Exploring Motion. Measurements with CMA Motion

Transcription

1 Exploring Motion Measurements with CMA Motion

2 February 2009, version 1 Hardware and software are distributed by the CMA foundation. The CMA foundation is affiliated to the AMSTEL Institute of Universiteit van Amsterdam. AMSTEL Institute/CMA Foundation Kruislaan 404, 1098 SM Amsterdam, The Netherlands Telephone: Fax: cmainternational@science.uva.nl Internet: CMA / AMSTEL Institute, Amsterdam, Text: Ewa Kędzierska, Vincent Dorenbos 2009 Foundation CMA/AMSTEL Institute, Universiteit van Amsterdam 2

3 Table of contents TEACHER GUIDE... 5 I. INTRODUCTION...5 II. MOTION A USB MOTION DETECTOR... 5 Tips on getting good results with the Motion... 6 III. SOFTWARE... 7 Coach Using Motion with Coach Coach 6 Activities... 7 IV. PEDAGOGICAL BACKGROUND... 7 Teaching approaches... 7 Learning benefits... 8 V. GUIDE THROUGH STUDENT ACTIVITIES Activity 1. How to use Motion Activity 2. Graphing distance Activity 3. Understanding velocity Activity 4. Graphing velocity Activity 5. Understanding acceleration Activity 6. Acceleration on an incline Activity 7. Periodic motion Activity 8. Match the graph x(t) Activity 9. Match the graph v(t) Activity 11. Bouncing ball Activity 12. Air resistance STUDENT ACTIVITIES...21 Activity 1. How to use Motion Activity 2. Graphing distance Activity 3. Understanding velocity Activity 4. Graphing velocity Activity 5. Understanding acceleration Activity 6. Acceleration on an incline Activity 7. Periodic motion Activity 8. Match the graph x(t) Activity 9. Match the graph v(t) Activity 10. Throwing a ball Activity 11. Bouncing ball Activity 12. Air resistance

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5 Teacher Guide I. Introduction One of the most effective methods of describing motion is to use graphs of motions: graphs of position vs. time, of velocity vs. time and of acceleration vs. time. The CMA Motion detector together with the Coach software can be an effective means of teaching students to understand concepts of kinematics. Students use the Motion to measure the motion of simple common objects such as toy cars, dynamics carts, or the motion of the students themselves. The collected distance and time data can be displayed in digital and graphical form on the computer screen directly during the measurement. Students can further process and analyze the collected data using the tools offered in Coach. The available Coach activities allow students to take an active role in their learning and encourage them to construct physical knowledge from actual observations. II. Motion a USB Motion detector The Motion is an ultrasonic motion detector that connects directly to a computer through a USBport. It measures the distance between its detector and a (moving) object. The Motion transmits short pulses of high frequency sound (approx. 50 khz), then detects the reflected pulses. The Coach program measures the time between the transmitted and received pulse and using the speed of sound in air, it calculates the distance to the reflecting object. The Motion can accurately detect objects between 20 cm and 6 to 10 m, depending on the size, shape, orientation and surface of the object that is detected. 1 It detects the closest object in a roughly 18 cone. While the Motion is operating, a ticking sound is heard. ~18 Central axis Ultrasound Motion 1 The maximum detection distance of 10 m can only be reached under good conditions, i.e. for a large, flat surface that is perpendicular to the Motion. 5

6 The sampling frequency used in experiments with Motion is limited by the speed of sound in air (about 340 m/s): if e.g. a distance of 10 m is measured (such a large distance can only be measured for large, flat objects), the sound pulse takes about 59 ms to travel from Motion to object and back. This means that if a sample frequency of more than 17 Hz is used, a new sound pulse is emitted before the previous one is received, leading to erratic readings. The maximal frequency is also limited by the conditions of the experiment. Typical sampling frequencies are: 1 m range 40 Hz 2 m to 6 m range 25 Hz 6 m to 10 m range 10 Hz. Tips on getting good results with the Motion The Motion will report the distance to the closest object that produces a sufficiently strong echo. Objects such as chairs and tables in the cone of ultrasound can be picked up by the Motion. For accurate measurements the object should have a flat front perpendicular to the line between the Motion and the object. If the room in which the Motion is being used has a lot of hard, sound-reflecting surfaces, you can get strange effects, caused by the ultrasound echoes bouncing around the room. Standing waves can be set up between the Motion and a sound reflector. Try placing a cloth horizontally just in front of and below the Motion. This sometimes helps eliminate ultrasound that is "leaking" into the Motion. Check for a stationary object (chair, table, etc.) in the cone of the ultrasound beam. This object may be detected when you are trying to study an object further away, even smaller objects can cause this kind of problems. If you have trouble with a stationary object causing unwanted echoes, try placing a cloth over it. This minimizes the sound reflection. Also note that the cone of ultrasound beam extends downward from the center line. This can cause problems if you are using the Motion on a horizontal surface. In these cases, aim the Motion slightly tilted back or place it somewhat higher above the surface. If there is another source of ultrasonic waves in the same frequency range (like motors, fans, air track blowers, the sound made by air exiting the holes of an air track, and even students making loud noises), this can cause erroneous readings. If you are studying people moving, have them hold a large, flat object (e.g. a large book) as a reflector. If you have an irregular reflecting surface, the waves will sometimes be reflected back to the transducer, and sometimes not. The result will be erratic (spikes). 6

