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Using Computer Software in the Teaching of Mechanics.

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Title: Using Computer Software in the Teaching of Mechanics.
Language: English
Authors: Graham, T, Rowlands, Stuart
Source: International Journal of Mathematical Education in Science and Technology. Jul-Aug 2000 31(4):479-493.
Peer Reviewed: Y
Page Count: 15
Publication Date: 2000
Intended Audience: Teachers; Practitioners
Document Type: Guides - Classroom - Teacher
Journal Articles
Descriptors: Computer Software, Computer Uses in Education, Higher Education, Mechanics (Physics), Physics, Science Instruction
ISSN: 0020-739X
Abstract: Discusses reasons for and ways of using computer software to teach mechanics. Describes using software to explore mechanics, challenge misconceptions, make links between mathematical representations and motion, and solve non-standard problems. Stresses the need for structured approaches to the use of software. (Contains 24 references.) (Author/ASK)
Entry Date: 2001
Accession Number: EJ612068
Database: ERIC
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  Value: <anid>AN0003462474;imt01jul.00;2003May13.13:48;v2.0</anid> <title id="AN0003462474-1">Using computer software in the teaching of mechanics </title> <sbt id="AN0003462474-2">1. Introduction</sbt> <p>The paper looks at ways of using computer software in the teaching of mechanics. The various reasons for using software are discussed to justify the use of software. A number of examples are then considered to show how different types of software can be used. Examples shown are taken from very specific types of software, more general simulation software and mathematical software. The paper discusses using software to explore mechanics, to challenge ‘misconceptions’, to make links between mathematical representations and motion and to solve non-standard problems. The paper also stresses the need for structured approaches to the use of software.</p> <p>There have been a number of initiatives that have made use of software in the teaching of mechanics. Many of these have been stimulated by the debates on how to teach mechanics, which have themselves been generated by research studies that have revealed the extent of student ‘misconceptions’ or ‘alternative conceptions’. Some examples of research into the use of computers in mechanics have focused on developing improved student understanding by challenging spontaneous and intuitive ideas that run counter to the Newtonian system (‘misconceptions’) and allowing students to construct an alternative consistent view. A good example of this is the work of Hewson [<reflink idref="bib1" id="ref1">1</reflink>], He developed and used a simple piece of software dedicated to removing misconceptions associated with relative motion. The key features of this software were a diagnostic phase and rebuilding phase where the students construct new strategies.</p> <p>Others have developed software packages that focus on specific topics in groups of topics within mechanics. Examples include the MIME project Bajpai et al. [<reflink idref="bib2" id="ref2">2</reflink>] and more recently the Consortium for Upper Level Physics Software (CUPS) project [<reflink idref="bib3" id="ref3">3</reflink>] and the Software Teaching of Modular Physics (STOMP) project [<reflink idref="bib4" id="ref4">4</reflink>]. In addition there are now powerful simulation packages available, most notably Interactive Physics [<reflink idref="bib5" id="ref5">5</reflink>]. This growing range of resources allows instructors to consider extending the range of resources they bring to bear in helping students to move from the world of intuitive ideas that they often inhabit when they arrive in the mechanics class to a Newtonian world. As computers develop, initiatives can rapidly become dated and more exciting and realistic options can become available.</p> <p>As well as providing a tool to undo misconceptions computers can allow students to consider problems or situations that were previously outside the scope of the more traditional laboratory or physics course. For example, when demonstrating damped harmonic motion, it is difficult, in a laboratory, to vary the damping coefficient, but this can be varied in any way in a computer simulation. It has been traditional to confine the world of mechanics to models that produce analytic solutions, but the power of modern computers allows them to facilitate solutions to non-standard problems.</p> <p>This paper aims to answer the question ‘why use software in the teaching of mechanics?’ and to provide some examples to illustrate strategies for using software.</p> <hd id="AN0003462474-3">Why use software?