your knees and jump. Keep your arms still while in the air. 5. If you do not see a smooth graph, you were most likely not in the beam of the motion detector. Make adjustments and repeat Steps 3–4 until you get a smooth graph. 6. Answer the Analysis questions for Part III before proceeding to Part IV. Part IV  A Mass Oscillating at the End of a Spring 1. Place the motion detector so it is facing upward, about 1 m below a mass suspended from a spring. Place a wire basket over the motion detector to protect it. 2. Sketch your prediction for the position vs. time and velocity vs. time graphs of a mass hanging from a spring as the mass moves up and down. Will the acceleration be constant? Will it change direction? Will there be a point where the acceleration is zero? 3. Lift the mass about 10 cm (and no more) and let it fall so that it moves up and down. 4. Click or tap Collect to start data collection. 5. If you do not see a smooth graph, the mass was most likely not in the beam of the motion detector. Make adjustments and repeat Steps 3–4 until you get a smooth graph. 6. Answer the Analysis questions for Part IV before proceeding to Part V. Part V  Ball Tossed into the Air 1. Place the motion detector on the floor pointing toward the ceiling, as shown in Figure 3. Place a protective wire basket over the motion detector. Figure 3    2. Sketch your predictions for the position vs. time and velocity vs. time graphs of a ball thrown straight up into the air. Will the acceleration be constant? Will it change direction? Will there be a point where the acceleration is zero? 3. Hold the rubber ball with your hands on either side, about 0.5 m above the motion detector. 4. Click or tap Collect to start data collection, then gently toss the ball straight up over the motion detector. Move your hands quickly out of the way so that the motion detector tracks the ball rather than your hand. Catch the ball just before it reaches the wire basket. 5. If you do not see a smooth graph, the ball was most likely not in the beam of the motion detector. Make adjustments and repeat Steps 3–4 until you get a smooth graph. 6. Proceed to the Analysis questions for Part V. Analysis Part I  Oscillating Pendulum 1. Export, print, or sketch the position and velocity graphs for one oscillation of the pendulum. Compare these to your predicted graphs and comment on any differences. 2. Was the acceleration constant or changing? How can you tell? 3. Was there any point in the motion where the velocity was zero? Explain. 4. Was there any point in the motion where the acceleration was zero? Explain. 5. Where was the pendulum bob when the acceleration was greatest? Part II  Dynamics Cart on an Incline 1. Export, print, or sketch the portions of the position and velocity graphs that represent the time that the cart was going up and down the incline. Compare these to your predicted graphs and comment on any differences. 2. Was the acceleration constant or changing? How can you tell? 3. Graphical Analysis can display the tangent line to a curve, as well as display the slope numerically. Click or tap Graph Tools, , and enable Tangent. Dismiss the Graph Tools box. Click or tap the data points on the graph to display and adjust the Tangent line. Use the Tangent line and the velocity graph to determine the acceleration of the cart when it was on the way up, at the top, and on the way down the incline. What did you discover? 4. Was there any point in the motion where the velocity was zero? Explain. 5. Was there any point in the motion where the acceleration was zero? Explain. Part III  Student Jumping in the Air 1. Export, print, or sketch the portions of the position and velocity graphs that represent the time from the first bend of the knees through the landing. Compare these to your predicted graphs and comment on any differences. 2. Click or tap Graph Tools, , and enable Tangent. Dismiss the Graph Tools box. Click or tap the data points on the graph to display and adjust the Tangent line. Determine where the acceleration was greatest. Was it when the student was pushing off the floor, in the air, or during the landing? 3. When the student was airborne, was the acceleration constant or changing? How can you tell? 4. Was there any point in the motion where the velocity was zero? Explain. 5. Was there any point in the motion where the acceleration was zero? Explain. Part IV  A Mass Oscillating at the End of a Spring 1. Export, print, or sketch the position and velocity graphs for one oscillation of the mass. Compare these to your predicted graphs and comment on any differences. 2. Was the acceleration constant or changing? How can you tell? 3. Was there any point in the motion where the velocity was zero? Explain. 4. Was there any point in the motion where the acceleration was zero? Explain. 5. Where was the mass when the acceleration was greatest? 