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Virtual PhysicsMechanics and Planetary Motion   Student Guide       Brigham Young University
Table of ContentsOverview ...................................................................................................
OverviewWelcome to Virtual Physics: Mechanics, a realistic and sophisticated simulation of mechanicsand planetary motion e...
are found in the Accessing Virtual ChemLab, Accessing Virtual Physics, Accessing VES, orAccessing VPS user guide found on ...
The Mechanics Laboratory Figure 1. The “hallway” leading into the different virtual rooms in Virtual Physical Science.    ...
Once in the laboratory (shown in Figure3), you will find nine differentlaboratory benches that represent ninedifferent phy...
Start a mechanics experiment by selecting an object and then choosing a gravity, friction, and/orforce to act upon the sel...
Simulation Principles and FeaturesThe important principles and features forming the foundation of the mechanics simulation...
dimensional motion is instructional to shown the expected angle bouncing and collisionpredictions for multiple balls set u...
Gravity In most cases the gravity is taken to be equal to one g on earth or 9.80665 m/s2. The           various types are ...
the ball reaches the critical barrier to roll without slipping, then the ball just rolls             with no frictional fo...
(RKF45) numerical method to solve the differential equations. This gave the angle of the rodover time. Then we calculated ...
orbits, while most of the starting positions are accurate. Since we only use multiple two bodyproblems to solve for the or...
Figure 4. The virtual mechanics laboratory. Each of the different parts of the main          laboratory are labeled. See b...
•   Bell. The bell located on the experiment table is used to access Help. Help can also be found    in the Pull-Down TV.•...
Figure 5. The mechanics stockroom. The equipment used for performing various experiments in          the laboratory is div...
•   Lab Book. The lab book is used to record procedures and observations while performing    experiments in the virtual la...
•   Sled. The sled is used in projectile motion experiments and on the ramp. It    can be made of several different materi...
Gravities• Upward Gravity. The upward gravity is used to apply gravity in an upward   direction. The strength of the gravi...
,       or           ,        ,        ,Preset ExperimentsWhen allowed by the instructor, the clipboard gives access to a ...
placed on the stockroom counter, then the appropriate equipment for the experiment will have tobe selected from the stockr...
Figure 6. The experiment view. Items selected from the stockroom are placed in the tray,              which can then be dr...
•   Bell. The bell is used to access the Help Menu.•   Coordinate View Buttons. The Cartesian coordinate button    switche...
indicated position of the planets) with the format yyyy:ddd where yyyy is the year and ddd is    the specified day of the ...
•   Planetary Control. During planetary experiments, the Planetary Control buttons    are used to control the various view...
set becomes too large, then new links will be automatically created. The lab book must be openfor data to be saved. Note t...
Bucket of BallsSelecting the material controls the friction coefficient for eachball. All of the balls are made of the sam...
Planetary ObjectsThe orbital variables for each planetary body are selected byclicking on the appropriate object button. T...
Sliding FrictionUsers can enter the material of the object and surface or enter thefriction coefficient directly.RocketUse...
Scaling                             The scale of the motion area is usually set automatically and                         ...