</hd> <p>Over the past two decades there has been much research into student understanding of scientific concepts and especially concepts in mechanics. What has become apparent in much of the research is that many students form the ability to tackle quantitative questions but are at the same time unable to explain the world qualitatively according to the Newtonian system. For example, many students can apply or even derive the formula for the range of a projectile, yet when asked to identify the forces acting on a thrown ball the very same students would respond in an Aristotelian manner — arguing that there is a force given by the thrower that enables the ball to overcome gravity. Many students develop a dual perspective in mechanics [<reflink idref="bib6" id="ref6">6</reflink>, 7]: as a set of formula and rule-of-thumb procedures in tackling quantitative questions, and their own spontaneous and intuitive ideas to explain physical phenomena. These spontaneous and intuitive ideas have been referred to as alternative frameworks [<reflink idref="bib8" id="ref7">8</reflink>], alternative conceptions [<reflink idref="bib9" id="ref8">9</reflink>], student prior conceptions [<reflink idref="bib10" id="ref9">10</reflink>], misconceptions [<reflink idref="bib11" id="ref10">11</reflink>], preconceptions [<reflink idref="bib12" id="ref11">12</reflink>] and conceptual profiles [<reflink idref="bib13" id="ref12">13</reflink>].</p> <p>Throughout the two decades of research, these spontaneous and intuitive ideas were spoken of as if they were fairly well formed prior to instruction (misconceptions as fairly well-defined concepts that are at odds with scientific ones). What has become apparent, however, is that these ideas are formed as the student attempts to make sense of the physical phenomena presented in instruction. Thus the idea of a force ‘pushing’ a thrown ball, for example, is formed when asked to account for the motion of a thrown ball for the first time. The Newtonian system seems counter-intuitive to what may be regarded as ‘common-sense’ when it comes to explaining why objects behave as they do — a thrown ball is overcoming gravity, so it is ‘obvious’ that there must be a force ‘pushing’ the ball. The Newtonian system is a structure that determines how particular phenomena are to be modelled, the difficulty is that teaching students how to model can run counter to the students own ideas that are forming in order to make sense of the phenomenon modelled.</p> <p>Mechanics is a way of understanding the physical world, but ironically it is built on idealized abstraction [<reflink idref="bib14" id="ref13">14</reflink>]. Idealized abstraction structures the way we can model the world — but the world appears contrary to this structure. For example, two balls of unequal weight (and unequal diameters) will not land at exactly the same time after being dropped simultaneously from a tower. Ice pucks do not move with uniform motion after being given a push. The weight of a body does not act through the centre of gravity (the centre of gravity may be defined as a point where the weight of the body is imagined to act — the weight of a body acts on the whole body, not at a point!). There is no such thing as a light framework or even a lamina. The terms light and smooth in mechanics may appear to be easily understood in the ways students respond to quantitative questions, but students appear to have tremendous difficulties in coming to terms with idealized abstraction with respect to qualitative modelling (Whitaker [<reflink idref="bib15" id="ref14">15</reflink>] raised the question: If students are specifically instructed to ignore air resistance, will they?) Idealized abstraction is a hypothetical situation whereby conditions are imposed in order to ‘simplify’. It asks of students: ‘Given such and such a situation, what happens and why?’ Students have to think accordingly to the parameters set by the conditions imposed. The difficulty of having to think abstractly in mechanics is augmented by the experience of the physical world as behaving differently.</p> <p>The difficulty with idealized abstraction is that it cannot be represented physically — e.g. frictionless surfaces, possible worlds of no gravity, etc. Computer simulation, such as Interactive Physics, can be used as a way of developing the ability to think of ‘possible worlds’ (thought experiments structured by idealized abstraction). Computer simulation enables the analysis of ideal experimental situations which most appropriately illustrates a theory [<reflink idref="bib16" id="ref15">16</reflink>], and enables a ‘feeling’ for reality while at the same time offering a ‘natural way to look for assumptions and simplifications which make it possible to explore reality’ [<reflink idref="bib17" id="ref16">17</reflink>]. Grayson and McDermott [<reflink idref="bib18" id="ref17">18</reflink>] reported on a computer program that combines the realism of animated motion with the idealizations of a textbook, and stated that the program could provide a useful bridge between ‘static, simplified textbooks and the dynamic, complicated real world’.