7 III. Software Coach 6 To use Motion you need Coach 6 Lite or Coach 6 version 6.25 or higher. The computer must have a free USB port, at least 256 MB of RAM and must run Windows 2000, XP or Vista. The first time a particular Motion is connected to a Windows computer (Windows 2000 or Windows XP) it will need to go through the process of installation hardware (Found New Hardware dialog). For this installation administrative rights are needed. Extensive information on working with Coach 6 Lite and Coach 6 can be found respectively in Guide to Coach 6 Lite and Guide to Coach 6 manuals, and in the on-line Coach Help System. Using Motion with Coach 6 To connect Motion to your computer simply plug its USB-plug into a free USB-port of the computer. When you work with Coach 6 Lite, you can start the program by automatic interface recognition. After Motion is detected, Coach 6 Lite starts in the folder Measurements with CMA Motion. Automatic interface detection can be switched off by right clicking the Coach 6 icon in the taskbar and selecting Stop. When you work with Coach 6, you have to open Coach via the Windows Start menu or by double-clicking a Coach Activity file (*.cma), a Coach Result file (*.cmr) or a Coach Project (*.cms). Coach 6 Activities The Project Measurements with CMA Motion included in Coach, offers a set of activities for studying some basic types of motion with Motion. For these activities students do not need advanced technical skills. The instructions are quite simple and their attention focuses on science investigations. Students store the results of their work in Result files of Coach. IV. Pedagogical background Teaching approaches In planning skills development, it is helpful for teachers to consider two types of student skills with software [6], [7]: 1. Operational skills which concern the manipulation of the computer hardware and knowledge of the features in the software. Exemplary operational skills, which are needed to perform activities with Coach and Motion are: students should be able to set up the equipment, to connect and use Motion and to be responsible for the equipment. 7

8 students should know how to work with the Coach program: start the program, open activity, make measurements, print information, etc. students should be able to use the information from graphs/diagrams: - read values from a graph; - zoom a part of a graph; - determine the scale of a diagram; - create a new graph; etc. 2. Procedural skills which concern the manner in which the software tools are employed in the lesson context for the purpose of achieving learning benefits. A dominant aspect of these skills is the development of an inquiring approach to the analysis and interpretation of data and to making links with previous knowledge. Exemplary procedural skills are: Observing the graph qualitatively; Reading values purposefully; Describing variables; Relating variables; Predicting new data; Applying mathematical description to data; Using the time bonus: by using a computer measurement system, it is easy to perform and repeat or modify experiments. It is important that students know how to exploit this spare time; Exploiting opportunities for new experiments; Active observation during real-time logging; Evaluating measurement quality; Analysing data using graphs. For the teacher, there are pedagogical skills which contribute to the effectiveness of the activities: 1. Clarity of learning objectives for each activity. 2. Understanding of the special value of the ICT method and exploiting its full potential in purposeful ways. 3. Managing the activity in a way which promotes appropriate rather than indiscriminate use of ICT. Learning benefits The following features of using Motion and Coach Activities are important to student learning: Students are able to watch the graph being drawn simultaneously on the screen as they perform the measurement moving carts or walking in front of the Motion. Displaying data as it is being collected reinforces the link between an experiment and its results, students get a better feeling for quantities like position, velocity, acceleration, and their changes. It helps them to understand the abstract graphs. Immediate feedback encourages critical thinking skills; students have more time to spend on observing and interpreting, discussing and analyzing data. They can simply repeat the experiments, change experimental conditions and explore the results of the changes. 8

9 By using the tools offered in Coach, students can process and analyze the collected data, and make calculations of other physical quantities like: velocity, acceleration, momentum, energy, etc. Students are actively involved in the learning process by having the possibility to make their own investigations. Properly performed student activities can help to improve students understanding of concepts of kinematics and overcome common student difficulties, like: Differentiating the concepts of position, velocity and acceleration. Confusing the graphical representations and motion paths of real objects e.g. plotting position and velocity as the path of motion. Distinguishing between slope and height of a graph. Separating slope from path of motion. Interpreting changes in height and changes in slope (e.g. when is the object slowing down, which motion is slowest). Understanding the physical significance of the sign of a body's velocity. Understanding that it is possible to have zero velocity and non-zero acceleration, or non zero velocity and zero acceleration. Understanding that the direction of acceleration relative to velocity determines whether an object speeds up or slows down. Understanding that a body can have a positive velocity and negative acceleration (or the reverse) simultaneously. The management of the classroom setting also has an important influence on the successful integration of activities. Students should perform the activities in small groups of three or four, allowing them to make their own investigations and at the same time discuss the results with peers. References: 1. Beichner, R. J., Testing student interpretation of kinematics graphs, American Journal of Physics, 62, 750, (1994) 2. F. M. Goldberg & J. H. Anderson, Student difficulties with graphical representations of negative values of velocity, Phys. Teach. 27, (1989). 3. R. F. Gunstone, Student understanding in mechanics: A large population survey, Am. J. Phys. 55, (1987) 4. Halloun & D. Hestenes, Common-sense concepts about motion, Am. J. Phys. 53, (1985). 5. McDermott, Lillian C., Mark L. Rosenquist & Emily H. Van Zee. Student difficulties in connecting graphs and physics: Examples from kinematics, American Journal of Physics, 55, 503, (1987) 6. Newton, L. & Rogers, L.T. Teaching Science with ICT. London: Continuum (2001) 7. Resource Guide, IT for US Project materials, 2007, 9

