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В2 Speed, Acceleration, and Free Fall

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INVESTIGATION B2 B2 Speed, Acceleration, and Free Fall Key Question: How does gravity affect the motion of a falling object? Earth’s gravity pulls objects downward toward the center Materials for each group of Earth. In Investigation B1, students learned to measure y Physics stand* the speed of a falling marble. In this investigation, students apply their knowledge to examine the speed y Gravity Drop catcher and dropper of the marble at several points along its path. With this y CPO Timer with 2 photogates* information, they determine how the speed of the falling y Plumb line marble changes as it falls. Students then learn to graph y Steel marble their results, find slope values, and create a mathematical model to confirm their measurements. y Metric ruler* y Calculator* Learning Goals *provided by the teacher ✔ Make a graph of the motion of a falling marble. Online Resources ✔ Interpret motion graphs. Available at curiosityplace.com ✔ Explain the difference between speed y Equipment Videos: Gravity Drop, CPO Timer and acceleration. y Skill and Practice Sheets y Whiteboard Resources GETTING STARTED y Animation: Acceleration Graph Time 100 minutes y Science Content Video: Speed vs. Time Graphs y Student Reading: Acceleration Setup and Materials 1. Make copies of investigation sheets for students. 2. Watch the equipment video. 3. Review all safety procedures with students. NGSS Connection This investigation builds conceptual understanding and skills for the following performance expectation. HS-PS2-4. Use mathematical representations of Newton’s Law of Gravitation and Coulomb’s Law to describe and predict the gravitational and electrostatic forces between objects. Science and Engineering Practices Disciplinary Core Ideas Crosscutting Concepts Using Mathematics and Computational Thinking PS2.B: Types of Interactions Patterns Gravity Drop 29 SPEED, ACCELERATION, AND FREE FALL Vocabulary In this investigation, students use the Gravity Drop to acceleration – the change in speed over time investigate the speed of the marble at different points along its downward path. The act of dropping the marble experiment – a procedure carried out under controlled past the photogates is a single event in time. Students conditions to test a hypothesis cannot measure every change in the marble’s motion free fall – occurs when an object is accelerating due to that occurs during this event. However, by repeating the force of gravity and no other forces are acting upon similar events, such as dropping the marble from the that object same height several times, students can gather data and hypothesis– a possible explanation that can be tested by infer what happens to the marble’s motion each time comparison with scientific evidence it falls. percent error – the difference between an approximate These inferences are captured by creating a graph or measured value and an exact or known value, that relates the observations of the marble’s speed at expressed as a percent of the known value photogate B to the time for which the marble has been slope – the ratio of the vertical distance to the horizontal falling. In this way, the graph that students create is a distance that separates any two points on a line model of the change in speed, or the acceleration, speed – a measure of the distance traveled in a given a marble will likely experience during its downward amount of time travel. Looking at this model, students can verify their trend line – a line that represents the general hypothesis and make predictions about future drops relationship among data on a graph of the marble. The process of repeatedly dropping the marble is an experiment designed to test student hypotheses about the motion of a falling object. BACKGROUND Once students have measured the speed of the falling marble at several points, they can plot their data and fit a Objects in free fall on Earth accelerate downward, trend line to their graphs. From this trend line, students increasing their speed by 9.8 m/s2 every second. can estimate the marble’s acceleration. Then, the The graph below shows data for the speed over time investigation asks students to use the algebraic equation: of an object in free fall. We know that the object has a constant acceleration because the shape of the graph y variable slope x variable y intercept is a straight line. Constant acceleration means that an object’s speed changes by the same amount over a given y = mx + b time interval. vaB =+tvAB A Free fall speed vs. time 50 Time (s) Speed (m/s) By substituting values for velocity, time, and slope into 40 the equation, students can calculate the speed of the 0 0 marble at different points. Finally, students can compare 30 1 9.8 their calculated values with experimentally-found values 2 19.6 20 and calculate percent error to