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Mechanics user guide

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Transcript of "Mechanics user guide"

  1. 1. Virtual PhysicsMechanics and Planetary Motion Student Guide Brigham Young University
  2. 2. Table of ContentsOverview ..................................................................................................................1The Mechanics Laboratory....................................................................................3 Quick Start ..........................................................................................................3 The Simulation.....................................................................................................5 Overview ........................................................................................................5 Simulation Principles and Features ...................................................................6 Simulation Assumptions and Equations.............................................................7 Laboratory......................................................................................................... 12 Overview ...................................................................................................... 12 Pull-Down TV................................................................................................ 13 Stockroom ......................................................................................................... 14 Overview ...................................................................................................... 14 Available Items ............................................................................................. 15 Allowable Combinations................................................................................. 17 Preset Experiments ....................................................................................... 18 Assignments ................................................................................................. 18 Experiment View ................................................................................................ 20 Overview ...................................................................................................... 20 Controlling Time ........................................................................................... 23 Saving Data.................................................................................................. 23 Parameters Palette........................................................................................ 24 Lab Book ........................................................................................................... 28 i
  3. 3. OverviewWelcome to Virtual Physics: Mechanics, a realistic and sophisticated simulation of mechanicsand planetary motion experiments. In this virtual laboratory, students are free to setup andperform a wide variety of experiments involving forces, frictions, and objects and, in turn,experience the results. As in all Virtual ChemLab and Virtual Physics laboratories, the mainfocus of the mechanics laboratory is to allow students the ability to explore and discover, in asafe and level-appropriate setting, the concepts and ideas that are important in the study ofNewtonian mechanics.The purpose of the mechanics laboratory is to allow students the ability to experiment with andunderstand the concepts of forces, frictions, acceleration, and collisions and their effect on themotion of objects under controlled conditions. A partial list of the experiments performed in themechanics laboratory include projectile motion in uniform or radial gravity, ramp motion inuniform or radial gravity, the collision of multiple balls with elastic or inelastic collisions, afalling rod, and the motion of planetary objects in the solar system viewed from variousperspectives. The laboratory allows complete control of nearly all parameters defining theexperiments including forces, gravity, frictions, mass, size, and direction. The difficulty level ofthese experiments ranges from basic to sophisticated, depending on the level of the class and thepurpose for performing the experiments.The set of Virtual ChemLab and Virtual Physics simulations are available in a network version, asingle user or student version, or a CD-Only version. In the network version (a typical computerlab installation) electronic assignments and notebook submissions are handled directly throughthe local area network or via the web through the web connectivity option. In the single user orstudent version, there is assumed to be no internet connection to receive or submit assignments;consequently, the simulations are limited to paper assignments contained in workbooks orassignments written by an instructor. However, a student version can be enabled to use the webconnectivity option, which allows the exchange of electronic assignments and notebook resultsusing a regular internet connection. In the CD-Only version, the simulations can be run directlyoff the CD without having to be installed on a hard drive. The CD-Only version comes packagedonly with textbooks and cannot be enabled to use electronic assignments. The CD-Only versionis designed explicitly to use workbooks that are included with the text. For increased speed thecontents of the CD can be copied to and run from the hard drive.Please note that this users guide provides information principally for the network or web-enabledversion of Virtual Physics. While reading through the users