</p> <p>In challenging ‘misconceptions’ much emphasis has been placed on causing cognitive conflict and the use of thought or simple practical experiments [<reflink idref="bib7" id="ref18">7</reflink>]. The major difficulties with this type of approach are the practical problems of setting up an experiment, the inability of the student or teacher to control all the variables in the experiment and the difficulties that students face when trying to use a ‘thought experiment’ or working in a possible world. Many of these difficulties can be removed through the use of software that can simulate many difficult physical situations, and present abstract situations that hitherto were only possible in thought. This is not to suggest that computer simulation should replace the ability to think within the constraints of a thought experiment, but what it can do is develop that ability. For example, the teacher can employ Interactive Physics Socratically — framing questions that demand a qualitative response to idealized scenarios that would be impossible to present physically.</p> <p>In figure 1, overleaf, the simulation shows clearly the trajectory of the horizontally thrown ball as a straight line relative to the lift (unfortunately this is not so clear in the printout illustration), and as a parabola relative to the outside observer. There is a ‘tilt’ in the trajectory of the lift due to the impact of the ball on the inside wall of the lift.</p> <p>In figure 2, overleaf, FT represents the resultant force acting on the particle (the anchor symbolizes a fixed object). The question is taken from MEW [<reflink idref="bib19" id="ref19">19</reflink>].</p> <hd id="AN0003462474-4">3. The primary advantages of using computer software in the development of mental models</hd> <p>The list below gives the primary advantages of computer software in this area.</p> <ulist> <item> The computer software can show much more information than can be seen in real life. Not only can the computer record details of speed, displacement etc., that can be hard to gather in reality, but some can also represent the forces acting on the model of a moving object. In this way the computer can give students a fuller, more complete picture of the features and factors that affect a particular situation. It enables students to ‘see’ abstract quantities such as force which cannot be seen in the real world (in the real world we can see the action of bodies and the resulting changes in motion; what we cannot see, however, are the forces acting between bodies).</item> <item> With physical experiments it is often hard to be able to reproduce experiments or to vary all parameters. The computer provides an environment which has the facility to provide a huge range of possible experiments.</item> <item> It takes very little time to set up and run a simulation, which means that the student can run many more simulations. This increases the profitability of students constructing correct mental models, because they can see the consistency or inconsistency of their evolving mental models.</item> <item> Students can form and test hypotheses. In particular they can ask the question ‘What happens if…?’</item> <item> Teachers can pose problems that will test students' understanding. In particular they can test for misconceptions, in the knowledge that the computer can be asked to reveal important features of the motion or situation and pose similar or parallel problems.</item> <item> The numerical power of the software, allows users to find solutions to nonstandard problems that cannot be solved analytically.</item> <item> Some software can make links between mathematical descriptions of motion and the motion itself.</item> </ulist> <p>To derive these benefits from the use of computer software it cannot be used in an informal or ad hoc manner. It is essential that it is used as part of a carefully prepared programme of study. The computer-based activities should relate to other aspects of the whole programme of study, so that they are not seen in isolation and are also relevant to end-of-course examinations or other assignments. Computer-based activities should be used in conjunction with practical experiments, analysis of quantitative questions (e.g. verification of results) and more importantly, Socratic tutoring, so that the students can develop a qualitative understanding of the physical world according to the Newtonian system.