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ICT for Innovative Science Teachers Leonardo da Vinci programme 2009-1-PL1- LEO05- 05046 Motion and Forces Motion is a feature of everyday life, whether it be walking, running, cycling, or travelling by road, rail or air, our daily experience is filled with motion. Scientists and engineers have devised numerous methods for measuring motion in a wide variety of contexts. To describe and calculate motion and to understand its causes, concepts of displacement, speed, velocity, acceleration and force are needed. CC 2011 ICT for IST This project has been funded with support from the European Commission under the Lifelong Learning Programme. This publication reflects the views only of the author, and the Commission cannot be held responsible for any use which may be made of the information contained therein. A. Introduction The theme of this module is the study of motion; how it may be measured, analysed and understood using simple experiments and mathematical models. To build an understanding, some basic concepts are required: displacement, speed, velocity, acceleration and force. The activities exploit the use of ICT to stimulate thinking about how these concepts are used to understand the motion of objects due to various forces acting on them. There are four types of activities: 1. Data logging: Four laboratory experiments: To record and analyse walking motion using a distance-time graph. To investigate the relationship between velocity and distance fallen for a card in free fall. To investigate the acceleration of a small trolley and its relationship with the force acting on it. To investigate the motion of a trolley rolling down a slope and rebounding due to the action of a spring buffer. 2. Video measurement: Four data-video activities: To measure and analyse motion of a free falling ball. To determine the acceleration due to the Moon gravity. To measure and analyse the motion of an accelerated car and to determine the force acting on the car. To investigate the motion of a badminton shuttlecock falling in the air and to determine its terminal velocity. 3. Simulation: Visual aids to assist understanding of the concepts of velocity, acceleration and force and the interpretation of the datalogging experiments involving motion: To study the motion of a ball moving in two dimensions. To investigate the motion of a trolley rolling down a slope and rebounding due to the action of a spring buffer. To investigate terminal velocity of a bicycle when a steady force is applied to the pedals. 4. Modelling: Models to show the relationship between velocity, acceleration and force in examples of uniform velocity, uniform acceleration and terminal velocity. Motion and Forces- 2 1. Background theory 1. BASIC CONCEPTS ABOUT MOTION When objects move, the rate of movement (described as the speed of the object) is defined as the distance moved per second. When the movement is considered in one direction in a straight line, the rate of movement is described as the velocity of the object. Thus: speed = distance travelled per second velocity = distance travelled in a particular direction in a straight line per second Velocity must be regarded as a vector quantity since it possesses both magnitude and direction. When an object travels at a steady (constant) speed in a straight line, its motion is described as uniform velocity. Any change of magnitude or direction of the velocity constitutes an acceleration, defined as the rate of change of velocity: acceleration = change of velocity per second Each of these is a calculation of a rate of change. They are „derived‟ quantities and, as such, are essentially abstract concepts. Their abstractness leads to difficulties for many pupils. The most common confusion is that between velocity and acceleration; it is very tempting to think that a fast moving object has a high acceleration. In the particular case of a swinging pendulum the exact reverse is the case; at the extremes of the swing where the pendulum momentarily comes to rest, the acceleration is a maximum; conversely, at the moment that the pendulum is moving at its fastest velocity, through its vertical position, the acceleration is actually zero. The essential idea to grasp is that acceleration is not about velocity, it is about changes of velocity. 2. THE CONCEPT OF FORCE Force is a fundamental concept in science and is widely experienced, however, it is very difficult to define. The problem is that, although we can personally feel forces when they directly push or pull our bodies, for bodies other than our own, we cannot see or feel forces; we can only detect them when we see their effects. Forces are only observable by their effects. A force can: • change the shape of an object, or • change the motion of an object, or • turn an object around When any of these effects are observed, we might conclude that they signal the presence of one or more forces. In nature there appears a variety of different types of force which are observable across a range of physical phenomena. The following names describe forces which arise in distinctive circumstances: elastic, gravity (weight), impact, electric, magnetic, nuclear, molecular, tension, compression, buoyancy, hydrostatic, friction, viscous, muscular. Although their origins might be very different physically, they are all capable of producing the same effects identified above. 3. BALANCED AND UNBALANCED FORCES Forces rarely occur as single forces. Pairs and multiples of forces are much more common. Paradoxically this often makes it difficult to detect Motion and Forces- 3 forces. It is very common for several forces to be acting on a body in a state of balance so that no net effect can be observed. For example, when a person is sitting on a chair, their body experiences a downward force of gravity (weight) which is counterbalanced by the upward reaction force of the seat which is supporting the body. Since these two forces are in a state of balance, there is no resultant force on the body and the normal effects produced by a force are not observed. Clearly, if one force is removed, (e.g. the chair is kicked away) the remaining force (weight) is unbalanced and the normal consequence of a force becomes painfully obvious! Thus the very common occurrence of balanced forces makes it often difficult to appreciate their presence and magnitude. Conversely, forces must be unbalanced for their effects to be observed. When several forces act on a body simultaneously, the total effect is called the RESULTANT FORCE. It is found by adding all the forces vectorially (i.e. with due regard to their direction as well as magnitude) on the body. Unbalanced forces imply a finite resultant force. Resultant force is not a type of force; it is simply the vector sum of the forces acting on a body. In a state of balance, the resultant force on a body is zero. It is incorrect to say that balanced forces cancel each other out. For example, the upward force of the seat does not cancel out my weight, it simply counter-balances it. It is preferable to speak of forces counterbalancing rather than cancelling each other out. 4. FORCE AND MOTION Forces are profoundly connected with the motion of objects. The absence or presence of motion, the magnitude of motion and the direction of motion all depend upon the resultant force. This connection is summarised in Newton‟s first two Laws of Motion: The First Law describes the situation for balanced forces: "When the resultant force on an object is zero, the object is either at rest or moving with a uniform velocity." The Second Law describes the situation for unbalanced forces: "An unbalanced force causes a change in velocity (acceleration) in proportion to the resultant force on the object" This second relationship can be expressed as an equation a F m where „a‟ is the acceleration produced by a resultant force „F‟ acting on an object of mass „m‟. The equation always describes the effect of the resultant force. If several forces are acting on the body concerned, it is essential that the resultant force is derived or calculated. Notice that the mass appears in the equation in such a way that it predicts the observation that larger masses experience smaller accelerations than smaller masses subject to the same resultant force. (The equation representing Newton's Second Law is usually written as "F = ma". This unfortunately tends to obscure the identity of the cause and Motion and Forces- 4 effect; the equation is better written as above which expresses the idea that acceleration is the effect of the force which is the cause.) 5. AIR DRAG AND TERMINAL SPEED As a free-falling object accelerates (downwards due to gravity), the drag force (caused by air resistance) acting on the object increases and its acceleration decreases. When the upward drag force (Fd) equals the downward force of gravity (Fg=mg), the resultant force on the object becomes zero and its acceleration becomes zero. At this point the object continues falling at a constant speed called terminal velocity. Terminal velocity varies directly with the ratio of gravity force to drag force. More drag means a lower terminal velocity, while increased weight means a higher terminal velocity. In motion through air the drag force is approximately proportional to the square of velocity: Fd k v 2 where k is a drag constant. The terminal speed for a human skydiver varies from about the 150 to 200 km/h. A parachute greatly increases the air resistance, so with an open parachute, terminal speeds can be cut down to 15-25 km/h which is enough to land safely. 6 . MEASURING MOTION Light gate method: A card of known width is attached to the object and the light gate is positioned so that the card cuts the light beam as the object moves. The computer measures the interruption time and uses this to calculate the velocity. If a double segment card is used, the computer can calculate the change of velocity and hence the acceleration. Motion sensor method: The sensor is positioned to reflect ultrasound pulses off a moving object. By detecting the echoes of the pulses from the object, the sensor enables the computer to calculate the distance of the object from the sensor. By continuously monitoring such distance measurements, a distance-time graph is plotted on the computer screen. Velocity and acceleration values and graphs may be derived from the plotted data. 7. GRAPHS OF MOTION Graphs may be plotted using measurements from a motion sensor. The two main types of graph are distance-time graphs (s-t) and velocity-time graphs (v-t) and great care is needed to distinguish which type is being dealt with. The features of the graph which convey physical meaning are shape, steepness (gradient), intercept, maxima, minima, and area. The basic measurements required for calculating speed, velocity or acceleration are those of distance and time. The experiments in this module use two types of sensor for making such measurements: the light gate (or photo gate) and the motion sensor (or motion detector). Motion and Forces- 5 s-t graph v-t graph A straight horizontal line represents a body at rest. A straight horizontal line represents a body moving with uniform velocity. A line sloping upwards represents a body moving away from an origin. A line sloping upwards represents a body accelerating. A line sloping downwards represents a body moving towards an origin. A line sloping downwards represents a body decelerating. A sloping straight line represents a uniform (steady or constant) velocity. A sloping straight line represents a uniform acceleration. A curve represents an acceleration. A curve represents a changing acceleration The area under a graph represents distance travelled. 