10 V. Guide through student activities This chapter describes each of the Coach activities included in the Coach project Measurements with CMA Motion. The description includes learning objectives, activity method, exemplary results, etc. Activity 1. How to use Motion LEARNING OBJECTIVES: Learn to use Motion Use Motion to measure distances to objects In this activity students learn how to use the Motion. They measure distances between the Motion and different objects. They measure how tall they are. Activity 2. Graphing distance LEARNING OBJECTIVES: Use Motion to measure the distance between objects and Motion Explore different graphs produced by walking in front of the Motion Interpret the resulting graphs Students are asked to walk in front of the Motion and a graph of distance vs. time is being plotted real-time on the computer screen during their motion. Students are asked to interpret resulting graphs. Questions about the graphical representations of fast, slow, away from and towards the motion detector are asked. In the second part of the activity students are asked to walk to create a motion graph which looks like a letter M, like the graph at the right. It is recommended that students save their data after each measurement. The default behavior of Coach is that when a measurement run is followed by another run, the data of the previous run is overwritten, and its graph becomes gray (it is only displayed on the screen). To keep previous runs active the option Copy Column should be used. This option is available after a measurement run, by right clicking the diagram or table. Activity 3. Understanding velocity LEARNING OBJECTIVES: Explore different graphs produced by a cart moving with a constant velocity in front of Motion Creating and interpreting a velocity vs. time graph Understanding the concept of constant velocity 10

11 Understanding the sign convention for velocities (what is the meaning of a negative velocity?) In this activity students are asked to record the distance vs. time graph of a cart moving with constant velocity. Based on the resulting graph they have to create the velocity vs. time graph and determine the velocity of the cart. The velocity can be determined in Coach in different ways: - by using the formula Delta(x)/Delta(time); 2 - by using the formula DeltaFil(x)/DeltaFil(time); 3 - by using the Slope option; - by using the Function fit option; - by using the Derivative option. To get a smoother graph it is better to use the Smooth Derivative variant. It could be useful to start analyzing a distance vs. time graph by using the Slope option and later to create a graph by using the function DeltaFil(x)/DeltaFil(time). Figure: Distance vs. time graph (top row) and velocity vs. time graph (bottom row) of a cart moving with a constant velocity. The velocity is calculated by using the Coach formula DeltaFil(x)/DeltaFil(time). The left column shows a movement away from the sensor, the right column a movement towards the sensor. 2 3 The Delta function calculates the difference between two successive values in the source column (in a forward sense). The DeltaFil function is a combination of the functions Delta(C) and Filter(C;n). For the filter interval n the fixed value of 2 is taken (in a forward sense). 11

12 Activity 4. Graphing velocity LEARNING OBJECTIVES: Exploring the distance vs. time and velocity vs. time graphs of a dynamics cart moving in a front of the Motion Interpreting the velocity vs. time graph Understanding the concept of changing velocity In this activity students are going to record distance vs. time and velocity vs. time graphs of a car which bounces between two limits set on the track. Such a set-up allows to record motions in two directions; when the cart bounces it changes the direction of its motion. In this activity the velocity vs. time graph will automatically appear on the screen, so students can directly focus on analyzing the different motions and their graphs. For analyzing both graphs at the same time the Scan option can be used. Figure: Motion graphs of the cart moving that bounce between two limits. The velocity is directly calculated by using SmoothDerivative function 4. Activity 5. Understanding acceleration LEARNING OBJECTIVES: Exploring the distance vs. time and velocity vs. time graph of a dynamics cart moving along an inclined track, in front of the front the Motion Creating and interpreting the acceleration vs. time graph Understanding the concept of constant acceleration (negative sign) 4 The Coach function DerivativeSmooth(x; ). 12

13 In this activity students are asked to record the distance vs. time and velocity vs. time graphs of a cart moving on an inclined track. Based on the resulting graph they have to create the acceleration vs. time graph and determine the acceleration of the cart. The velocity can be determined in Coach in different ways: - by using the formula Delta(v)/Delta(time); 5 - by using the formula DeltaFil(v)/DeltaFil(time); 6 - by using the Slope option; - by using the Function fit option; - by using the Derivative option. To get a smoother graph it is better to use Smooth Derivative variant. It could be useful to start analyzing the distance vs. time graph by using the Slope option and later to create a graph by using the function DeltaFil(v)/DeltaFil(time). Figure: From top to bottom: a distance vs. time, a velocity vs. time and an acceleration vs. time graph of a cart moving down on an inclined track. The acceleration is calculated by using the Coach formula DeltaFil(v)/DeltaFil(time). An interesting motion is that of a cart rolling up an inclined ramp, coming to rest, and rolling back down. The velocity and acceleration graphs are shown in the graphs on the next page. These graphs illustrate the advantages of tools that allow students to 5 6 The function Delta calculates the difference between two successive values in the source column (in a forward sense). The function DeltaFil is a combination of function Delta(C) and Filter(C;n). For the filter interval n the fixed value of 2 is taken (in a forward sense). 13

14 extend their observation beyond specialized cases such as uniform motion on a nearly frictionless track. When a toy car or a dynamics cart is used then the different slopes of the velocity graph on the way up and the way down, combined with the different heights of the acceleration of the acceleration graph, are convincing evidence for a frictional force that changes its direction when the cart reverses direction at the top. (The large accelerations at the begin and end points are the result of the cart being pushed up and hitting the barrier at the end). Figure: Motion graphs of the cart a cart rolling up an inclined ramp, coming to rest, and rolling back down. Additionally you can discuss with students how the motion graphs will look like when the friction force would be relatively low. Such a situation you can get when you use a heavy cylinder instead of a cart. Activity 6. Acceleration on an incline LEARNING OBJECTIVES: Recording motion of a cart moving along an inclined track Determining acceleration for different angles of inclination Calculating the gravitational acceleration, based on the measured angle and the respective measured acceleration Comparing the measured g values with the theoretical value In this activity students determine accelerations of the cart as it moves down on an inclined track for various angles of inclination. Two ways of measurement can be 14