6. How does the motion of the oscillating spring compare to the pendulum? Part V  Ball Tossed into the Air 1. Export, print, or sketch the portions of the position and velocity graphs that represent the time the ball was in the air. Compare these to your predicted graphs and comment on any differences. 2. Was the acceleration constant or changing? How can you tell? 3. Identify three positions of the ball: when it was on the way up, at the top, and on the way down. For each section, apply a linear curve fit to determine the slope (acceleration). To apply a linear curve fit, select a region of data, click or tap Graph Tools, . Choose Linear, and click or tap Apply. Do this for each of the three positions. What did you discover? 4. Was there any point in the motion where the velocity was zero? Explain. 5. Was there any point in the motion where the acceleration was zero? Explain. Analysis of All Parts 1. State two features that the five position graphs had in common. State two ways that the five position graphs were different from one another. 2. State two features that the five velocity graphs had in common. 3. State two ways that the five velocity graphs were different from one another. 4. Reevaluate your answer to Preliminary Question 4. What evidence do you have that you answers were correct or not? Physics with Vernier ©Vernier Software & Technology 1 2 Physics with Vernier Physics with Vernier 3 Group # Name1, Name2 Name3, Name4, Name5 Math and Sciences department, MIAMI-DADE College PHY2053L-7283 Date Lab Report: Back and Forth Motion Purpose: asqsqs asqsqs asqsqs asqsqs asqsqs asqsqs asqsqs asqsqs asqsqs asqsqs Example: asqsqs asqsqs asqsqs asqsqs asqsqs asqsqs asqsqs asqsqs asqsqs asqsqs asqsqs The purpose of this experiment is to analyze and interpret the kinematic graph, ……………..we will also be examining the back and forth motion of objects. Specifically, analyzing and comparing graphs………. Understanding and visualizing the relationship between position, velocity, and acceleration………. asqsqs asqsqs asqsqs asqsqs asqsqs asqsqs asqsqs asqsqs asqsqs asqsqs asqsqs asqsqs asqsqs asqsqs asqsqs asqsqs asqsqs asqsqs asqsqs asqsqs Apparatus: asqsqs asqsqs asqsqs asqsqs asqsqs asqsqs asqsqs asqsqs asqsqs asqsqs asqsqs asqsqs asqsqs asqsqs asqsqs asqsqs asqsqs asqsqs asqsqs asqsqs asqsqs asPart I Oscillating Pendulum Swinging pendulum and motion sensor. Example: Here, the physical quantities that we will measure with the motion detector will be.... Position, x Velocity and acceleration Part II Dynamics Cart on an Incline Rubber stopper. Low-friction cart, and motion sensor. The incline is between 5 to 10 degrees. asqsqs asqsqs asqsqs asqsqs asqsqs asqsqs asqsqs asqsqs asqsqs asqsqs asqsqs asqsqs asqsqs asqsqs asqsqs asqsqs asqsqs asqsqs asqsqs asqsqs asqsqs asqsqs asqsqs asqs asqs Part III Student Jumping in the Air asqsqs asqsqs asqsqs asqsqs asqsqs asqsqs asqsqs asqsqs Create a figure that describes the experiment. In the figure show clearly the variables to be measured. asqsqs asqsqs asqsqs asqsqs asqsqs asqsqs asqsqs asqsqs asqsqs asqsqs Example (done in PowerPoint) You can make a drawing on the computer or tablet and then take a screenshot (obviously, drawing skills don't matter here). Please, just make sure that the variables to be measured should be clearly Position, x Velocity and acceleration Motion detector represented in the figure. Also, you can take screenshots of the demo video (Blackboard > LABS > 02-Back and Forth> Demonstrations). In summary, use the method that is easiest for you to represent the experimental situation and the variables to be measured. Part IV A Mass Oscillating at the End of a Spring Create a figure that describes the experiment. In the figure show clearly the variables to be measured. Part V Ball Tossed into the Air Create a figure that describes the experiment. In the figure show clearly the variables to be measured. Procedure: Part I Oscillating Pendulum This section should identify and name all experimental variables and briefly describe how the independent variables are controlled. By watching the video of the experiment in (Blackboard > LABS > 02-Back and Forth> Demonstrations) and using the PROCEDURE section of the laboratory instructions(Blackboard > LABS >02-Back and Forth>Lab: 02-Back and Forth), make a brief summary of the steps that were followed to do this part. Example: In this part we launch Graphical Analysis……. With the motion detector we measure….. Part II Dynamics Cart on an Incline This section should identify and name all experimental variables and briefly describe how the independent variables are controlled. By watching the video of the experiment in (Blackboard > LABS > 02-Back and Forth> Demonstrations) and using the PROCEDURE section of the laboratory instructions(Blackboard > LABS >02-Back and Forth>Lab: 02-Back and Forth), make a brief summary of the steps that were followed to do this part. Part III Student Jumping in the Air The same idea as in the previous parts Part IV A