2. Pre-requisite knowledge required Definitions of speed, velocity and acceleration 3. Science concepts developed in the module Concepts of force and mass Newton‟s Laws of Motion 1 and 2 Units for measuring all of the above quantities Fluid friction giving rise to terminal velocity Types of force: gravity causing weight and tension in string when stretched Motion and Forces- 6 B. Didactical approach 1. Pedagogical context The activities here concern basic concepts related to motion and its causes through the application of forces. Since motion is a common everyday experience, there are numerous contexts which may call upon basic concepts for understanding. For example: Walking Cycling Transport Sport 2. Common student difficulties Confusion between 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 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 Belief that the motion implies a force (so no movement means no forces) Many students assume a linear relationship between force and velocity Vectorial addition of forces Using the concept of resultant force in the Laws of Motion Acceleration in free fall is independent of mass The presence of friction obscures evidence for the First Law of Motion Motion and Forces- 7 REFERENCES: 1. Beichner, R. J., Testing student interpretation of kinematics graphs. American Journal of Physics, 62, 750, (1994) 2. F. M. Goldberg and J. H. Anderson, Student difficulties with graphical representations of negative values of velocity, Phys. Teach. 27, 254-260 (1989). 3. R. F. Gunstone, Student understanding in mechanics: A large population survey, Am. J. Phys. 55, 691-696 (1987 4. A. Halloun and D. Hestenes, Common-sense concepts about motion, Am. J. Phys. 53, 1056-1065 (1985). 5. McDermott, Lillian C., Mark L. Rosenquist, and Emily H. Van Zee. , American Journal of Physics, 55, 503, (1987) 3. Evaluation of ICT This section considers some of the practical arrangements for exploiting the use of ICT to best effect, and discusses the qualities of the ICT methods which make a special contribution to students‟ learning. DATA-LOGGING A previously described, there are two main types of sensors useful for measuring motion; the light-gate and the ultrasonic motion sensor. The former gives discrete measurements whilst the latter delivers a continuous stream of data which may be immediately plotted on a distance-time graph in real time. Each illustrates how data-logging enhances the value of practical experiments beyond the limitations of conventional methods. The software program can perform instant calculations to make available the derived quantities of velocity and acceleration. It can also present graphs in real-time and offer a range of analysis tools which assist the exploration and interpretation of the collected data. Activity 1. Analysing motion This data-logging experiment introduces the motion sensor in an informal manner which has proved very successful with younger and secondary age pupils. As the pupil walks forwards and backwards in front of the sensor, the immediate display of the distance-time graph allows the pupil to associate clearly the shape of the graph with the type of motion. The intimate connection between the personal Motion and Forces- 8 movement and the data appearing on the screen provides a compelling experience for the pupil, which has excellent potential for developing skills with graphs: With suitable prompting from the teacher, the pupil may be led to understand better how to interpret the shape of the graph. A valuable extension activity consists of displaying a pre-set graph on the screen and then asking the pupil to move in such a way that the data from the sensors produces a similar graph. Activity 2. Free fall In this data-logging experiment a light gate is used which provides very accurate time measurements. As a card passes through the gate, a light beam becomes interrupted, and the time for the interruption may be used to calculate velocity and acceleration. The calculation is done automatically by the program such that values for velocity become instantly available. In effect the light gate system becomes a „velocity meter‟ which is a great advance on methods that employ manual calculation. Thus the thinking activity of the experiment can clearly focus on a relationship between variables, rather than upon the procedure of obtaining data. In the experiment on free fall, students can quickly obtain a series of readings for the velocity of the card and relate these to the height fallen in each case. Activity 3A. Force and acceleration (using Insight ILOG) In this experiment, the double segment card placed on the trolley allows the calculation of two velocities in rapid succession so that acceleration may be calculated. The activity of the experiment is then to investigate the relationship between the acceleration of the trolley and the force causing the acceleration. The expected results should match Newton‟s Second Law of Motion. In both experiments, the prompt display of graphs and the use of curve fitting tools allow trends to be evaluated and measured. Motion and Forces- 9 Activity 3B. Force and acceleration (using Coach 6) In this experiment the force sensor is attached to the trolley. The string runs from the force sensor, over a pulley, to a hanging mass. The force sensor measures the tension force. The motion detector records the motion of the trolley as the string pulls it. Such set-up allows delivering a constant force to the cart via the string and hanging mass. The experiment is then repeated for different hanging masses. The activity of the experiment is then to investigate the relationship between the acceleration of the trolley and the force causing the acceleration. The expected results should match Newton‟s Second Law of Motion. In both experiments, the prompt display of graphs and the use of curve fitting tools allow trends to be evaluated and measured. Activity 4. Rebounding trolley In this data-logging experiment the motion sensor is used to monitor the motion of a trolley. As in the first experiment, the distance data appears on the screen as a continuous stream giving a smooth distance vs. time graph. For the rebounding trolley, the graph shows distinctive features which can be associated with motion down and up the runway, and points where the trolley either comes to rest or collides with the spring buffer at the bottom of the runway. At any point on the graph the gradient indicates the velocity which can be measured using the gradient tool. The program can also calculate and plot a further graph showing velocity vs. time. Motion and Forces- 10 Careful examination of this shows that the velocity after rebound is slightly less than the velocity before. The gradient of this graph indicates acceleration which is shown to be different for motion up the slope compared with motion down the slope. The difference may be accounted for by considering the role of friction. VIDEO MEASUREMENT In the video-measurement activities students are able to consider events, which happen outside the classroom. The position and time data are collected in the selected video frames manually by clicking, or automatically, by tracking a selected moving object e.g. a ball. The video data can be displayed in graphs and tables and can be used for further analysis and processing. Graphs and tables are synchronized with the video frames. When scanning the data in the graph the corresponding video frames are shown. This helps students to bridge the gap between the concrete visual display of a motion event and its abstract graphical representation. Activity 5. Falling ball The video of the ball dropped from a ladder allows analyzing the motion of a free falling ball. Before the measurement the perspective distortion has to be corrected and distance calibration has to be performed. During the measurement the vertical position data are plot immediately and are used to determine the velocity and acceleration of the falling ball. In this measurement measurement results. the manual measurement Motion and Forces- 11 gives more accurate Activity 6. Moon jump The events analysed via video measurements can be more unusual. In this activity such example is used, the jump on the Moon. Based on the video measurements students determine the acceleration due to the Moon gravity. Activity 7. Find a force In this activity students measure the position of the moving car. They determine its acceleration and the acting force. Activity 8. Falling shuttlecock This activity makes use of the video clip recorded with a high-speed digital camera. Such camera is useful in cases where motion is too quick for recording with a normal digital camera or webcam, e.g., data collection of human and animal locomotion or motion in sports. The video clip used in this activity shows the motion of the free falling badminton shuttlecock in which the effects of air resistance are important and measurable. Students investigate the motion and have to explain how a constant terminal velocity is reached. The video clip reveals the small but for the required accuracy substantial problem of perspective distortion. In the prepared video the perspective correction is already applied. Picture at the right shows the experimental setting after the correction of perspective distortion. Motion and Forces- 12 SIMULATION The simulations presented here are best used as teacher demonstrations for facilitating class discussions of the concepts involved. Their use needs to be carefully managed and integrated with discussion in order to develop clear logical thinking. Random clicking on the various program features is unlikely to benefit thinking about subtle concepts, about which pupils often have very confused ideas, so a structured approach is essential. The simulations for this module have been chosen to illustrate the power of this type of program to facilitate discussion leading to an understanding of abstract concepts. They provide visualisations of examples of motion which may be imagined in real life, but the software allows experimentation well beyond what is feasible in reality. Activity 9. Rolling ball This simulation can promote thinking about the independence