15 compared: accelerations read directly from the acceleration graphs with the accelerations calculated from the slopes of portions of the velocity graphs. In the second part of the activity students use the collected height and acceleration data to calculate the gravitational acceleration g. The resulting experimental g values can be compared with theoretical value of g. Figure: Exemplary motion graphs of a cart moving along an inclined track. In the exemplary data above: the acceleration read from the acceleration vs. time graph is around 0.8 m/s 2 ; the acceleration determined from the slope of the portion of the velocity graph is circa 0.84 m/s 2 ; the acceleration determined by using function fit of the distance vs. time graph is 0.8 m/s 2. The length of the track is 1 m; the height of the track is 10 cm, so sinθ = For this data measured the calculated value of g is 8.2 m/s 2. Activity 7. Periodic motion LEARNING OBJECTIVES: Collecting position, velocity, and acceleration data during the periodic motion of a mass hanging on a spring Determining the period of oscillations Analyzing the relationship between a spring displacement and the period of oscillations 15

16 Analyzing the relationship between a spring s mass and the period of oscillations In this activity students record position vs. time, velocity vs. time and acceleration vs. time data of the periodical motion of a mass hanging on a spring. They interpret the resulting graphs and determine the period of the spring oscillations. Figure: Typical data recorded during the periodic motion. The Scan option allows studying the three motion graphs simultaneously. Activity 8. Match the graph x(t) LEARNING OBJECTIVES: Recording distance vs. time graphs of one s own walking Interpreting the distance vs. time graphs Matching the distance vs. time graph given on the computer screen In this activity students record motions of their own bodies. They walk in front of the Motion to match the distance vs. time graph given on the computer screen. At the right an exemplary distance vs. time graph to match is shown. The Activity offers 5 distance vs. time graphs under the yellow button Diagram. 16

17 Activity 9. Match the graph v(t) LEARNING OBJECTIVES: Recording velocity vs. time graphs of one s own walking Interpreting the velocity vs. time graphs Matching the velocity vs. time graph given on the computer screen In this activity students record motions of their own bodies. They walk in front of the Motion to match the velocity vs. time graph given on the computer screen. At the right an exemplary velocity vs. time graph to match. There are 5 velocity vs. time graphs available under the yellow button Diagram. Activity 10. Throwing a ball LEARNING OBJECTIVES: Recording of a motion of a ball travelling straight up and down Analyzing the resulting position vs. time, velocity vs. time, and acceleration vs. time graphs Determining the best fit equations for the position vs. time and velocity vs. time graphs Determining the mean acceleration from the acceleration vs. time graph In this activity students record and analyze the motion of a ball thrown straight upward. They interpret the recorded graphs and identify different regions of the ball motion in the graphs. They should discover that when the ball is at its highest point, its velocity is equal to 0 m/s and its acceleration is not equal to 0 m/s 2. The acceleration is approximately equal to the free fall acceleration. The acceleration can be determined from the motion equations: y = y 0 + v 0 t + ½ at 2 and v = v 0 + at. 17

18 Figure: Exemplary motion graphs of a ball thrown straight upward. The acceleration determined: - from the position vs. time graph by using a quadratic function fit is approximately 9.82 m/s 2 ; - from the velocity vs. time graph by using a linear function fit is approximately 9.82 m/s 2. The function fit was performed on a selected, free-fall part of the graphs. Activity 11. Bouncing ball LEARNING OBJECTIVES: Measuring the position of the bouncing ball Determining the collision speed and rebound speed of the ball Calculating the change of momentum Understanding the meaning of the coefficient of restitution. In this activity students investigate the motion of a ball which bounces on the floor directly under the Motion. Based on the distance vs. time graph, measured between the Motion and the ball, they have to create the position relative to the floor graph. This position can be calculated as the Motion to floor distance minus the measured distance between Motion and the ball. As a next step, students create and interpret the velocity vs. time graph and calculate the ball momentum before and after the collisions and the coefficient of restitution of the ball. 18

19 Figure: Exemplary data of a bouncing soccer ball; the Motion was positioned at m above the floor and the ball has a diameter of 0.22 m. The bouncing ball experiment can be used to illustrate many physical phenomena like motion, free fall, elastic and inelastic collisions and energy transformation. It is not the main issue of this experiment but it would be nice to discus how energy changes as the ball bounces - from gravitational potential energy, to kinetic energy, to elastic potential energy (in the ball), to kinetic energy, and back to gravitational potential energy. Activity 12. Air resistance LEARNING OBJECTIVES: Observing the effect of air resistance on falling objects Understanding the concept of air friction - air resistance Understanding the concept of terminal velocity In this activity students investigate and compare motions of two falling objects, a heavy object like a book and a light object like a balloon or paper coffee filter. Students interpret the velocity vs. time graph and try to explain why the heavy book falls faster than the balloon. Here the discussion about the acting forces and existence of the air resistance force should be activated (additional explanation is available in the activity). Finally students try to estimate the terminal velocity of the balloon as the book did not reach its terminal velocity yet. 19