</p> <p>One possible drawback with computer simulation is the element of perceived ‘contrivance’. Hennessy and O'Shea [<reflink idref="bib20" id="ref20">20</reflink>] have observed the tendency in some secondary school children to attribute ‘magic properties’ to the computer or deviousness to the programmer if there is a conflict between their expectation and what is observed. However, the use of Interactive Physics is not to provide ‘evidence’ as to what would happen under certain circumstances within idealized abstraction, but to encourage students to reason what would happen given such-and-such circumstances. For example, it is not to show that two stones of unequal weight dropped simultaneously from the same height land at the same time, but to encourage the student to explain why that would be the case if air resistance is ignored. If a student were to express disbelief at a simulation of idealized abstraction, then the student has not developed the appropriate ideas necessary to explain what is happening — and that would be a cue for the teacher to ask an appropriate qualitative question.</p> <hd id="AN0003462474-5">4. Different types of software</hd> <p>There are now four different categories of software that are available for use in the teaching of mechanics. This paper will now briefly describe these and then give some specific examples of their use.</p> <p>The four different categories of software are:</p> <ulist> <item> Specific simulation software, such as that produced by the CUPS program. This type of software is limited in use to a range of pre-determined situations that can be varied in a number of ways. Generally this type of software is easy to use, but restricted because it does not extend beyond the area for which it was intended. This paper will discuss the use of some of the CUPS software and an oscillations simulation package developed at the University of Plymouth to support a specific text [<reflink idref="bib21" id="ref21">21</reflink>].</item> <item> General simulation software, such as Interactive Physics or the Logo Microworld Newton. These packages are far more general and so are much more flexible in the range of simulations that can be presented. However, these packages can be harder for students to use because of the wide range of facilities on offer and the need to learn how to use the package. When using software of this type it is advisable for teachers to create, and save on file, situations that students can use as starting points for their own activities. This means that students do not have to learn how to set up situations before they can begin to use the package. This paper will show some examples of the use of Interactive Physics.</item> <item> Mathematical software can be used, particularly to solve non-standard problems, but also to show the paths of objects when their motion is defined.</item> </ulist> <p>Some examples using DERIVE are considered in this paper, but the arguments can also be applied to other packages such as Mathwise, MathCad and Maple.</p> <ulist> <item> Multimedia software is now very much the order of the day and will make an interesting and valuable contribution to any aspect of science. An example is the Software Teaching of Modular Physics [<reflink idref="bib4" id="ref22">4</reflink>] project for first-year undergraduate physics. The key features of this type of software will be to provide structure and further stimulus through sound and video to the contents of the other three categories above. It should be possible to imagine a package that brings together real examples, simulation facilities and mathematical tools to provide a powerful environment in which to learn physics and mechanics.</item> </ulist> <hd id="AN0003462474-6">5. Examples of the application of software in the teaching of mechanics</hd> <p>A number of examples of specific simulation software will be considered. The first concerns the use of the Oscillations software developed at the University of Plymouth. This was designed specifically for students meeting the ideas of damping for the first time, and allows students to compare the motion of any two systems. The spring on the left-hand side (figure 3) moves as the graphs are traced out. The software can be used to determine which factors affect the amplitude. It can also be used to find the conditions under which light, critical and heavy damping are produced. Figure 3 shows a screen that demonstrates that the initial position does not affect the period. This software is very simple for students to use, provides a good exploratory environment and is intended to be used alongside a set of structured instructions.</p> <p>The second example is taken from the CUPS software. This package contains a large variety of examples that allow many different simulations to be viewed. Figure 4 shows a screen that shows the motion of a particle attached by two springs to parallel walls. The package provides a huge amount of information about the motion. Shown in figure 4 are a graph of displacement against time, potential energy against time and a phase plot, as well as a simulation of the actual motion. The features of this package are very similar to the Oscillations software described above, but are much more flexible and sophisticated, covering a wide range of potential examples of motion.