guide, keep in mind that a studentversion and CD-Only version of the software are almost identical to a network version except fortwo main differences. (1) In both student and CD-Only versions, the hallway contains anelectronic workbook from which students select experiments that correspond to assignments intheir accompanying “real” workbooks. Details on using the electronic workbook are given in theGetting Started section of the “real” workbook. (2) In the CD-Only version, no electronicassignments can be given or received, although preset and practice experiments will be available.Note, however, that a student version can be used to receive electronic or custom assignmentsfrom the instructor via the internet by accessing the simulations through the card reader andproviding a user name, password, and URL address. Details on accessing electronic assignments 1
  4. 4. are found in the Accessing Virtual ChemLab, Accessing Virtual Physics, Accessing VES, orAccessing VPS user guide found on the CD. 2
  5. 5. The Mechanics Laboratory Figure 1. The “hallway” leading into the different virtual rooms in Virtual Physical Science. The Stockroom door accesses the Instructor Utilities, and the Physical Science door accesses nine different physical science laboratories.Quick StartFrom the hallway (Figure 1), click on the Physical Science Laboratory door and using the cardreader (Figure 2) enter your user name, password, and (for web connections) the URL addressfor your Y Science server. These will be provided by your instructor. If you do not know thisinformation contact your instructor. If you do not need to receive electronic assignments, clickon the Guest button on the card reader to gain access to the laboratory. If your version containsan electronic workbook on a table in the hallway, you can enter the physical science laboratoryby clicking on the electronic workbook and selecting an assignment. Details on accessing thevirtual laboratory are found in the Accessing VPS user guide found on the CD. 3
  6. 6. Once in the laboratory (shown in Figure3), you will find nine differentlaboratory benches that represent ninedifferent physical science laboratories.Mousing over each of these laboratorybenches pops up the name of theselected laboratory. To access themechanics laboratory, click on the firsttable on the left. On the far right-handside of the room there is a chalkboardused to display messages from theinstructor or display a summary ofassignments. If one or more messagesare available from the instructor, the text“Messages” will be displayed repeatedlyon the chalkboard. Clicking on the Figure 2. The card reader where you enter yourchalkboard will bring up a larger image user name, password, and for webof the chalkboard where messages and connections the URL address of yourassignments can be viewed. Messages Y Science server.can be deleted by clicking on the eraser. Figure 3. The physical science laboratory. The physical science laboratory contains nine different laboratories, each of which is accessed by clicking on the appropriate lab bench. The chalkboard to the right in the laboratory is used to access messages from the instructor and to see a summary of assignments.Once inside the mechanics laboratory, go to the stockroom counter by clicking on the stockroomwindow. Located inside the stockroom are uniform or radial gravities; objects such as a ball,sled, a bucket of balls, or a rod; forces such as a rocket or plunger; frictions; a ramp; and planets. 4
  7. 7. Start a mechanics experiment by selecting an object and then choosing a gravity, friction, and/orforce to act upon the selected object. Begin a planetary motion experiment by selecting some orall of the planetary objects. Select items by double clicking on the item or by clicking anddragging the item down to the tray. Clicking on the green Return to Lab arrow will return you tothe laboratory where the selected items will be located on the tray.Once in the laboratory, clicking on the experiment camera or the virtual lab bench will bring youto the Experiment View. Set up an experiment by dragging the desired items to the motion areaand clicking on the Start button. An experiment can also be started by clicking on the Forcebutton if a force is placed on the object. Important areas in the Experiment View include theCartesian or polar coordinate system buttons, the Parameters Palette for controlling theexperimental variables, the Units buttons, time control, data recording, and the data display. TheClear and Reset buttons are useful for performing multiple experiments and systematicallychanging variables.Other important items in the laboratory include the pull-down TV in the upper right-hand cornerwhere Help and assignment instructions are accessed. Access the electronic lab book by clickingon the lab book lying on the table. The lab book is used to record procedures, observations,experimental data, and conclusions. Time, position, velocity, acceleration, and momentum datafrom the experiments can be saved to the lab book by clicking on the Record button located inthe Experiment View. This data is saved in the form of links that can be opened and then copiedand pasted into a spreadsheet program for further calculations and graphing. The physicalscience laboratory is accessed by clicking on the exit sign.The SimulationOverviewThe primary purpose of the mechanics simulation is to provide students a realistic environmentwhere they can explore and better understand the concepts in Newtonian mechanics usingfundamental mechanics methods. In Virtual Physics: Mechanics, experiments