20 Figure: Exemplary data: position vs. time (top row) and velocity vs. time graphs (bottom row). Left column: a falling book. At the end of its motion the book is still nearly in free fall, the air resistance force is very small compared to the weight of the book. Right column: a falling balloon. After 1.5 s the balloon stops to accelerate. Its velocity is nearly constant. The terminal velocity is about 1.1 m/s. The table below gives some relevant data for the objects used in the exemplary measurements, in case you want to build a model for these objects (to compare the model data with the experimental data). In this way you will be able to determine the air friction coefficient for these objects. Mass (kg) Area (m²) (perpendicular to direction of motion) Book Balloon

21 Student Activities Activity 1. How to use Motion The CMA Motion is a device to measure the position of objects. It sends out sound pulses that reflect from objects, such as a wall or your body. Based on the amount of time it takes the pulse to bounce back, Motion calculates the position of the object. Motion is able to measure distances from 20 cm up to 10 m. A very similar technique is used by bats to locate prey and other nearby objects. Bats emit a series of short, high-pitched sounds. These sounds travel out away and then bounce off objects and surfaces creating an echo, which returns to the bat. A bat can determine an object's size, shape, direction, distance, and motion. This technique is called echolocation and it is so accurate that bats can detect insects the size of gnats and objects as fine as a human hair. In this activity, you are going to learn how to use Motion. In your experiment you need Motion. 1. Make sure Motion is connected to the USB port of the computer. 2. Open Coach Activity 01. How to use Motion. 3. Put the Motion on a table with the detector facing up towards the ceiling. The Motion is taking readings when you hear it ticking; the computer displays the measured values. 4. Make sure there is nothing in the path of the signal coming out of detector. 5. Read the distance to the ceiling. 6. In a similar way try to measure: - the distance between a book placed above the detector. Remember Motion is not able to measure distances shorter than 20 cm; - the distance between the table and the floor; - your length; - the length of a classmate; - any distance you like. 7. Write down your measurements in the worksheet. 21

22 Measurement The distance between table and ceiling The distance between a book placed above the detector The distance between table and floor Your length Your classmate s length.. Measured distance

23 Activity 2. Graphing distance Motion graphs provide an opportunity to analyze changes in distance and time. For example in the diagram below you see a graph of a jogger running in 10 minutes. Can you tell what happened during her run? In this activity you are going to use Motion to record a motion graph. You will record a distance versus time graph of your own motion. In this experiment you need Motion. 1. Place Motion on a table so that there is an open path at least 2 meters wide and 3 meters long in front of it. During your walk you should face the sensor and must also be able to see the computer screen. 2. Open Coach Activity 02. Graphing distance. 3. First you are going to stand still in front of Motion for 10 seconds: - When you are ready let your classmate start the measurement. Motion is taking readings when you hear it ticking fast. As the detector takes readings, the computer produces a graph that shows your distance on the vertical axis and the time on the horizontal axis. - How far were you standing from the Motion? 4. Now you are going to move slowly towards the Motion. Before you start the measurement, draw a prediction of your distance versus time graph by using the option Sketch. Then take your position again. Let your classmate start a measurement, and when you hear Motion ticking fast, start to walk. - What was your initial position? - What was your greatest distance? - Was your predicted graph similar to the recorded graph? 5. Save the results of your work. 6. Repeat this experiment but now move more quickly; your initial position should be the same as in the previous measurement. - What was your maximal position? - Describe the difference between this and the previous graph. - Describe the difference between moving slowly and moving fast towards the Motion. 7. Save the results of your work. 23

24 8. Record motions graphs when you move slowly away and then quickly away from the Motion. For each measurement store the results. - Describe the difference between these two graphs. - Describe the difference between moving slowly and moving fast away from the Motion. - How these graphs different from the graphs made when you were walking towards Motion? 9. Now you are going to create a motion graph which looks like a letter M. See the exemplary graph displayed below. 10. Write down which steps (in time intervals) were necessary to create your M shape motion graph. Use words like: stand still, move forward/backward, move slow/fast. 11. Similarly, try to create a W - motion graph. 24

25 Activity 3. Understanding velocity Speed is a measure of how fast something is moving, for example a car can move with 80 km/h. Speed informs how the distance, traveled by a moving object, changes in a certain amount of time. In other words, it is the rate 7 at which distance is covered. Velocity is speed in given direction. Velocity can be expressed by the formula v = x/ t where: v = velocity (in m/s), x = distance covered (m), t = amount of time (s). In this activity you are going to determine the velocity of a cart which moves with a constant velocity. In this experiment you need: - Motion; - a cart which moves with constant velocity; - optional: a track as shown on the photo below. A possible set-up is shown below. 1. Place Motion on the table in front of a cart. Take care that the cart does not come closer than 20 cm to the detector. 2. Open Coach Activity 03. Understanding velocity. 3. Place the cart 20 cm from Motion, start the measurement and let the cart move away from the detector with constant speed. 4. Determine the velocity of the cart by creating a graph of velocity versus time. Discuss with your classmates how to do it. Tip: Calculate the velocity by using the following formula in Coach: 7 A rate is the change in a quantity divided by the amount of time for this change to take place. In other words, it tells how fast something is changing in a certain amount of time. 25