of the vertical and horizontal components of motion when a body is moving in two dimensions. The vertical acceleration of the ball is demonstrated to be the same irrespective of its horizontal velocity, making the „fall time‟ always the same. Similarly, the ball‟s horizontal velocity remains constant throughout the whole trajectory before reaching the ground. The effect of the magnitude of horizontal velocity on „roll time‟ may be studied by setting different initial values. When the bounce condition is switched on it becomes harder to study time values but the graph of vertical velocity shows the reversals and decay of velocity. Activity 10. Rebounding trolley This simulation is a virtual version of the data-logging experiment 4. The graph initially shows the distance vs. time data. As with the experiment, the features of the graph may be associated with the to-and-from motion of the trolley, but with the additional visual aid in the Scene window. Dragging the cursor across the graph shows very clearly the correspondence between the trolley motion and the graph. Analysis of the graph can follow similar lines to that of the data collected in the experiment: show derived graphs for velocity and acceleration and think about how they are related to each other. The simulation also offers a view of the variation of the friction force during the motion of the trolley. When the model for the simulation is visible, the physical basis for the calculations may be explored and further investigations are possible through varying the slope angle and friction constant. These activities will be discussed in the „Modelling‟ Activity 14 below. Activity 11. Terminal velocity This simulation can be a useful tool for discussing the validity of Newton‟s laws of Motion which seem to be contradicted in many natural situations in everyday life, largely due to the invisible presence of friction. In this example of pedalling a bicycle, it is clear that, having obtained some speed, if the cyclist stops pedalling, motion does not continue with uniform velocity, as predicted by the First Law. Of course this is a false conclusion because the force of friction has Motion and Forces- 13 been ignored; the law requires thinking about the resultant of all forces acting on the cyclist in the direction of motion. Similarly, when pedalling with a steady force, the bicycle does not experience a steady acceleration as predicted by the Second Law. Again, this is a false conclusion due to the neglect of friction. The simulation shows that, for a given pedalling force, there is an initial period of acceleration as predicted by the Second Law, but the rate of acceleration diminishes as the opposing friction force reaches parity with the pedalling force making the resultant force zero. At this stage the bicycle reaches a steady velocity as predicted by the First Law. This steady velocity is usually called „terminal velocity‟. The dynamic character of the frictional force, increasing with velocity, is well illustrated using the simulation; graphs of velocity, acceleration, pedalling force and friction force may be readily compared. MODELLING The purpose of the modelling activities is to give pupils an insight into the physical and mathematical basis of the calculations performed by the model. The essence of modelling is to experiment with adjusting the model so that it gives results which best match data from real experiments. The results from the models may be compared directly with those obtained from the data-logging activities and simulations. Activity 12. Free fall The model is based upon the simple assumption that the acceleration of an object freely falling due to gravity is constant. From this, calculations are made of velocity and vertical distance using the basic definitions of their relationships with time. In the Insight modelling system the first formula calculates the change of velocity Δv during the time interval Δt: v where a t a is the acceleration (due to gravity) The second formula calculates the change of vertical distance Δs during the time interval Δt: s where v t v is the current value of velocity. Motion and Forces- 14 The Insight calculates these changes in repeated cycles and automatically updates the values of v, s and t in each cycle by summing the respective changes. As the model runs, velocity increases linearly, but the distance increases non-linearly. The graphs may be explored by finding gradients: the gradient of the velocity-time graph indicates acceleration; the gradient of the distance-time graph indicates velocity. Use of the cursors allows values to be conveniently compared. In the Coach 6 modeling system the change of vertical position y and the change of velocity v of a moving object are found by numerical integration of equations: v dy dv and a= dt dt By using the acceleration due to the moon‟s gravity (which can be determine experimentally in the Activity 6) model can be modified to observe a fall on the moon. In both systems the data generated by the model is usefully compared with the results for the falling card in Activity 2 or with the results for the falling ball in Activity 5. The relationships represented in the model illustrate the physical principles which govern the motion of falling objects. This is an example of how the methods of data-logging, video measurements and modelling can provide complementary learning experiences. Activity 13. Force and acceleration This model builds upon the previous model for free fall, but in this case the acceleration „a‟ is not assumed to be constant but is calculated from the resultant force „F‟ acting on the object of mass „m‟: a F m This is no less than Newton‟s Second Law of Motion. The model generates data in a similar way to the previous model, except that in this case the mass of the object and the resultant force acting on it may be specified freely. Again the model invites comparison with data collected in a real Motion and Forces- 15 experiment, in this case Activity 3a and 3b where a trolley is pulled by a constant force in the string. Activity 14. Rebounding trolley This model is yet a further development of the previous models. The newly introduced factor here is a second force, that of friction, in addition to the component of gravity causing the trolley to roll down the slope. There are two interesting features of the frictional force: it varies with the speed of the trolley and its direction changes, always opposing the motion of the trolley. Both of these features are implicit in the formula for calculating the force of friction „Ff‟: Ff where c v c is a constant representing the degree of friction v is the velocity of the trolley The component of gravity down the slope is calculated thus: Fs where mg sin(b) m is the mass of the trolley g is the strength of gravity b is the angle of the slope To calculate acceleration, the Resultant force must be calculated as Fs + Ff. This model complements the data-logging experiment in Activity 4 and the simulation in Activity 10 and similar activities for investigating the data may be used. Those activities become extended by exploiting the possibility of choosing different values for the angle of slope, the strength of gravity and the mass of the trolley. As with previous models, this model illustrates the physics principles involved in the motion of the trolley; a complex problem is broken down into simple stages. Activity 15. Terminal velocity As with the previous model, two forces are applied to the object requiring the resultant force to be calculated before calculating the acceleration. In Insight the model is similar to the one employed in the simulation of the bicycle Activity 11 in which a constant force is applied to the pedals and is opposed by the force of air resistance (fluid friction). The latter force (Ff) is assumed to depend upon the square of velocity: Ff k v 2 where k is a drag constant As with activity 11, both the acceleration phase and terminal velocity phase may be explored by studying the graphs. The resultant force is seen to follow the same pattern as the acceleration, becoming zero when terminal velocity is established and negative when velocity reduces. The frictional force increases and decreases according to the velocity, but changes are amplified compared with changes in velocity, a result to be expected as the force depends upon the square of velocity. Motion and Forces- 16 The Coach 6 model can be used to compare theoretical predicted data with experimental data from Activity 8 in which the motion of the free falling shuttlecock, where the effects of air resistance are important, is recorded. During the fall of the shuttlecock two forces act on it: the gravitational force and the drag force depending on the shuttlecock‟s velocity. There are two types of drag possible: - linear drag Fdrag - quadratic drag Fdrag k v , or k sign(v ) v 2 where k is a drag constant. Students investigate which model better match the experimental data. Once again, the modelling activity complements the data-logging and simulation activities, each method providing different insights and opportunities for learning. 4. Teaching approaches The three groups of activities presented here offer distinctive but complementary insights into the science involved in this topic. For the activities to be effective for teaching and learning, it is helpful for teachers to consider two types of skills in using the software tools: Operational skills which concern the manipulation of the computer hardware and knowledge of the features in the software. 