</p> <p>The examples described above are excellent for extending students' knowledge given a sound base, but often do not provide such a good medium in which to challenge discrepant intuitive ideas and to facilitate the construction of mental models that are in accord with the Newtonian system. The Oscillations software for example is an ideal medium in which students can extend a knowledge of simple harmonic motion, but does not provide an environment in which to challenge more fundamental ideas, such as what forces are acting. It is when student reasoning needs to be challenged that packages such as Interactive Physics have a real advantage as they can for example, help students to visualize the forces that are acting in any given situation. This paper will now turn its attention to some examples for the use of the general simulation software package Interactive Physics.</p> <p>Interactive Physics is an environment in which almost any physical situation can be recreated and monitored. Paths can be traced, and vectors, such as force or velocity, can be added to moving objects. Graphs can be plotted to show energies or other quantities. The beauty of the package is its huge flexibility, but its disadvantage is that students will need some time to develop a familiarity that will allow them to create situations for themselves. However, it is very easy for an experienced member of staff to create situations for the students to call up and use or modify.</p> <p>One classic problem from particle dynamics concerns the path of a parcel released from an airplane following a horizontal path. Students often expect the parcel to fall vertically while the plane continues. Research by Graham and Berry [<reflink idref="bib22" id="ref23">22</reflink>] found that only 39% of a large sample of students gave correct responses to a problem of this type with 50% expecting the parcel to fall straight down. It is very easy to recreate this situation. Figure 5 shows the plane represented by the larger rectangle and constrained to travel horizontally, with the parcel represented by the smaller rectangle, that has the same initial velocity. The figure shows clearly how the parcel is always below the plane. The figure also includes details of the velocities of each object, which give the values of the velocities at the instant at which the motion was frozen, just before it hit the target.</p> <p>Another interesting problem from particle dynamics concerns the reaction force acting on a bouncing ball. A sample of 632 students were asked whether or not the forces on the ball were in equilibrium and if not to state the direction of the resultant force. Of this sample 59% stated that there was a zero resultant force because the ball was at rest. It can be difficult to convince students that there is in fact a very large reaction force that acts for a short time while the ball is in contact. This problem can easily be set up in Interactive Physics. Figure 6 shows the path of a bouncing ball and the reaction forces acting on the ball. When viewed in real time on the screen the effect can be quite dramatic as the reaction force appears and disappears very rapidly.</p> <p>The final example to be considered with Interactive Physics concerns the motion of two cylinders rolling down a slope. A demonstration that has often been used is to roll two cans down a slope (a practical demonstration of rolling cylinders that can be used in exploring intuitive ways of thinking about some aspects of rigid body motion has been reported by Graham and Peek [<reflink idref="bib23" id="ref24">23</reflink>]). One can is empty and one is full and conducting the experiment reveals that the full can rolls more quickly than the empty can reaching the bottom of the slope first. While this result can be explained in terms of the shapes of the bodies and their different moments of inertia, the ‘natural’ reasoning of the students may be that because the full can is heavier it rolls down more quickly than the empty can. The following series of experiments designed for use on Interactive Physics are intended to demonstrate to students that it is the distribution of the mass that is important in this situation rather than the mass itself. Figure 7 shows the path of two cylinders with the same cross-section, but very different masses rolling from rest down a slope. The similar positions are reinforced by including tables to show the velocities.</p> <p>It is also possible to examine the energies of the rolling bodies to show the significance of the different masses. Figure 8 shows the same situation as in figure 7, but with energies displayed instead of velocities. This illustrates the fact that the kinetic energies are in the same proportion, but that one is very much greater due to the larger mass. These type of activities can be used to expose the weakness of arguments based on the masses of the bodies.