26 DeltaFil(x)/DeltaFil(time). Display the calculated velocity along the vertical axis, and time along the horizontal axis. 5. What was the velocity of the cart during its motion? What was its speed? Explain the difference between these. 6. Now you are going to record the motion when the cart is moving toward Motion; before you start the measurement predict the velocity versus time graph by using the option Sketch. 7. Place the cart circa 100 cm from Motion and let it move with constant speed towards the detector. - What was the velocity of the cart during its motion? What was its speed? - Describe the difference between this and the previous graph. - Explain the meaning of negative and positive velocity. 8. Explain the meaning of the slope of the distance-time graph. - How does the slope change during the motion of the cart? - What does this tell about its motion? 26

27 Activity 4. Graphing velocity Velocity versus time graphs give also information about the motion of an object. For example how fast an object is moving, in what direction, when it is slowing down or speeding up. In this activity you are going to analyze a velocity versus time graphs of a cart moving forth and back on a horizontal track. In your experiment you need: - Motion; - a dynamics cart with bumpers; - A track with bouncing limits. A possible set-up is shown on the picture below. 1. Open Coach Activity 04. Graphing velocity. 2. Place Motion on the table, or on a track, in front of a cart. Take care that the cart does not come closer than 20 cm to the detector. 3. You are going to record the motion of a cart when it bounces between two limits set on the track. 4. Give the cart a push and start your measurement. 5. Interpret your recorded motion graphs: - Describe how the position of the moving cart changes in time. - Describe how the velocity of the moving cart changes in time. (Read the initial, the maximum and the minimum velocity of the cart). - Was the velocity equal to zero at any moment during the motion? Explain. 6. Place the cart in a different position on a track. Start the measurement and give it a push in the other direction. 7. Interpret your recorded motion graphs: - Describe how the position of the moving cart changes in time. - Describe how the velocity of the moving cart changes in time. (Read the initial, the maximum and minimum velocity of the cart). - Was there any moment in the motion where the velocity was zero? Explain. - How does the slope of the velocity vs. time graph change during the motion of the cart? 27

28 8. Explain the meaning of the slope of the position-time graph. 9. Explain the meaning of the area under the velocity-time graph. 28

29 Activity 5. Understanding acceleration The state of motion of an object can be changed by changing its speed, by changing its direction of motion, or by changing both. Any of these changes is a change in velocity. The rate at which the velocity is changing is called acceleration; it is a measure of how fast the velocity is changing per unit of time. Acceleration can be expressed by the formula: a = v/ t where: a = acceleration (m/s 2 ), v = change of velocity (m/s), t = amount of time (s). In this experiment you will determine the acceleration of a dynamics cart as it moves on an inclined track. In your experiment you need: - Motion; - a dynamics cart; - an inclined track. If you do not have such a track you can simply stack a few books beneath a wooden board. A possible set-up is shown on the photo below. 1. Set up the track as shown on the photo. Motion should be placed at the top of the track pointing downward to the cart. The cart will move along the track in front of the detector. 2. Open Coach Activity 05. Understanding acceleration. 3. Hold the cart on the track 20 cm from Motion. Start the measurement and let the cart roll down. 4. Determine the acceleration of the moving cart by creating a new graph of acceleration versus time. Tip: calculate the acceleration by using the formula: DeltaFil(v)/DeltaFil(time). 29

30 Display the calculated acceleration along the vertical axis, and time along the horizontal axis. 5. What was the acceleration of the cart? 6. Now you are going to record the motion of the cart moving toward Motion. Before you start the measurement, predict the velocity versus time graph by using the option Sketch. 7. Hold the cart at the bottom of the track. Start the measurement and give the cart a push up the incline. - Describe the acceleration versus time graph. - Determine the cart s acceleration. - Describe how this graph differs from the previous graph. 8. Explain the meaning of the slope of the velocity versus time graph. - How does the slope change during the motion of the cart? - What does this tell you about its motion? 30

31 Activity 6. Acceleration on an incline In this experiment you will measure the acceleration of a dynamics cart as it moves down on an inclined track for various angles of inclination. From the data you collect you can determine the gravitational acceleration constant. In your experiment you need: - Motion; - a dynamics cart; - an inclined track which height can be changed. If you do not have such a track you can simply stack a few books beneath a wooden board. A possible set-up is shown on the picture below. 1. Set up the track as shown on a photo. Motion should be placed at the top of the ramp pointing downwards towards the cart. The cart will move along the track in front of the detector. 2. Open Coach Activity 06. Acceleration on an incline. 3. Measure the height and the length of you track and write down these values in the data table in your worksheet. 4. Hold the cart at the track 20 cm from the motion detector. Start the measurement and let the cart roll down. 5. Determine the cart s acceleration. Write down this value in your worksheet. 6. Increase the inclination angle, measure the height of the track and write down this value in your worksheet 7. Repeat your experiment. 8. Determine the cart s acceleration for this angle. Write down this value also in the data table in your worksheet. 9. Again increase the inclination angle and repeat the procedure described in steps The acceleration of a cart rolling down the inclined is related to the angle of inclination θ in the following way: 31

32 a = g*sin θ where g represents gravitational acceleration Based on your data, determine the gravitational acceleration constant. Tip: You can create a new graph of acceleration vs. sin θ. 10. How well does your measured value agree with g s theoretical value of 9.81 m/s 2? If your value is different, can you think of reasons for this? Length Height Calculated of the of the Determined gravitational track track sin θ acceleration acceleration (m) (m) a (m/s 2 ) g (m/s 2 ) 32