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. Such skills are important for the preparation of pupils for the activities, and the activity sheets below each contain indications of the skills needed for the particular activity. For the teacher, there are further 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. To manage the activity in a way which promotes „appropriate‟ rather than „indiscriminate‟ use of ICT. 4. To integrate the learning from each activity to develop pupils‟ understanding of the topic. The development of the last of these is a particular aim of the ICT for IST Project, and the activities presented below have been specially selected to illustrate how integration might be achieved. The different types of activities are intended to be complementary both to each other and to further practical activities away from the computer. Teachers Motion and Forces- 17 will usually have their preferred sequence of teaching themes involving, demonstrations, explanations, class experiments, but the table below suggests a suitable Teaching sequence sequence exemplifying a logical development of concepts. The right hand column shows how the activities in this module may be chosen to enhance the teaching sequence ICT for IST Activities Define concepts of speed and velocity from distance and time * Experiments measuring distance and time to calculate speed D-Logging:1 Record walking motion Define acceleration Discuss gravity and free fall * Observe independence of vertical and horizontal components of motion Simulation: 9 Rolling ball D-Logging: 2 Investigate free fall Model: 12 Uniform acceleration *Experiment to investigate the relationship between the force on an object and the resulting acceleration. Introduce concept of mass and inertia D-Logging: 3 Force acting on a trolley Model: 13 Force, mass and acceleration *Experiment to study the effect of an object‟s mass on its acceleration Introduce the effect of frictional forces Define Resultant force * Experiments with runways to compensate for friction Introduce concept of terminal velocity D-Logging: 4 Rebounding trolley Simulation: 10 Rebounding trolley Model: 14 Rebounding trolley Video measurement: 10 Terminal velocity Simulation: 11 Terminal velocity Model: 15 Terminal velocity The non-computer experiments (*) are not described here, since their details are well established in conventional teaching schemes and text books. Motion and Forces- 18 Comparisons of the observations and results of each activity form a central role in this integration process. For example: Compare the graphs obtained in the data-logging experiments; a velocity-time graph may be derived from the slope of a distance-time graph; acceleration is indicated by the slope of a velocity-time graph; Compare the results from the simulations and data logging experiments to make links between the results of experiments and their theoretical explanation. In these, the graph is a key tool in facilitating comparisons and interpretations and skills with graphs generally provide a common thread in exploiting ICT for IST activities. In several cases, the graph is a key tool in facilitating comparisons and interpretations and skills with graphs generally provide a common thread Activity Data-logging 1 & 3B, 4. Motion sensor graphs 2 & 3A. Light gate measurements Video measurement in exploiting ICT for IST activities. The management of the classroom setting also has an important influence on the successful integration of activities. For this module, in view of the fact that an understanding of motion requires clear thinking about several interrelated concepts, we suggest that the teacher needs to provide a strong guidance structure in the use of the activities. Most teachers will achieve this through didactic demonstrations linked with whole class discussion. However, there are still opportunities for follow-up work (reinforcement, extension, revision etc.) by pupils working individually or in pairs or in groups. Again, it is usually advisable to provide a structure for activities using some of the worksheet suggestions. In both planning and teaching, it is important to have clear learning objectives for the use of the activities, and to assist this, the table below summarises their distinctive potential learning benefits. Potential learning benefits, ‘ICT value’ Graph of distance vs. time is displayed during experiment Changes are observable immediately. Graph analysis tools facilitate detailed investigation of data. Instant calculations of velocity and acceleration Allows detailed analysis of the motion of moving objects. 6. Moon jump A graph of position versus time is created during the measurement. This graph can be used for calculating the velocity and the acceleration. 7. Find a force Graph analysis tools facilitate detailed investigation of data. 8. Falling shuttlecock The motion of a moving object can be easily compared with its graphical representations. 5. Falling ball Motion and Forces- 19 Simulation 9. Vertical & horizontal motion 10. Rebounding trolley Animated graphics provide visualisation of the abstract concepts involved in analysing motion: - Independence of vertical and horizontal components of motion in two dimensions - Relating graph features to motion events 11. Terminal velocity - The distinction between velocity and acceleration Modelling The models demonstrate how the relevant physical principles can be expressed in simple stages using mathematical formulae. They help to break down complex physical phenomena into simple understandable stages. 12. Free fall 13. Force and acceleration - The role of friction in interpreting the Laws of Motion 14. Rebounding trolley The models calculate data which may be compared with data obtained from the real experiments (data-logging) with circuits. 15. Terminal velocity The effect of altering parameters such as air resistance, gravitational field strength, friction may be investigated. Model 1 shows how basic definitions of velocity and acceleration can be related to experimental data. Model 2 illustrates how Newton‟s Second Law of Motion can be used for predicting motion. Models 3 and 4 illustrate the role of dynamic friction in motion. Motion and Forces- 20 5. Resources for Student Activities USING INSIGHT SOFTWARE Activity 1. Data-logging Software program Insight iLOG Files available 1. walking set up 1. walking data (sample data) 2. Data-logging Insight iLOG 2. free fall set up 2. free fall data (sample data) 3. Data-logging Insight iLOG 3. acceleration set up 3. acceleration data (sample data) 4. Data-logging Insight iLOG 4. rebounding set up 4. rebounding data (sample data) 9. Simulation Simulation Insight 9. rolling ball simulation 10. Simulation Simulation Insight 10. rebounding simulation 11. Simulation Simulation Insight 11. terminal simulation 12. Modelling Simulation Insight 12. free fall model or Insight iLOG 13. Modelling Simulation Insight 13. acceleration model or Insight iLOG 14. Modelling Simulation Insight 14. rebounding model or Insight iLOG 15. Modelling Simulation Insight 15. terminal model or Insight iLOG Motion and Forces- 21 USING COACH SOFTWARE Activity Software program 1. Data-logging Coach 6 Files available 01.Analysing motion.cma (activity file) 01.Analysing motion.cmr (result file) 2. Data-logging Coach 6 02.Relation between velocity and distance fallen for a card in free fall.cma (activity file) 3. Data-logging Coach 6 03.Force causes acceleration.cma (activity file) 03.Force causes acceleration.cmr (result file) 4. Data-logging Coach 6 04.Rebounding trolley.cma (activity file) 04.Rebounding trolley.cmr (result file) 5. Video measurement Coach 6 05.Falling ball.cma (activity file) 6. Video measurement Coach 6 7. Video measurement Coach 6 8. Video measurement Coach 6 12. Modelling Coach 6 13. Modelling Coach 6 13.Model of force and acceleration.cma (activity file) 14. Modelling Coach 6 14.Model of a rebounding trolley.cma (activity file) 15. Modelling Coach 6 15.Model of terminal velocity.cma (activity file) 05.Falling ball.cmr (result file) 06.Moon jump.cma (activity file) 06.Moon jump.cmr (result file) 07.Find a force.cma (activity file) 07.Find a force.cmr (result file) 08.Falling shuttlecock.cma (activity file) 08.Falling shuttlecock.cmr (result file) 12.Model of free fall.cma (activity file) 15.Model of terminal velocity - linear.cmr (result file with experimental data) 15.Model of terminal velocity - quadratic.cmr (result file with experimental data) Motion and Forces- 22 EQUIPMENT AND MATERIALS FOR DATA-LOGGING ACTIVITIES Computer Software – See table above Interface (data-logger) Light gate. motion sensors, force sensor Dynamics trolley Runway Adjustable masses, string, pulley in clamp Black card and scissors Clamps and stands Low voltage fan and power supply Motion and Forces- 23 C. Student Activities ACTIVITY 1. ANALYSING MOTION Learning Objectives: 1. To obtain distance-graphs of pupils‟ motion as they walk in front of a motion sensor. APPLIED ICT TECHNOLOGY: DATA LOGGING 2. To relate the shape of the graphs to the motion which produced them. STUDENT LEVEL: AGE 14-17 3. To obtain measurements for finding velocity from the graph. 4. To derive a velocity-time graph from data for distance. RECOMMENDED SETTINGS: STUDENT ACTIVITY IF ENOUGH EQUIPMENT IS AVAILABLE, OTHERWISE TEACHER DEMONSTRATION Operational Skills: Connecting sensors and interfaces Choosing logging parameters Starting and finishing real-time logging Using the cursor tools for obtaining measurements from the graph Changing the designation of the graph axes Deriving secondary data by calculation Procedural Skills: Evaluating measurement quality Analysing data using graph Reading values/slopes Materials: Interface (data-logger) Motion sensor Stand and clamp Motion and Forces- 24 Activity method: 1. Set up the motion sensor clamped to a stand at chest height as shown. Take care that there is an open path at least 2 metres wide and 3 metres long in front of it. 2. Set the data logging software to record distance for about 30 seconds. 3. Starting from about 30 cm from the sensor, start recording data. The motion sensor is taking readings when you hear it “ticking” fast. First stand still then move forwards and backwards. 4. Observe the graph and relate it to the original motion. 5. Obtain other graphs which represent different types of motion such as steady speed and acceleration. Analysing activities (using Insight iLOG): 1. Sweeping cursors After the experiment, the real-time experience can be re-lived to a certain extent using the graph cursors and bar display: Drag the X cursor slowly across the screen, and note how the bars grow and shrink in the same manner as the changes of the values recorded during the experiment, creating an „action replay‟ effect. 2. Taking measurements from the graph Use the cursor to find the furthest distance recorded by the sensor. Then take measurements to find the distance moved in 1 second at different places on the graph. 3. Calculate speed Measure the gradient of the graph line to find the speed of movement at different times during the experiment. Questions and Assignments (using Coach 6): Describe how the distance between you and the sensor changes with time. Read out the initial, smallest and the greatest distance from the sensor. Describe the motion graph shape. Explain the significance of the slope of the distance-time graph. How does the slope change during the motion of the cart? Motion and Forces- 25 What does this tell you about its motion? Measure the slope of the graph line (use the Slope option) to find the velocity of movement at different times during the experiment? Create a motion graph which looks like a letter M? 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. Analysing activities (using Coach 6): Students walk in front of the motion sensor 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. 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 behaviour 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. Further work: Use the software to derive a graph of speed against time. Record a graph for walking at a steady speed, then look carefully at the speed graph for evidence of your reciprocating leg movement whilst walking. Motion and Forces- 26 ACTIVITY 2. RELATIONSHIP BETWEEN VELOCITY AND DISTANCE IN FREE FALL Learning Objectives: 1. To obtain a graphs of velocity against height fallen for a weighted card falling vertically. 