</p> <p>The next stage of the activity is to encourage students to form an alternative argument to explain the phenomena. An approach to this is to change the mass distribution of one of the cylinders. This is simple to do and can easily be done by a student as part of an activity. Figure 9 shows the motion in this case. Students can be encouraged to also consider examining energies rather than velocities and changing the masses of the cylinders.</p> <p>Finally students can be asked to consider motion of cylinders that have difficult radii. Figure 10 shows the motion of two cylinders with the same shape. They clearly reach the bottom of the slope at the same time, and this is confirmed by the components of the velocity, while the differing angular velocity provides a good point at which to begin to explain why the cylinders roll at the same rate. It is of course also possible to make some very interesting comparisons of the energies of the cylinders.</p> <p>In summary a quality simulation package can provide excellent visual images in conjunction with numerical, graphical or vector representations of different quantities. These can be very useful when trying to present students with activities that are designed and structured to challenge their intuitive ideas and to help them construct proper mental models. The appendix contains a set of instructions for students working on the rolling cans problems with Interactive Physics. These show a structured approach to the problem that includes problems to challenge students' thinking, and concludes with a related problem for them to report, in order to encourage them to reflect on their experiences.</p> <p>The final type of software to be considered is the use of mathematical software such as DERIVE, Maple or MathCad. The simulation software described above provide excellent facilities for conducting experiments in an electronic laboratory, but they do not often make explicit links between motion and the mathematical equations that describe that motion. Mathematical software can be used to find and/or display solutions to mathematical equations of motion. One of the key skills for those who study mechanics to develop is to be able to formulate the equations that describe motion in any given situation. The models that are used to provide these equations are often restricted to simple cases so that mathematical solutions can be obtained analytically. With many modern packages it is possible to find solutions very easily and this will allow many more realistic and interesting problems to be considered. Two examples of the use of DERIVE will be considered to illustrate the potential of such packages.</p> <p>The first example is very simple and shows how DERIVE can be used to show the paths of particles that are defined in a parametric form. Figure 11 shows how this has been applied to the motion of a projectile. By verifying different parameters it is possible to see how each aspect of the mathematical equations relates to the actual motion. Figure 11 illustrates a number of different projection angles.</p> <p>The second example concerns the path of a golf ball, where the model takes account of the effects of the spin of the ball. The model for the lift force, used by Townend and Pountney [<reflink idref="bib24" id="ref25">24</reflink>] in this context, is that the lift force is given by λ(w × V) where w is the angular velocity, V the velocity and λ a constant. Solutions to the problem can be obtained using a Runge-Kutta method in a mathematical package, once a student has formulated the appropriate equations of motion. Figure 12 shows the paths obtained as a solution to this problem. The shortest range corresponds to the case of topspin, the next to no spin and the other examples to increasing backspin.</p> <p>Mathematical software can provide solutions to virtually any set of equations, and provide an environment that links mathematical and graphical representations of motion. While there are many powerful applications of mathematical software to problems involving particle dynamics, it is difficult to deal with rotational problems such as the rolling cylinders discussed earlier.</p> <hd id="AN0003462474-7">6. Conclusions</hd> <p>There is a variety of software available for use in the teaching of mechanics. Because their advantages are different in different situations, teachers must consider carefully the aims of the activities before selecting the software. It is also important that teachers decide how to structure software activities, in order to challenge existing ideas or extend existing ideas, and encourage students to construct new mental models. In addition activities should be designed to demand student participation and reflection on the activities they have carried out.