are performed in aframework consistent with the other Virtual ChemLab simulations; that is, students are put into avirtual environment where they are free to choose their objects and equipment, build aconceptual experiment of their own design, and then experience the resulting consequences. Thefocus in the mechanics simulation is to allow students the flexibility to perform manyfundamental experiments to teach the basic concepts of Newton’s laws and planetary motion thatare easier to model in a simulated situation rather than a real laboratory. The ability to control thefrictions, forces, and physical parameters of motion allows students the ability to easily useequipment that can be found in most instructional laboratories and some equipment that wouldbe less readily available. Students are able to measure speeds and distances, describe the motionof objects using graphs, interpret data, understand our solar system, and gain a foundation forconcepts in physics. These results can then be used to validate Newton’s laws; demonstrate theinterplay between force and motion; calculate conservation of momentum; and study theintricacies of the solar system under variable initial conditions and parameters. 5
  8. 8. Simulation Principles and FeaturesThe important principles and features forming the foundation of the mechanics simulation arelisted below. There are five different types of experiments within the mechanics simulation: FreeMotion, Ramp Motion, Billiards Ball Motion, Falling Rod Rotational Motion, and PlanetaryMotion. Each experiment operates within the general framework of the lab and many of the sameobjects and forces are used with each type of experiment.Free Motion. The purpose of the free motion experiments is to model the behavior of objects inbasic projectile motion. The effects of air resistance, continuous or impact forces, and gravitycan be studied and data can be saved for later graphical and numerical analysis. The experimentsallow students complete control over the forces acting on objects in motion, which allows themto understand the ideal and real behavior behind Newton’s Laws. Within these experiments thestudent can choose either a ball or sled and watch how it moves through the air when differentforces are applied, in the presence of air resistance, and with a variety of types of gravity. Thebasic principles of projectile motion can easily be studied by examining the trajectories bothqualitatively and quantitatively. Orbital motion is also simple to simulate by choosing a radialgravity field or gravity sink and then studying the initial velocities or forces that would benecessary to put an object into orbit around the origin. The principles of angular velocity andacceleration can be examined by studying the motion in polar coordinates. These simulations areuseful to study kinematics by teaching about free falls with constant acceleration, the affects ofthe initial angle of velocity to determine the range and components of velocity, the concept ofterminal velocity, and the principle of what variables affect the speed of an object falling throughthe air.Ramp Motion. Planar motion is the focus of motion experiments on an inclined plane. Motionwithout slipping and with slipping is presented so students can investigate the effects of surfacefriction on the motion of an object. Rotational velocity and angular acceleration are displayed toteach how the angle and material of the ramp affects the rotational and translational motion.Various materials are simulated so students can learn about coefficients of friction. Allmechanics experiments allow students to record data from the equations of motion for latergraphical and numerical analysis, which in the case of ramp motion is very useful because of thedifficulty of obtaining real life data without complex equipment. Ramp experiments can be setup with either uniform downward gravity or a radial gravity source within the ramp. Traditionalramp experiments can be set up with uniform downward gravity and a ball set on the ramp. Bychoosing the materials of the ball and ramp, the kinetic and static coefficients of friction are setand air resistance and forces can then be applied to enhance the experiment. The radial gravitysource can be used to teach oscillating motion with or without damping. The radial gravity is setinside of the ramp and the chosen object can be observed oscillating up and down the ramp overthe point sink.Billiard Balls Motion. The purpose of the billiard balls experiments (or what we call “Bucket ofBalls”) is to teach conservation of momentum principles and to show the effect of table frictionon the motion of balls. Traditional air tracks or frictionless surfaces are modeled to showperfectly elastic collisions and momentum transfers. Inelastic properties, table friction, theinfluence of gravity, and impact forces can also be simulated to expand the functionality. Themost fundamental conservation principles can be shown with one dimensional motion but two 6