2. To interpret the graphs so as to describe the relationship between the velocity of the card and the height fallen. 3. To investigate the effect of the mass or the shape of the card on the final velocity. APPLIED ICT TECHNOLOGY: DATA LOGGING STUDENT LEVEL: AGE 14-17 RECOMMENDED SETTINGS: STUDENT ACTIVITY IF ENOUGH EQUIPMENT IS AVAILABLE, OTHERWISE TEACHER DEMONSTRATION Operational Skills: Connecting sensors and interfaces Choosing logging parameters Managing the collection of timing data Using the cursor tools for obtaining measurements from the graph Procedural Skills: Evaluating measurement quality Analysing data using graph Reading values/slopes Materials: Interface (data-logger) Light gate sensor Black card weighted with two blobs of plasticine Ruler (1 metre) Stand and clamp Motion and Forces- 27 Activity method: 1. Assemble the apparatus so that the lightgate sensor is about 20cm above the bench. 2. Hold the card 10 cm above the sensor, set the software to record velocity and release the card. Note the velocity and enter the height fallen against this value in the table. Repeat this four times for the same starting height. 3. Repeat the whole process several times, dropping the card from different heights. 4. Observe the graph of velocity against height fallen. Analysing activities (using Insight iLOG): 1. Observe the graph Use the cursor to study how the values vary from one point to the next. Is there a simple pattern in the results? 2. Fit a line to the points Use a best-fit line to pass through all the points and identify the formula which describes this line. 3. Search for a pattern in the results Theory predicts that velocity varies according to the square root of height. Test this by building a formula to calculate the square root of height and plot these values on a new graph against velocity. A straight line confirms the theoretical prediction. Questions and Assignments (using Coach 6): Use the Scan option to study how the values vary from one point to the next. Is there a simple pattern in the results? Does the card fall twice as fast if you drop it from twice the height? What is the relationship between the velocity and the height fallen? Use a best-fit line to pass through all the points and identify the formula which describes this line. Theory predicts that velocity varies according to the square root of height. Test this by building a formula to calculate the square root of height and plot these values on a new graph against velocity. A straight line confirms the theoretical prediction. Motion and Forces- 28 Analysing activities (using Coach 6): In this activity the time interval of the black card passing along the light gate is measured. The velocity is calculated based on this measured interval and the length of the card. In Coach Activity it is assumed that the card has 10 cm length. The respective dropping height has to be typed in. Students investigate how the velocity of the card depends upon the height it falls. Motion and Forces- 29 Activity 3A. INVESTIGATING FORCE AND ACCELERATION (USING INSIGHT iLOG) Learning Objectives: 1. To obtain a graph of acceleration against force for a trolley pulled by string attached to a falling mass. 2. To interpret the graphs so as to describe the relationship between the acceleration and the force causing it. 3. To investigate the effect of the mass on the acceleration. APPLIED ICT TECHNOLOGY: DATA LOGGING STUDENT LEVEL: AGE 14-17 RECOMMENDED SETTINGS: STUDENT ACTIVITY IF ENOUGH EQUIPMENT IS AVAILABLE, OTHERWISE TEACHER DEMONSTRATION Operational Skills: Connecting sensors and interfaces Choosing logging parameters Managing the collection of timing data Using the cursor tools for obtaining measurements from the graph Changing the designation of the graph axes Procedural Skills: Evaluating measurement quality Analysing data using graph Reading values/slopes Materials: Interface (data-logger) Light gate sensor clamped on a stand Trolley fitted with double segment black card String and pulley Stackable masses: 4 x 50g Motion and Forces- 30 Activity method: 1. Prepare the card with two accurately cut vertical segments and attach it to the trolley. 2. Clamp the lightgate sensor so that the card passes through the beam when the trolley moves along the bench. 3. Clamp the pulley on the edge of the bench, tie one end of the string to the slotted mass holder, run the string over the pulley and attach the other end to trolley. 4. Begin with a falling mass of 100g giving a tension of 1 newton. Place the spare 300g mass on the trolley. 5. Pull the trolley away from the pulley so that the slotted mass is raised to a point just below the pulley. Start logging and release the trolley, allowing the mass to fall and the trolley to move along the bench 6. Repeat the measurement several times, each time recording the force of 1 newton in the table. 7. Take one of the 100g masses from the trolley and add it to the falling mass, making the tension force 2 newton. Pull back and release the trolley to make more measurements. 8. Repeat the process to obtain measurements for 3 and 4 newtons. Each time you release the trolley, record the string tension in the 'Force' column of the table. Analysing activities (using Insight iLOG): 1. Look at the bar chart In the Table, click on the heading of the 'Acceleration' column to highlight all the acceleration values and click on the 'Chart' button. What does the shape of the chart tell you about the range of results for acceleration? 2. Look at the graph of acceleration vs. force Move the cursor across the graph, and observe the bar display which shows how the Motion and Forces- 31 acceleration varied during the experiment. Think about the connection between the acceleration and the force. 3. Find out what sort of line fits the graph: Use the „Trial Fit‟ option to find a formula which gives the best fit straight line through the data. Theory predicts that the acceleration varies in proportion to the applied force. Do your results indicate this? Further work: Find out how the graphs are affected by the mass of the trolley: Add mass to the trolley, repeat the measurements and compare the results with the first set. Motion and Forces- 32 Activity 3B. INVESTIGATING FORCE AND ACCELERATION (WITH COACH 6) Learning Objectives: 1. To obtain a graph of acceleration against force for a trolley pulled by string attached to a falling mass. 2. To interpret the graphs so as to describe the relationship between the acceleration and the force causing it. 3. To investigate the effect of the mass on the acceleration. APPLIED ICT TECHNOLOGY: DATA LOGGING STUDENT LEVEL: AGE 14-17 RECOMMENDED SETTINGS: STUDENT ACTIVITY IF ENOUGH EQUIPMENT IS AVAILABLE, OTHERWISE TEACHER DEMONSTRATION Operational Skills: Connecting sensors and interfaces Choosing logging parameters Managing the collection of timing data Using the cursor tools for obtaining measurements from the graph Changing the designation of the graph axes Procedural Skills: Evaluating measurement quality Analysing data using graph Reading values/slopes Materials: Interface (data-logger) Force sensor Motion sensor String and (low-friction) pulley Track system with a low friction trolley Hanging mass set Motion and Forces- 33 Activity method: 1. Mount the pulley to the edge of the table or at the end of the Dynamics Track, allowing the string to hang over the edge. 2. Place the motion detector (default 0664) at the other side of the table or the track, allowing for the 20 cm minimum distance between the motion detector and the cart. 3. Attach the force sensor to the top of the cart, oriented so that the horizontal tension on the string will be detected. 4. Run the string from the force sensor, over a pulley, and to a hanging mass. Initially use about 20 g. 5. Start your measurement and at the same time release the cart. Let the car roll toward the pulley. Be sure that the mass is free to fall for the entire distance the cart travels and the cables are not hindering motion. Catch the cart before it hits the pulley. 6. Measure the combined mass of your cart and the force sensor. 7. Repeat the experiment for 3 additional hanging masses. 8. Perform assignments given in the Data Analysis. Questions and assignments: Look at the recorded data. What kind of motion do you observed? What does a slope of velocity represent? Determine the average acceleration during the cart's rolling time. Determine the average force applied during the cart's rolling time. Repeat the experiment for 3 additional hanging masses (every time add 20 g extra). Note: You can keep all runs in the same diagram by using the 'Copy Motion and Forces- 34 column' option available in the Tool menu of the Diagram window. Now you have several data runs. What was the effect of adding masses? Can you see a pattern in the data over the course of several runs? Write down the force and acceleration values for each trial. Are force and acceleration related? Analysing activities: The force sensor is attached to the trolley. The string runs from the force sensor, over a pulley, to a hanging mass. The force sensor measures the tension force. The motion detector records the motion of the trolley as the string pulls it. Such set-up allows delivering a constant force to the cart via the string and hanging mass. The experiment is then repeated for different hanging masses. Students should discover first that the constant force causes constant accelerated motion and second that larger force produces higher acceleration; the force is proportional to the acceleration. Further work: Find out how the graphs are affected by the mass of the trolley: Add mass to the trolley, repeat the measurements and compare the results with the first set. Motion and Forces- 35 ACTIVITY 4. INVESTIGATING THE MOTION OF A REBOUNDING TROLLEY Learning Objectives: 1. To obtain graphs of distance against time and velocity against time for a trolley rolling up and down a slope. 2. To associate the features of the graphs with the observed motion. 3. To interpret the shapes of the graphs in terms of the forces acting on the trolley. APPLIED ICT TECHNOLOGY: DATA LOGGING STUDENT LEVEL: AGE 14-17 RECOMMENDED SETTINGS: STUDENT ACTIVITY IF ENOUGH EQUIPMENT IS AVAILABLE, OTHERWISE TEACHER DEMONSTRATION Operational Skills: Connecting sensors and interfaces Choosing logging parameters Starting and finishing real-time logging Using the cursor tools for obtaining measurements from the graph Changing the designation of the graph axes Deriving secondary data by calculation Procedural Skills: Evaluating measurement quality Analysing data using graph Reading values/slopes Materials: Interface (data-logger) Motion sensor Stand and clamp Trolley Runway Spring buffer attached to a trolley or to a runway Motion and Forces- 36 Activity method: 1. Assemble the apparatus so that the trolley can move up and down the sloping runway (exemplary setup shown on the picture below). 