Mass Oscillating at the End of a Spring The same idea as in the previous parts Part V Ball Tossed into the Air The same idea as in the previous parts Data: Data consists only of those values measured directly from the experimental apparatus. Although to analyze the data (next section) you use all the rows of the tables. In this section, just copy and paste a few rows of data from the datafile. Part I Oscillating Pendulum Part II Dynamics Cart on an Incline Copy and paste a few rows of data from the datafile. Part III Student Jumping in the Air Copy and paste a few rows of data from the datafile. Part IV A Mass Oscillating at the End of a Spring The same idea as in the previous parts Part V Ball Tossed into the Air dsddsdsdsdsdsdsdsdsdsdfsfsfsfdsfdfdfgdgfdgffsfdsfdfdfgdgfdgffsfdsfdfdfgdgfdgdggdgdfg The same idea as in the previous parts Evaluation of Data: General instructions for this section: This selection Should include all graphs, analysis of graphs, and post lab calculations.State each formula, and if necessary, identify the symbols used in the formula. If repetitive calculations are to be performed, substitute only one set of data into each formula & then construct a table of values for all additional calculated values. Be certain that your finals calculated values are expressed in the correct number of significant figures. DO NOT SHOW YOUR ARITHMETIC CALCULATIONS. Specifically, in this laboratory we will not have to use any formula. Part I: Oscillating Pendulum Predicted graphs. Graphs from data (datafile) Sketches: Vernier: Graphs Example: My predicted or sketched graphs were very similar to the graphs recorded by the Vernier Graphical Application and the Sensor. This is because I previously knew that a Position Vs. Time graph ……., while a Velocity Vs. Time graph looks……. As we can see from the acceleration vs. time graph of the graph below, the acceleration is …. Here you answered question 2 (Was the acceleration constant or changing? How can you tell?) of the ANALYSIS section of the laboratory instructions). The following graph shows the velocity vs time for the pendulum. Here you can see that since the movement is periodic there are several moments where the graph cuts the time axis (points with zero speed). In the experimental demonstration, these points correspond to the highest position of the pendulum ......... In the previous sentence, you answered question 3 (Was there any point in the motion where the velocity was zero? Explain.) Then, you answer questions 4 and 5. They are: Was there any point in the motion where the acceleration was zero? Explain. Where was the pendulum bob when the acceleration was greatest? I suggest you answer these questions in paragraph format and always using graphs in the datafile. Part II: Dynamics Cart on an Incline The same idea as in the previous part I suggest you answer these questions in paragraph format and always using graphs in the datafile. Part III: Student Jumping in the Air The same idea as in the previous part Part IV: A mass Oscillating at the End of a Spring The same idea as in the previous part Part V: Ball Tossed into the Air The same idea as in the previous part Analysis of All Parts Example: All the Position vs. Time graphs are have in common that…., as well as… Here you must answer the questions in this section of the lab instructions file. Conclusion: In the conclusion you must do the following: a) State the relationship between the variables identified in the purpose in a clear, concise English sentence. b) When a mathematical expression can be derived from graphical analysis, write it, making sure to include the appropriate units. State the meaning of the slope and discuss the significance of the y-intercept (when appropriate). c) Describe any new terms that arise as a result of your evaluation of data. d) When your results differ from what is expected, provide a plausible explanation Example: Each of the graphs of motions we studied displayed back and forth motion, they each had similar graphs of position vs time in that they oscillated to a certain degree, but their velocity vs time and acceleration vs time graphs tended to be quite different…… The y-intercept of a position vs. time graph tells us what our initial position is…….. Part I Oscillating Pendulum Part II Dynamics Cart on an Incline Part III Student Jumping in the Air Part IV A Mass Oscillating at the End of a Spring Part V Ball Tossed into the Air Part I Oscillating Pendulum Part II Dynamics Cart on an Incline Part III Student Jumping in the Air Part IV A Mass Oscillating at the End of a Spring The same idea as in the previous parts Part V Ball Tossed into the Air dsddsdsdsdsdsdsdsdsdsdfsfsfsfdsfdfdfgdgfdgffsfdsfdfdfgdgfdgffsfdsfdfdfgdgfdgdggdgdfgThe same idea as in the previous parts Part V Ball Tossed into the Air dsddsdsdsdsdsdsdsdsdsdfsfsfsfdsfdfdfgdgfdgffsfdsfdfdfgdgfdgffsfdsfdfdfgdgfdgdggdgdfgThe same idea as in the previous parts