check the accuracy of Speed (m/s) 3 29.4 their data. 10 4 39.2 5 49.0 0 0 1 2 3 4 5 Time (s) 30 B2 5E LESSON PLAN Engage Draw the following three graphs on the board: Graph A Graph B Graph C Speed (cm/s) Science Content Video Animation Time (s) Time (s) Time (s) Speed vs. Time Graphs Acceleration Graph Explain to students that these graphs show the motion of an object over time. Ask students to describe the motion Elaborate of the object in each graph. Then ask students to suggest In working with the gravity drop, students learn quickly different objects whose motion might be similar to these that they need to pay attention to their dropping graphs. Answers will likely vary. Accept all reasonable technique. More often than not, students will obtain answers. Students should be able to identify that speed results that indicate some experimental error, which is increasing in graph A, staying constant in graph B, can generally be attributed to a misalignment between and decreasing in graph C. This Engage activity can be the diameter of the marble and the beams of the used as a formative assessment to determine student photogates. The percent difference between your readiness for the graphing activities in this investigation. acceleration value and 9.8 m/s2 indicates the percent error in the experiment. This is explained in Part 7 of Explore the investigation. Have students complete Investigation B2, Speed, Identifying and controlling errors in measurement is an Acceleration, and Free Fall. Students apply their important scientific practice. Consider using Part 7 to knowledge to examine the speed of the marble at conduct a class discussion about error and experimental several points along its path. With this information, they design. Alternatively, you may have students conduct determine how the speed of the falling marble changes trials of this investigation with the specific goal of over time. examining error in their technique. Explain Evaluate Revisit the Key Question to give students an opportunity y During the investigation, use the checkpoint to reflect on their learning experience and verbalize questions as opportunities for ongoing assessment. understandings about the science concepts explored in y After completing the investigation, have students the investigation. Curiosityplace.com resources, including answer the assessment questions on the Evaluate student readings, videos, animations, and whiteboard student sheet to check understanding of the resources, as well as readings from your current concepts presented. science textbook, are other tools to facilitate student communication about new ideas. Gravity Drop 31 SPEED, ACCELERATION, AND FREE FALL Explore INVESTIGATION B2 Explore INVESTIGATION B2 Name ____________________________________________ Date ________________________ Setting up the experiment 1. Attach the catcher at the first hole of the physics stand. B2 Speed, Acceleration, and Free Fall Materials: ✔ Physics stand 2. Attach the dropper at the nineteenth hole of the physics stand. How does gravity affect the motion of a falling object? ✔ Gravity Drop catcher and 3. Attach photogate A at the seventeenth hole of the physics stand. Earth’s gravity pulls objects downward toward the center of Earth. In dropper 4. Attach photogate B so that it is 5 cm below photogate A. This will be Investigation B1, you learned how to measure the speed of a falling marble. ✔ CPO Timer and 2 photogates at the sixteenth hole of the physics stand. In this investigation, you will apply your knowledge to examine the speed ✔ Plumb line of the marble at several points along its path. With this information, you can 5. Connect photogates A and B to the timer. Set the timer to interval ✔ Steel marble determine how the speed of the marble changes as it falls. mode. ✔ Metric ruler 6. Use the plumb line to align the dropper and catcher. Adjust the ✔ Calculator Formulating a hypothesis physics stand if necessary. 7. Use the steel marble to conduct a test drop and ensure that the a. If you dropped a stone off a bridge into a river, how would you describe the motion of the falling stone? dropper and catcher are aligned. If necessary, repeat Steps 6 and Does the speed of the stone change during the fall? 7 until you obtain a good drop. Check the display on the timer to ensure that the photogates are recording time intervals, or “times,” accurately. Conducting the experiment 1. Begin Trial 1. Drop the steel marble until you get a good drop. In Table 1, record the time registered by photogate A (tA ). Then record the time registered by photogate B (tB ). Finally, record the time registered when the marble passed from photogate A to photogate B (tAB ). As the stone falls, its speed steadily increases until it hits the water. 2. For Trial 2, move photogate B so that it is 10 cm below photogate A. Again, drop the steel marble until you get a good drop and b.
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