2. Set the data logging software to record data and plot a graph of distance against time. 3. Move the trolley by hand up and down the runway in the following different ways and observe the shape of the graph in each case: - a constant velocity away from the sensor, a faster or slower constant velocity, an acceleration, a deceleration, an oscillation. 4. Reset the software to record a new set of data, release the trolley from the top and allow it to roll down and bounce off the block at the lower end. 5. Observe the graph showing the forwards and backwards motion. Analysing activities (using Insight iLOG): 1. Sweeping cursors After the experiment, the real-time experience can be regenerated using the graph cursors and bar display: Drag the X cursor slowly across the screen, and note how the bars grow and shrink in the same manner as the changes of the values recorded during the experiment, creating an „action replay‟ effect. What parts of the graph are associated with the collisions with the barrier? What parts of the graph are associated with the trolley at rest? 2. Taking distance measurements from the graph Select „Change‟ and use the cursor to find the distances moved by the trolley after each rebound. Describe the pattern of results for successive oscillations. 3. Taking time measurements from the graph Select „Interval‟ and find the time intervals between the successive Motion and Forces- 37 collisions with the barrier. Describe the pattern of results between successive collisions. 4. Calculate velocity Measure the gradient of the graph line to find and compare the velocities before and after each collision with the barrier. What does this tell you about the type of collisions with the barrier? 5. Use the software to derive a graph of velocity against time. What does the graph indicate about the acceleration of the trolley? Questions (using Coach 6): What parts of the graph are associated with the collisions with the barrier? What parts of the graph are associated with the trolley at rest? Describe the pattern of results for successive oscillations. Find the time intervals between the successive collisions with the barrier. Find and compare the velocities before and after each collision with the barrier. What does this tell you about the type of collisions with the barrier? Use the software to derive a graph of velocity against time. What does the graph indicate about the acceleration of the trolley? Further work: The basic experiment can be applied to several investigations: Find out how the slope of the runway affects the graph. Find out the effect of increasing the mass of the trolley by attaching further masses. Add a wind brake to the trolley to increase air friction. Replace the spring buffer with a cardboard „crumple zone‟. Motion and Forces- 38 ACTIVITY 5. FALLING BALL Learning Objectives: 1. To obtain graphs of height versus time and velocity versus time for a free falling ball 2. To interpret the motion graphs 3. To determine the acceleration of a freely falling ball APPLIED ICT TECHNOLOGY: VIDEO MEASUREMENT STUDENT LEVEL: AGE 14 - 17 RECOMMENDED SETTINGS: STUDENT ACTIVITY Operational Skills: Making measurements on the Video Screen Using the Perspective correction, Function fit and Derivative options Procedural Skills: Analysing data using a graph Reading values/slopes Evaluating measurement quality Materials: Video film which shows a person standing on a ladder and dropping a ball. Activity method: 1. In the Data-Video Window you see a video clip of a person standing on a ladder and dropping a ball. Watch the video clip. 2. In this video you are going to measure the height of the falling ball. To perform correct measurement first you need to correct the perspective distortion. 3. Right click the Data-Video window and select the menu option Perspective correction. A red perspective rectangle is placed on the top of the video screen. Drag the corners of the rectangle one by one to the corners of an object in the video clip which has rectangle form. Every time a corner of the perspective rectangle is moved the video screen is distorted. After mapping all four corners the distorted rectangle is transformed. Now deselect the menu item Perspective correction and the red rectangle disappears. 4. Now you are going to scale your video. Right click the Data-Video window and select the Change Scale... option. Move the origin of the coordinate Motion and Forces- 39 system to a convenient position. Each tile on the wall has height of 2.2 m. Move the scale-ruler to match the tile height and fill in the scale length 2.2 m. 5. Carry out measurements on the position of the ball. Start the measurement by clicking the green Start button. Collect points by clicking on the ball. 6. The collected data appears on the graph of the height of the ball versus time. Questions: Describe the height versus time graph. What was the initial height of the ball? How long was the motion? What can you deduce about the ball's speed? What can you deduce about the ball's acceleration? Create a graph of the horizontal velocity versus time. What was the initial velocity of the ball? What was the final velocity of the ball? What can you deduce about the ball's acceleration? Determine the acceleration of the ball. How did you find it? Compare this experimental value with the theoretical value of the Earth‟s gravity. How close is you measured value to the theoretical value? Lists some reasons why your values of the ball‟s acceleration may be different from the accepted value for g. Analysing activities: Students measure the position of the falling ball, the height versus time graph appears simultaneously. Students create velocity versus height graph and analyse both graphs. They determine the ball‟s acceleration; different ways are possible e.g. by using the Function fit, Derivative, or Slope options. Motion and Forces- 40 The height versus time and the velocity versus time graphs of the falling ball. Coach 6 Activity: 05. Falling ball Motion and Forces- 41 ACTIVITY 6. MOON JUMP Learning Objectives: 4. To measure a position of an astronaut during its jump on the moon 5. To interpret position versus time graph with respect to the visualized motion of the astronaut APPLIED ICT TECHNOLOGY: VIDEO MEASUREMENT STUDENT LEVEL: AGE 14 - 17 RECOMMENDED SETTINGS: STUDENT ACTIVITY 6. To determine the acceleration due to the moon gravity 7. To calculate the astronaut‟s weight on the moon Operational Skills: Making measurements on the Video Screen Using the Scan, Function fit and Derivative options Procedural Skills: Analysing data using a graph Reading values/slopes Materials: NASA Video film which shows the astronaut‟s jump on the moon (taken from NASA web site) Activity method: 1. In the Data-Video Window you see the first frame of the movie Moon jump. This movie shows an astronaut jumps and salutes the American flag. Watch the movie. 2. Carry out measurements on the position of the astronaut. The movie is already scaled and the graph of position versus time is prepared. It is assumed that the astronaut's height is 2 m. Notice how the coordinates system is positioned in the Video screen. 3. From the position versus time graph determine the acceleration due to the moon's gravity? Questions: What is the acceleration due to the moon's gravity? Motion and Forces- 42 Compare this experimental value with the theoretical value of the moon‟s gravity. Assume that the astronaut mass is 95 kg. What is the weight of the astronaut on the moon? How did his mass and weight on the moon compare to his mass and weight on Earth? What would be your weight on the moon? Analysing activities: The video clip shows a jump of an astronaut on the moon. Students measure the position of the jumping astronaut on the video and determine the acceleration of the astronaut due to the moon's gravity, for example by using the „Function-fit‟ option. The measured data, the estimated acceleration due to the moon's gravity is -1.6 m/s2. Coach 6 Activity: 06. Moon jump Motion and Forces- 43 ACTIVITY 7. FIND A FORCE Learning Objectives: 1. To obtain graphs of position versus time and velocity versus time for a moving car 2. To interpret the motion graphs 3. To explain how force, acceleration and mass are APPLIED ICT TECHNOLOGY: VIDEO MEASUREMENT STUDENT LEVEL: AGE 14 - 17 RECOMMENDED SETTINGS: STUDENT ACTIVITY related 4. To be able to state Newton‟s second law of motion Operational Skills: Making measurements on the Video Screen Using the Scan, Function fit and Derivative options Procedural Skills: Analysing data using a graph Reading values/slopes Evaluating measurement quality Materials: The movie „Motion of the car‟ was taken from the web site http://itsserver.tamu.edu/bryan/ITS_project/phys_video_sim.htm (free for educational purposes) Activity method: 1. In the Data-Video Window you see the first frame of the movie „Motion of the car‟. The small car is being pulled by a hanging mass. Watch the movie. 2. Carry out measurements on the position of the car. The movie is already scaled and the graph of position versus time is prepared. 3. The horizontal position versus time graph of your measurements appears on the screen. Questions: Describe the motion of the car. - What was the initial position of the car? Motion and Forces- 44 - What was the final position of the car? - How long was the motion? - What can you deduce about the car's speed? Create a graph of the horizontal velocity versus time (use the Derivative option). What was the initial velocity of the car? What was the final velocity of the car? What can you deduce about the car's acceleration? Determine the acceleration of the car. How did you find it? What is the net force that causes motion of the car? How did you find it? Tip: Information about the masses used in the experiment is given on the first frame of the video clip. Analysing activities: On the video students measure the position of the car, the horizontal position versus time graph appears simultaneously. Students create velocity versus time graph and analyse both graphs. They determine the car‟s acceleration; different ways are possible e.g. by using the Function fit, Derivative, or Slope options. The determined car‟s acceleration is circa a = 0.26 m/s2. Using the Second Newton‟s law students can calculate the force acting on the car. The total mass = mass car + mass in car + mass hanger = 0.575 kg The calculated force is: F= m*a = 0.575 kg * 0.26 m/s2 = 0.1495 N Coach 6 Activity: 07. Find a force Motion and Forces- 45 ACTIVITY 8. FALLING SHUTTLECOCK Learning Objectives: 1. To obtain graphs of position versus time and velocity versus time for the falling badminton shuttlecock 2. To interpret the motion graphs 3. To observe the effect air resistance APPLIED ICT TECHNOLOGY: VIDEO MEASUREMENT STUDENT LEVEL: AGE 14 - 17 RECOMMENDED SETTINGS: STUDENT ACTIVITY 4. To determine the terminal velocity of the falling shuttlecock Operational Skills: Making measurements on the Video Screen Using the Scan, Function fit and Derivative options Procedural Skills: Analysing data using a graph Reading values/slopes Evaluating measurement quality Materials: The motion of the falling shuttlecock was recorded with a digital camera at a resolution of 384 512 and a frame rate of 300 fps. A commonly available synthetic badminton shuttlecock of brand name “Angel Sports”, weighing 3.28 g and having a maximum skirt diameter of 6.5 cm was used. The picture shows the experimental setting. The annotation points at the shuttlecock and it is above the meter stick that was positioned on a little cart for calibrating distance. The video is already corrected for the perspective distortion on the basis of a known rectangle shape in the scene. Activity method: 1. In the Data-Video Window you see a video clip of a person dropping a badminton shuttlecock. Watch the video clip. Motion and Forces- 46 2. You are going to measure the vertical position of the falling shuttlecock. The video is already scaled; 1 meter stick that is positioned on a little cart is used for calibrating distance and the rate of 400 frames per second for calibrating time. Also the perspective distortion is corrected. The original video is shown in the Video pane. 3. Carry out measurements on the position of the shuttlecock. Because there are many frames in this video you are going to use point tracking. Right click the Data-Video window and select Point Tracking. Move the tracking are (P1) on the tracking frame over the white shuttlecock. Start measuring by clicking the green Start button. 