  9. 9. dimensional motion is instructional to shown the expected angle bouncing and collisionpredictions for multiple balls set up on a table with four walls. Experiments can be set up with upto 15 balls and a plunger can be set to impact any of them to set the collisions in motion. Thelocation, velocity, and momentum of each ball can be tracked and recorded to further instructstudents in the mathematical predictions of conservation equations.Falling Rod Motion. This experiment is a simulation of a traditional physics problem of a fallingchimney. A rigid rod is constrained to rotate at constant angular velocity. However, by varyingthe length of rod, the angular acceleration is determined, so longer rods have slower rotationalacceleration. The speed of the tip of the rod can reach extremely large speeds as a result of therotational velocity addition and can actually fall faster than would be predicted in free fallmotion. Various materials for the rod can be chosen to simulate the tensile strength and materialdensity so the rod will snap and break at various points as the material strains to reach the rigidrod predicted speeds. The simulation is instructional to teach about the strength of differentmaterials and the effects of length on angular velocity. The position and velocity of the tip of therod are recorded to further model and analyze the motion.Planetary Motion. This simulation includes many different experiments to qualitatively modelthe motion of planetary bodies within the solar system. Students can observe the motion ofplanetary objects in the solar system from above and from a side view to learn about, forexample, the inclined orbit of Pluto. They can also zoom down above an object to watch it andits moons orbit, noting the wobble in the orbits of planets and moons with similar masses.Students can then place themselves on the surface of an object and look out into the solar systemand watch the object’s moons and other planetary bodies move in the sky. The experiments areuseful to teach basic concepts like eclipses, the phases of the moon, retrograde motion of planets,and shapes of orbits. The planetary simulation is interactive and encourages students to exploreand observe the solar system from different points of view. It is a useful tool to allow students tosee the whole scheme of the solar system, but also to show them individual orbital characteristicsand specific planetary facts. This simulation is a qualitative teaching tool and a model of thesolar system and not meant to be an exact quantitative representation.Simulation Assumptions and EquationsFree Motion. Basic Newtonian force equations were used to model the motion of the objectswithin these experiments. All force equations were solved using a Runge Kutta Fehlberg Forth-Fifth (RKF45) numerical method to solve the differential equations. The two second derivativeequations were manipulated into four first order equations and then integrated through RKF45 tofind the position and the velocity equations of motion of the objects. The assumptions andgeneralizations made are described below. Objects We have not modeled the twisting, bending, compression, or other physical deformations that could occur throughout the experiments. The ball is assumed to be a point mass with a defined radius. The sled does not rotate when it is used in projectile motion but moves just like the ball but with a different coefficient of air resistance due to its shape. The surface of the sled is also perfectly smooth. 7
  10. 10. Gravity In most cases the gravity is taken to be equal to one g on earth or 9.80665 m/s2. The various types are described below. There are four types of uniform gravity: up, down, left, and right. These create a gravitational field in the chosen direction whenever they are placed in the motion area. The limitation is one gravity can be chosen at a time, which implies that no gravity fields can be created in the diagonal direction. In addition to the uniform gravities, there is also a radial gravity or gravitational sink. When applied to the motion area, it pulls all objects toward the origin.The assumptions and limitations of forces and air resistance are described below as they arecommon to multiple experiments.Ramp Motion. Newtonian force equations were used as the equations of motion for simulatingthe ramp motion experiments. All force equations were solved using a Runge Kutta FehlbergForth-Fifth (RKF45) numerical method to solve the differential equations. The one secondderivative equation was manipulated into two first order equations and then integrated throughRKF45 to find the position and the velocity equations of motion of the objects. The friction forceis a linear force dependent only on the coefficient of kinetic friction and the force of gravity. Thefriction can be strong enough that the initial conditions of the ball do not permit it to overcomethe static friction barrier, but once the object starts moving, the frictional force is constant and isnot dependent on the velocity. Objects The ball rolling down the inclined plane can be either a solid or hollow sphere. The material density affects the moment of inertia of the ball, which is manifest under the rolling conditions. The ball is assumed to be perfectly circular with no deformities; therefore it touches the ground at exactly one point. The balls can either slide or roll without slipping when on the ramp. The rolling has been modeled as idealized rolling without slipping, which means that there is no friction once the rolling condition is reached. The sled slides on the ramp with a constant frictional force resisting the direction of motion. To see damped oscillating motion on a ramp with radial gravity, the sled is the best option, since it does not encounter rolling conditions. Ramp The ramp surface can be made of different materials to set the friction coefficient. The surface has no imperfections, and is uniformly consistent in the chosen texture. For non-friction experiments the ramp is considered perfectly smooth. It can be set to any angle between 0 to 90 degrees. Gravity Uniform gravity down and radial gravity are the only gravities that can be applied to the ramp. Radial gravity, when applied to the ramp, is located directly below the center of the ramp perpendicular to the surface at a distance the user chooses. The default distance is 1 m. Rolling The friction icon is what is used to apply friction between a ball and the table. The simulation calculates the point at which perfect rolling without sliding occurs and applies sliding friction to the ball until that point. When the rotational velocity of 8