33 Activity 7. Periodic motion A periodic motion is a motion that repeats itself over and over again. Examples of such motions are: the motion of a pendulum or a swing, the motion of a bungee jumper, the motion of a spring. In this activity you are going to record motion graphs of the periodic motion of a spring and analyze how the displacement of the spring and the mass hanging on the spring influence the period of the motion. In your experiment you need: - Motion; - a spring; - hanging masses; - ring stand; - clamp. A possible set-up is shown on the picture to the right. Before you start the measurement, write down your hypotheses in your worksheet: When the spring displacement is larger, the period of oscillations will be: shorter, longer, or the same. When a mass hanging on a spring is heavier, the period of oscillations will be: shorter, longer, or the same. 1. Hang the spring vertically from a support rod and attach a mass (e.g. 50 g) to the spring. 2. Place Motion face up on the floor. 3. Open Coach Activity 07. Periodic motion. 4. Adjust the height of the support so that the mass does not come closer than 20 cm to the detector. 5. With the mass resting in its equilibrium position, right click the sensor icon on the Motion panel in Coach and click Set to zero to zero the detector. 6. Pull the mass straight down about 5 cm from its resting position and let it go. Make sure you pull the mass straight down otherwise it will swing around. 7. Start the measurement when you are ready. The fast ticking sound indicates that the Motion is collecting data. 8. Examine the position vs. time graph and the velocity vs. time graph. How do they differ? - What is the amplitude of the spring s oscillations? - What is the position of the mass when the velocity is maximal? - What is the position of the mass when the velocity is zero? 9. Determine the period of the spring s oscillations. 10. You will now repeat the measurement, but this time with a larger displacement. Repeat steps 4, 5, 6 and 8 pulling the mass down 10 cm instead of 5 cm. 33

34 11. What is the relationship between a spring s displacement and its period? Was your hypothesis correct? 12. You will now repeat the measurement, but this time with a heavier mass. Repeat steps 4, 5, 6 and 8, pulling the mass down again 10 cm. 13. Repeat the experiment for another mass. 14. What is the relationship between a spring s mass and its period? Was your hypothesis correct? 34

35 Activity 8. Match the graph x(t) In this activity you are going to walk to match several given distance-time graphs. In this experiment you need Motion. A possible set-up is shown on the photo below. 1. Place Motion on the table in front of you so that it points toward an open space at least 4 m long. To help you walk, mark the origin and the 1m, 2m, 3m and 4m distances from the Motion. 2. Open Coach Activity 08. Match the graph x(t). 3. In the diagram pane you see a distance (x) versus time (t) graph. - Describe the motion represented by this graph. - How do you have to walk to produce this graph? 4. Take the correct starting position. Let your classmate start the measurement. As soon as you hear the detector ticking fast, walk to match the shape of the graph. The graph will be drawn as you walk. If you are not successful, repeat the process until your motion matches the graph on the screen as well as you can. 5. Perform a second distance-time match. Press the yellow Diagram button and select the diagram Distance vs. time graph 2 from the list. Replace the old diagram by the new diagram. - Describe the motion represented by this graph. - How do you have to walk to produce this graph? 6. Take your position and start the measurement and walk to match this new graph. 7. Perform the third distance-time match in the same way. 8. Record your own distance vs. time graph by walking in front of the motion detector. Ask your classmate to walk your graph. Tip: First save your recorded data as a result, then use these data as a background graph in a newly created graph. 35

36 Activity 9. Match the graph v(t) In this activity you are going to walk to match several given velocity-time graphs. In this experiment you need Motion. A possible set-up is shown on the photo below. 1. Place Motion on the table in front of you so that it points toward an open space at least 4 m long. To help you walk mark the origin and the 1m, 2 m, 3 m and 4 m distances from the Motion. 2. Open Coach Activity 09. Match the graph v(t). 3. In the diagram pane you see a velocity (v) vs. time graph. - Describe the motion represented by this graph. - How do you have to walk to produce this graph? 4. Let your classmate start the measurement. As soon as you hear fast ticking, walk to match the shape of the graph. The graph will be drawn as you walk. If you are not successful, repeat the process until your motion matches the graph on the screen as well as you can. 5. Perform a second velocity-time match. Press the yellow Diagram button and select the diagram Velocity vs. time - graph 2 from the list. Replace the old by the new diagram. - Describe the motion represented by this graph. - How do you have to walk to produce this graph? 6. Start the measurement and walk to match the new graph. 7. Perform the third velocity-time match in the same way. 8. Record your own velocity vs. time graph by walking in front of the motion detector. Ask your colleague to walk your graph. Tip: First save your recorded data as a result, then use these data as a background graph in a newly created graph. 36