4. The collected data appears on the graph of the vertical position versus time. Questions: Describe the motion of the shuttlecock. Describe the vertical position versus time graph: - What was the initial position of the shuttlecock? - How long was the motion? - What can you deduce about the shuttlecock‟s speed during its motion? Create a graph of the vertical velocity versus time. Describe the resulting graph. - How the velocity of the shuttlecock changes in time? - Determine the terminal velocity of the shuttlecock. Explain why the velocity of the shuttlecock does not change after some time. What forces are acting on the falling shuttlecock? Analysing activities: In this activity students investigate the motion of the falling badminton in which the effects of air resistance are important and measurable. Students interpret the resulting vertical position versus time graph of the falling shuttlecock and create the velocity versus time graph. Motion and Forces- 47 In the position versus time graph the position curve straightens out and linear function fit of the position-time graph shows the approach to linear motion after about 0.8 second. The velocity-time graph indicates that the falling shuttlecock reached after a short time a constant velocity. Students should interpret the motions graphs, discuss the forces acting on the falling shuttlecock and estimate the terminal velocity of the shuttlecock. Coach 6 Activity: 08. Falling shuttlecock Motion and Forces- 48 ACTIVITY 9. STUDYING THE MOTION OF A BALL MOVING IN TWO DIMENSIONS Learning Objectives: 1. 2. 3. To understand the concepts of uniform velocity and uniform acceleration To understand that the vertical motion of a body is independent of the horizontal motion. APPLIED ICT TECHNOLOGY: SIMULATION STUDENT LEVEL: AGE 14-17 RECOMMENDED SETTINGS: TEACHER DEMONSTRATION To understand that when a ball bounces, the velocity AND CLASS DISCUSSION becomes reversed. Operational Skills: Using the software controls for running the simulation Procedural Skills: Describe observations and link these with theoretical explanation Activity method (using Simulation Insight): 1. Open the Insight file „5. Rolling ball simulation‟. 2. Click 'Roll' to begin. 3. Observe the ball rolling along the shelf and then falling to the ground. Discuss the main differences between the motion on the shelf and the motion as the ball falls. 4. Reset and roll the ball again, but this time note the times taken to (a) reach the end of the shelf (b) fall to the ground. 5. Reset the ball on the shelf, set the horizontal velocity to a new value and repeat the observations. 6. Repeat this for a series of different values for horizontal velocity. 7. Tick the 'Bounce' checkbox and compare the motion resulting from different values of horizontal velocity. Motion and Forces- 49 Discussion: Use the results to discuss the effect of the horizontal motion on the time to fall to the ground. Discuss the effect of the horizontal velocity on the time to reach the end of the shelf. Thinking about your observations, discuss the correctness of the following statements: As the ball rolls along the shelf it experiences no acceleration. The time for the ball to fall to the ground depends upon the acceleration due to gravity and the height of the shelf above the floor. When the ball bounces on the floor or the wall, its horizontal component of velocity does not change. After the ball bounces, its velocity only changes in direction. Motion and Forces- 50 ACTIVITY 10. INVESTIGATING THE MOTION OF A REBOUNDING TROLLEY Learning Objectives: 1. To associate the features of the graph with the observed motion of the trolley. 2. To understand how the forces acting on the trolley are combined to calculate the resultant force. 3. APPLIED ICT TECHNOLOGY: SIMULATION STUDENT LEVEL: AGE 14-17 RECOMMENDED SETTINGS: TEACHER DEMONSTRATION To understand the relationship between the distance AND CLASS DISCUSSION moved, the velocity and the acceleration of the trolley. Operational Skills: Using the software controls for running the simulation Procedural Skills: Describe observations and link them with theoretical explanation Activity method (using Simulation Insight): 1. Open the Insight file „6 Rebounding simulation‟ 2. Run the simulation and observe the shape of the distance vs. time graph. 3. On the graph, identify the points where the trolley hit the fixed barrier. Identify also the points where the trolley came to rest after rolling up the runway. 4. Select „Gradient‟ and move the cursor across the graph to show how the gradient changes. The gradient indicates the velocity of the trolley. Find the point on the runway where the trolley reached its maximum velocity. 5. What happens to the velocity when the trolley hits the fixed block? 6. On the Control panel, click the data button to show the velocity data on the second graph. Review your answers to (4) and (5) above. 7. In a similar way show the graph of data for acceleration. Compare this with the previous graphs for distance and velocity. 8. Show the graphs of the force down the slope, the force of friction and the resultant force on the trolley. Use the cursors to take some measurements to show that the resultant force is equal to the sum of the slope force and friction force. Motion and Forces- 51 Discussion: Thinking about your observations, discuss the correctness of the following statements: The force of gravity on the trolley remains constant throughout the motion. The force of gravity has a component down the slope in the direction of motion. The force of friction depends upon the velocity of the trolley. The resultant force is always in the direction of motion of the trolley. The acceleration is always in the direction down the slope. Motion and Forces- 52 ACTIVITY 11. INVESTIGATING THE TERMINAL VELOCITY OF A BICYCLE Learning Objectives: 1. To associate the features of the graph with the observed motion of the bicycle. 2. To understand how the forces acting on the bicycle are combined to calculate the resultant force. 3. To understand why the velocity of the bicycle becomes constant when the resultant force becomes zero. APPLIED ICT TECHNOLOGY: SIMULATION STUDENT LEVEL: AGE 14-17 RECOMMENDED SETTINGS: TEACHER DEMONSTRATION AND CLASS DISCUSSION Operational Skills: Using the software controls for running the simulation Procedural Skills: Describe observations and link these with theoretical explanation Activity method (using Simulation Insight): 1. Open the Insight file „7. Terminal simulation‟. 2. Adjust the pushing force to 100 newton and start the simulation running. Observe the graph of velocity against time. 3. Repeat your observations with smaller and larger pushing forces. 4. Vary the size of the pushing force and observe the effect on the velocity. Motion and Forces- 53 Discussion: Thinking about your observations, discuss your answers to the following questions: When a constant pushing force is applied, why is the increase in velocity limited? Why does the force of friction (air resistance) increase as the velocity increases? What happens to the friction force and resultant force when the velocity reaches a steady value (terminal velocity)? What happens to the acceleration while the velocity increases? Motion and Forces- 54 ACTIVITY 12. FREE FALL Learning Objectives: 1. To use a model to obtain and analyse graphs of velocity and acceleration for an object falling due to gravity. 2. To interpret the properties of linear and non-linear graphs for indicating rate of change. 3. To understand the relationships between distance moved, velocity and acceleration. APPLIED ICT TECHNOLOGY: MODELLING STUDENT LEVEL: AGE 14-17 RECOMMENDED SETTINGS: STUDENT ACTIVITY OR TEACHER-LED CLASS DISCUSSION Operational Skills: Using the software controls for using the model Using the cursor tools for obtaining readings from the graph Procedural Skills: Use the shape of the distance vs. time graph to make predictions about the velocity of the object To relate the shape of the graph with the formulae in the model Activities (using Simulation Insight or Insight iLOG) 1. Open the Insight file „12. free fall model‟. 2. Click on the START button to see the model run. 3. Click on the SPACE bar to show calculated values. The time increases for each press of the space bar. If the space bar is held down, a continuous stream of values is calculated. 4. Observe the differences and similarities between the graphs for distance and velocity. 5. Stop the model and select „Change‟ („Analyse‟ menu). Use the cursors to measure the change in distance moved during 2 second intervals at different starting points on the graph. Explain the pattern in the results. 6. Compare the results for similar measurements of „Change‟ on the velocity vs. time graph. Explain why the results are different from those for the distance vs. time graph. 7. Select „Gradient‟ from the „Analyse‟ menu. Measure the gradient on the Motion and Forces- 55 distance vs. time graph at 5, 10, 15 and 20 seconds. Describe the pattern in the results. 