</p> <p>In conclusion there are an increasingly powerful range of software tools that can help teachers, through their abilities to provide electronic laboratories and powerful mathematical tools, and it is important that they are integrated into programmes of study in order to meet specific goals and objectives. While the use of software requires careful planning, when used effectively it has the potential to make a very significant contribution to the teaching and learning of mechanics, especially in the development of a qualitative understanding of the physical world with respect to the Newtonian system.</p> <p>(Received 2 November 1998)</p> <p>© 2000 Taylor & Francis Ltd</p> <p>GRAPH: Figure 11</p> <p>GRAPH: Figure 12</p> <p>PHOTO (BLACK & WHITE): Figure 1. A lift is in free-fall. A ball is thrown horizontally and a ball is released a few centimetres from the floor. Describe and explain the motion of each ball with respect to an observer inside the lift, and with respect to a stationary observer.</p> <p>PHOTO (BLACK & WHITE): Figure 2. A particle slides down a smooth incline plane as shown. What forces are acting on the particle, and what is the resultant force at each stage of the motion?</p> <p>PHOTO (BLACK & WHITE): Figure 3</p> <p>PHOTO (BLACK & WHITE): Figure 4</p> <p>PHOTO (BLACK & WHITE): Figure 5</p> <p>PHOTO (BLACK & WHITE): Figure 6</p> <p>PHOTO (BLACK & WHITE): Figure 7</p> <p>PHOTO (BLACK & WHITE): Figure 8</p> <p>PHOTO (BLACK & WHITE): Figure 9</p> <p>PHOTO (BLACK & WHITE): Figure 10</p> <ref id="AN0003462474-8"> <title> References </title> <blist> <bibl id="bib1" idref="ref1" type="bt">[1]</bibl> <bibtext> HEWSON, P. W., 1985, Am. J. Phys., 53, 878.</bibtext> </blist> <blist> <bibl id="bib2" idref="ref2" type="bt">[2]</bibl> <bibtext> BAJPAI, A. 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Technol., 28, 373.</bibtext> </blist> <blist> <bibl id="bib24" idref="ref25" type="bt">[24]</bibl> <bibtext> TOWNEND, M. S., and POUNTNEY, D. C., 1995, Learning Modelling with DERIVE (Hemel Hempstead: Prentice Hall).</bibtext> </blist> </ref> <hd id="AN0003462474-9">Appendix: The rolling cans problem</hd> <p>1. This activity concerns what happens when two cans are allowed to roll down a slope. Consider two cans, one empty, one full, which are allowed to roll down a slope.</p> <ulist> <item> Which can do you think gets to the bottom of the slope first?</item> <item> Give reasons for your answer.</item> <item>Interactive Physics and load the file ‘Rolling 1’. Run the experiment. Describe what happens and why you think this may be the case.</item> <item>he file ‘Rolling 2’. This contains the same situation as ‘Rolling 1’, but displays energies instead of velocities. Run the experiment. Explain how the energies that are displayed support or disagree with your answers to 2. Use Object, Properties to reveal the mass of each cylinder. You can change the mass of either cylinder and check that they both still roll down at the same time.</item> <item>k to ‘Rolling 1’. Use Object, Properties to make sure that both cylinders have the same mass. Then for one cylinder select Planar rather than Shell. Describe what difference this makes. What happens if you change the mass?</item> </ulist> <p>Now think back to the coke can problem. What factor causes one to roll faster?</p> <ulist> <item>5. Now load ‘Rolling 3’. Run the experiment. What features do you think that the two cylinders have in common? Use Object, Properties to check. Try changing the mass and the radius. How do these factors affect the motion?</item> <item>6. Look carefully at the velocities displayed when you run ‘Rolling 3’. Why is there a difference between the angular velocities?</item> <item>7. Use Object, Properties to change shell to planar for one cylinder. How does this affect the motion? Compare with your answers to 4 and comment.</item> </ulist> <hd id="AN0003462474-10">Further problem</hd> <p>Describe how the following objects would roll down a slope, making suitable comparisons and giving reasons for your responses.</p> <p>(i) Football</p> <p>(ii) Table tennis ball</p> <p>(iii) Golf ball</p> <p>(iv) Cricket ball</p> <aug> <p>By Ted Graham, Centre for Teaching Mathematics, University of Plymouth, Drake Circus, Plymouth, PL4 8AA, England and Stuart Rowlands, Centre for Teaching Mathematics, University of Plymouth, Drake Circus, Plymouth, PL4 8AA, England</p> <p></p> <p>e-mail: srowlands@plymouth.ac.uk</p> </aug>
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  Data: <searchLink fieldCode="SO" term="%22International+Journal+of+Mathematical+Education+in+Science+and+Technology%22"><i>International Journal of Mathematical Education in Science and Technology</i></searchLink>. Jul-Aug 2000 31(4):479-493.
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  Data: Discusses reasons for and ways of using computer software to teach mechanics. Describes using software to explore mechanics, challenge misconceptions, make links between mathematical representations and motion, and solve non-standard problems. Stresses the need for structured approaches to the use of software. (Contains 24 references.) (Author/ASK)
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