37 Activity 10. Throwing a ball From everyday experience you know that when you throw a ball up in the air, it will continue to move upward for a short time, stop momentarily at the peak, and then change direction and begin to fall. What is the acceleration of the ball at the top of its movement? Write down your hypothesis: At the top, the ball s acceleration =. In this activity you will record and analyze motion graphs of the movement of a ball thrown straight upward. In your experiment you need: - Motion; - a soccer ball, volleyball or basketball. A possible set-up is shown on the photo below. 1. Place the Motion on the floor facing up. 2. Open Coach Activity 10. Throwing a ball. 3. Hold the ball at least 20 cm above Motion. 4. When you are ready, let your classmate start a measurement. As soon as you hear the sensor ticking fast, toss the ball straight upward above Motion and let it fall back towards the ground. Catch the ball before it hits the Motion but stay out of the way of the detector signal. This may require some practice beforehand. 5. Examine the position vs. time, velocity vs. time and acceleration vs. time graphs: - Identify the region when the ball was being tossed but still in your hands; - Identify the region when the ball was freely moving up; - Identify the region when the ball was at its top position; - Identify the region when the ball was moving downward. - Identify the region when the ball was caught by you. 6. From the position vs. time graph, locate the maximum height of the ball during the free fall. Use the option Scan. 7. From the velocity vs. time graph: - Describe the way the velocity changes during the motion of the ball. - Determine the velocity of the ball at the top of its motion. 8. What was the acceleration of the ball at the top of its motion? 9. Find the free-fall acceleration of the ball during its motion. Tip: Use the Function fit option. The motion of a uniformly accelerated object can be described by the following equations y = y 0 + v 0 t + ½ at 2 and v = v 0 + at. First zoom the interesting region of the graph and then fit the zoomed region with the option Function fit. 10. How close is your measured value of the gravitational acceleration compared to the theoretical gravitational acceleration g = 9.81 m/s 2? List some reasons why your values for the ball s acceleration may be different from the accepted value for g. 11. Repeat the measurement for different balls. 37

38 Extra tasks: 1. Create graphs of the Potential Energy (E p ), Kinetic Energy (E k ), and Total Energy (E tot ). Use the position of Motion as the zero point of your gravitational potential energy. 2. How well does your data demonstrate conservation of energy? 38

39 Activity 11. Bouncing ball When a rubber ball is released from rest and allowed to bounce on the floor, the height to which the ball rebounds is typically less then its initial height. This is because some of the ball energy is dissipated as it collides with the floor. In this activity you are going to investigate bouncing. In your experiment you need: - Motion; - ring stand; - clamp; - a soccer ball, volleyball or basketball. A possible set-up is shown on the photo below. 1. Secure Motion to a ring stand using a clamp as shown on the photo. 2. Open Coach Activity 11. Bouncing ball. 3. Hold the ball circa 20 cm below Motion. 4. When you are ready, let your classmate start a measurement. As soon as you hear the sensor ticking fast, drop the ball and allow it to bounce up and down directly under the detector. 5. The graph displays the distance between the sensor and the ball. As you are interested in the heights of the bounces, then based on this graph you need to create a graph showing the distance between the floor and the bouncing ball. (Tip: height can be calculated as: distance between Motion and floor minus the measured distance between the sensor and ball). Create this graph. 6. Create the velocity vs. time graph. 7. What is the direction of the velocity before and after a bounce? 8. Calculate the momentum of the ball before and after a bounce. Tip: momentum can be calculated from the following formula: Momentum = mass * v 39

40 9. Repeat your measurements for different balls. 10. Which ball undergoes the greatest change in momentum after colliding with the floor? 11. You have seen that some balls bounce better than others. A particular ball can be characterized by its coefficient of restitution, the ratio of its rebound speed to its collision speed when it bounces off a hard, stationary, immobile surface. coefficient of restitution = velocity just after bounce / velocity just before bounce Calculate the coefficient of restitution of your bouncing balls. What is the coefficient of restitution of your best bouncing ball? The coefficient of restitution can be used to characterize the type of collision. A perfectly elastic collision has a coefficient of restitution of 1. In such collisions both momentum and kinetic energy are conserved. Perfect elastic collisions can only occur in reality on an atomic scale. An inelastic collision has a coefficient of restitution between 0 and 1. In such collisions only momentum is conserved, but kinetic energy is not. The kinetic energy can be converted into thermal energy (i.e. heat, as usually happens), or perhaps into elastic potential energy of deformation. This is the most common type of collision. A complete inelastic collision has a coefficient of restitution of 0. In such collisions two bodies stick together after impact. The loss of kinetic energy is large but not complete. 40

41 Activity 12. Air resistance On August 2, 1971 a demonstration was conducted by Apollo Astronaut David Scott on the Moon. He simultaneously dropped a heavy hammer and light feather from the same height (circa 1.6 m) above the moon's surface. Within the accuracy of the simultaneous release, both objects fell straight down and reached the Moon surface at the same moment. Does this phenomenon happen in the same way on Earth? Why not? Write down your hypothesis. In this activity you are going to perform a similar experiment and answer these questions. Instead of a hammer and feather you will use a book and a balloon. In your experiment you need: - Motion; - ring stand; - clamp; - a book; - a balloon or a suitable coffee filter. A possible set-up is shown on the photos below. 1. Support the Motion as high as possible (at least 2 m) above the floor, pointing downward. 2. Open Coach Activity 12. Air resistance. 3. Hold a book 20 cm under the Motion. 4. When you are ready let your classmate start the measurement and release the book so that it falls on the floor. 5. Describe the velocity-time graph. Determine the final velocity of the book. 6. Inflate a balloon. 7. Hold the balloon 20 cm below the Motion. 8. Start the measurement and carefully release the balloon. Note that the balloon should fall in a straight-line path below the detector. 9. Describe the velocity-time graph of the balloon s motion. Determine the final velocity of the balloon. 10. Compare the final velocities of both objects. 11. Explain why the book is falling faster than the balloon. Tip: What forces are acting on falling objects in air? Which factors influence these forces? 12. Because of air resistance, falling objects can reach a maximum constant velocity also called the terminal velocity. - Does the book reach its terminal velocity? - Does the balloon reach its terminal velocity? - For which object you are able to determine the terminal velocity? How do you know this? 41