8. Describe how the velocity vs. time graph may be predicted from the measurements of gradient. Questions and Assignment (using Coach 6): Click the Start button to run the model. What are the similarities and differences between the graphs for height and velocity? Measure the slope (by using the Slope option) of the height vs. time graph at different times 0.3, 0.6, 0.9 and 1.2 seconds. Describe the pattern in the results. What is the meaning of these values? Compare the displacement of a falling ball in equal time intervals. Look also on the animation Free Fall 1 available under the yellow button Animation. In this animation the falling ball “leaves” its picture in equal time intervals. Describe how the velocity of the ball changes in time? - What is the initial velocity of the ball? - What is the final velocity of the ball? - Compare the changes of velocity in equal time intervals. - What is the average velocity of the ball? Measure the slope of the velocity vs. time. What is the meaning of this value? Find in the model the value of the acceleration due to gravity on the Earth? Simulate the motion of the ball on the Moon? Describe the similarities and differences between the motion on the Moon and on the Earth. Analysing activities (using Coach 6) The model calculates the height and the velocity of an object in free fall due to Earth's gravity. The activity is enriched with an animation showing a free falling ball which motion is controlled by the model variable y. Motion and Forces- 56 Students analyse the resulting motion graphs. Coach 6 model and animation with trace turned on (each 35 time steps) Motion and Forces- 57 ACTIVITY 13. FORCE AND ACCELERATION Learning Objectives: 1. To use a model to obtain and analyse graphs of velocity and acceleration for an object to which a constant force is applied. 2. To understand the relationship between the acceleration of the object and, its mass and the force applied to it. APPLIED ICT TECHNOLOGY: MODELLING STUDENT LEVEL: AGE 14-17 RECOMMENDED SETTINGS: STUDENT ACTIVITY OR TEACHER-LED CLASS DISCUSSION Operational Skills: Using the software controls for using the model Using the cursor tools for obtaining readings from the graph Procedural Skills: Explaining the physical basis of each formula employed in the model Activities (using Simulation Insight or Insight iLOG) 1. Open the Insight file „13. acceleration model‟. 2. Click on the START button to set the model to run and note the values of force and mass. 3. Hold down the SPACE bar to calculate a series of values and observe the graphs which are colour coded to show distance, velocity and acceleration against time. 4. Compare the shapes of the graphs and think about what these indicate about the three variables. 5. Stop the model and use „Duplicate‟ („Data‟ menu) to copy the data for distance and velocity. 6. Run the model again, set the force to 10 newtons and obtain another set of data. 7. Comparing the new graphs with the first set, describe the main differences. 8. Repeat step 6, but this time change the mass. 9. Summarise the effects of force and mass on the acceleration of the object. Motion and Forces- 58 Questions and Assignment (using Coach 6): Look at the model and notice that in the model the acceleration variable is not defined, shows question mark. Which model variables influence the acceleration? How do you know? Double-click the acceleration variable and define its formula. Click on the Start button to run the model. Describe distance vs. time graph. Describe velocity vs. time graph. Measure the slope of the velocity vs. time. What is the meaning of this value? What is the calculated value of the acceleration? Investigate (by using the Simulate option) what is the effect of bigger/smaller resultant forces on the object‟s motion. In similar way investigate what is the effect of more heavy/less heavy objects. Summarise the effects of force and mass on the acceleration of the object. Analysing Activities (using Coach 6) The model in this activity has to calculate the distance moved, velocity and acceleration of an object caused to accelerate by a steady resultant force. Students first have to finish model by defining the formula for the acceleration variable. They analyse the resulting motion graphs and investigate the effects of force and mass on the acceleration. Motion and Forces- 59 ACTIVITY 14. REBOUNDING TROLLEY Learning Objectives: 1. To use a model to obtain and analyse graphs of velocity and acceleration for a trolley rolling down a slope and rebounding against a spring buffer. 2. To understand the relationship between the acceleration of the trolley and, its mass and the force applied to it. APPLIED ICT TECHNOLOGY: MODELLING STUDENT LEVEL: AGE 14-17 RECOMMENDED SETTINGS: STUDENT ACTIVITY OR TEACHER-LED CLASS DISCUSSION Operational Skills: Using the software controls for using the model Using the cursor tools for obtaining readings from the graph Procedural Skills: Explaining the physical basis of each formula employed in the model Comparing the graphs obtained for different values of force and mass Activities (using Simulation Insight or Insight iLOG) 1. Open the Insight file „14. rebounding model‟. 2. Click on the START button to set the model running and observe the shape of the distance vs. time graph. 3. On the graph, identify the points where the trolley hit the fixed barrier. Identify also the points where the trolley came to rest after rolling up the runway. 4. Select „Gradient‟ and move the cursor across the graph to show how the gradient changes. The gradient indicates the velocity of the trolley. Find the point on the runway where the trolley reached its maximum velocity. 5. What happens to the velocity when the trolley hits the fixed block? 6. On the Control panel, click the data button to show the velocity data on the second graph. Review your answers to (4) and (5) above. 7. In a similar way show the graph of data for acceleration. Compare this with the previous graphs for distance and velocity. 8. Show the graphs of the force down the slope, the force of friction and the resultant force on the trolley. Use the cursors to take some measurements to verify that the resultant force is equal to the vector sum of the slope Motion and Forces- 60 force and friction force. Questions and Assignment (using Coach 6): Click on START to see the model run. On the Distance vs. Time graph, which points show where the trolley hit the buffer? Which points show where the trolley came to rest after rolling up the runway? Which points show where the trolley came to rest after rolling up the runway? At what point on the runway did the trolley reach a maximum velocity? What happens to the velocity when the trolley hits the buffer? Think about the connection between the velocity graph and the distance graph. Use the Scan option to analyse both graphs simultaneously. Show the graph of acceleration. Click the Diagram button and select User defined < Acceleration versus time. Think about the connection between the acceleration graph and the previous graphs. Look at the model. Move the mouse pointer over each of the variables in turn to see how they are calculated. In particular notice how the forces are calculated. The force down the slope is calculated from the strength of gravity and the angle of the slope. The force of friction depends upon the velocity of the trolley. Investigate the effect on the graphs of (use the Simulate option): - altering the angle of the slope; - making the friction constant zero; - altering the mass. Motion and Forces- 61 Analysing Activities (using Coach 6) The model calculates the forces on the rebounding trolley, its distance moved, velocity and acceleration as it moves down and up after bouncing a spring buffer at the bottom of a runway. Motion and Forces- 62 ACTIVITY 15. TERMINAL VELOCITY Learning Objectives: APPLIED ICT TECHNOLOGY: MODELLING 1. To use a model to obtain and analyse graphs of STUDENT LEVEL:to the velocity and acceleration for a bicycle when a steady force is applied A GE 14-17 pedals. 2. To understand how the forces acting on the bicycle are calculated and combined to calculate the velocity and acceleration. RECOMMENDED SETTINGS: STUDENT ACTIVITY OR TEACHER-LED CLASS DISCUSSION 3. To understand why the velocity of the bicycle becomes constant when the resultant force becomes zero. Operational Skills: Using the software controls for using the model Using the tools for altering the graph display Procedural Skills: Explaining the physical basis of each formula employed in the model Interpreting the graphs to describe relationships between variables Activities (using Simulation Insight or Insight iLOG) 1. Open the Insight file ‟11. terminal model‟. 2. Click the START button to set the model running. Note that the pushing force is steady at 100 newton. 3. Observe the graph of velocity against time. When the velocity reaches a steady value, adjust the pushing force to 200 newton. (Right click on the „pushing force‟ box.) 4. Observe the effect on the velocity of increasing the pushing force. 5. Show the graph of acceleration and explain how it may be predicted from the velocity graph. 6. Show the graphs of all the force variables against time. Describe how they are related to each other. 7. Show the graphs of velocity and resultant force against time and explain the relationship between these variables. Motion and Forces- 63 Questions and Assignment (using Coach 6): Play the video “Falling shuttlecock” to see the experiment.. In the model is assumed that during an object‟s fall the two forces are acting on the object. Look at the model and indicate which forces are acting on the object? Move the mouse pointer over the drag force variable. As you can see this force is not defined. How would you define this force? The drag force (also called air resistance) depends on the velocity of the falling object. Theoretically there are 2 models which can be used to describe the drag force: - linear model – the drag force is proportional to velocity Fdrag = - kv, and - quadratic model - the drag force is proportional to the square velocity Fdrag = - k*sign(v)*v2. Investigate which model, linear or quadratic, better match the experimental video-data. The experimental data are already placed in the distance vs. time and velocity vs. time graphs as the pink background graphs. To define the drag force double-click the drag force variable symbol in the model and type it the formula. Which model is better? Why? What is the terminal velocity reached by the falling shuttlecock? How do you know? Activities (using Coach 6) The model in this activity calculates the forces acting on a falling object, its distance moved, velocity and acceleration as it falls down. The video “Falling shuttlecock” shows such an experiment in which the falling object is a badminton shuttlecock. Motion and Forces- 64 The drag force is not defined in the model. Students have to fill in the formula describing this force. They investigate which formula, linear Fdrag = - k*v or quadratic Fdrag = - k*sign(v)*v2 better match the experimental data given as the background graphs. For the investigation students need to adjust the values of mass, initial height y, and constant k. The experimental data are taken from the video measurement of activity 08.Falling shuttlecock. Motion and Forces- 65