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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