  11. 11. the ball reaches the critical barrier to roll without slipping, then the ball just rolls with no frictional forces being applied. The assumption is taken that the perfectly round ball only comes in contact with the ground at exactly one spot and when perfectly rolling, the velocity of the ball at that point is zero, so no forces act upon it. For this reason, once a ball reaches perfect rolling conditions, it will roll without resistance. Sliding Here we assume the sled will slide uniformly, and the surface area will determine the amount of friction being generated.The assumptions and limitations of forces and air resistance are described below as they arecommon to multiple experiments.Billiard Balls Motion. These balls are similar to the single ball in that they are all treated as pointmasses with a defined radius. The material of the balls can be chosen to set the frictioncoefficient with the table. When the rolling friction icon is applied, it essentially applies a slidingfriction force. The balls do not roll in this simulation.There are two types of collisions that we simulate. The one dimension view is used to show theconservation of momentum between collisions of similar masses or different masses. The ballsare constrained to the y = 0 line. When rolling friction is turned on then there is a normal gravitypulling the balls into the table. (This gravity is not shown.) However, uniform gravity in any ofthe four directions can be applied by the user to pull the balls downward, upward, left, or right.No radial gravity is allowed.Due to the fact that we do not have a conservative system, we do not use a Lagrangian solutionfor the motion of the balls. We are able to integrate the equations because they are second orderseparable equations that are easy to integrate explicitly. For collision purposes we takeconservation of momentum and energy in order to determine the out going velocities of the balls. 2 2 m1 v12 m2 v 2 m1 v1 2 m2 v 2This is simply m1 v1 + m2 v 2 = m1 v + m2 v and 1 2 + = + 2 2 2 2respectively. Solving these equations we have two equations for v1 and v2 that are the resultingvelocities, and we can then solve for our coefficient of restitution, which can be found in manybooks.In order to do this for two dimensions we examined the angle of the collisions. Since in onedimension the balls hit at exactly the center of mass (direct collisions), it is easy to see that theresulting velocities will only be in the same direction as the initial. However for two dimensionsthis is not the case. We determined the resultant angles and velocities by considering the centerof the balls and the radius and determining the time of collision and then using projectiongeometry on two lines, one connecting the two centers and the other is at the point of impactperpendicular to the first line. From here we project the velocities onto this new respective axisand then use conservation of momentum and energy to solve for the final velocities.Falling Rod Motion. Lagrangian equations were set up to model the angular acceleration andangular velocity of the rod. The equations were solved using a Runge Kutta Fehlberg Forth-Fifth 9
  12. 12. (RKF45) numerical method to solve the differential equations. This gave the angle of the rodover time. Then we calculated the tensile force on the leading and trailing edge of the rod todetermine when these forces exceeded the ultimate tensile strength of the rod.The rod is meant to simulate a solid hard cylinder of the chosen material, and it can only break asit falls due to tensile stress. We have not accounted for sheer strain, cracking, or otherimperfections in the material. Also, we have not accounted for the air drag of the falling rod.Uniform downward gravity is the only gravity that can be applied and there can be no airresistance or other forces applied.Forces. The forces applied in the lab can be one of two types, a rocket force or a plunger force.The rocket force is a continual force of a chosen magnitude which can either be applied for a settime period or indefinitely. The impulse force (plunger) hits the object with a chosen magnitudefor a short period (default 0.05 seconds) of time thus giving the object an almost instantaneousinitial velocity. The assumptions are those of a perfect rocket force with no flaws in ignition andan exact central hit from the plunger to prevent spin.Frictions. A friction is considered something that opposes an object’s motion. In thesesimulations there are three types of frictions available. Some depend on the speed of the movingobject and others depend on the surface area of the object. The rolling and sliding friction weredescribed previously under ramp motion. For air friction, we have combined linear and quadraticair resistance terms to create a general air resistance. Linear air resistance is modeledproportional to the velocity, radius, and a constant generally agreed to be = 0.000155. Thequadratic air resistance term is proportional to the cross sectional area of the object, the airdensity at the chosen altitude, the square of the velocity and a constant describing the irregularityof the surface Cp = 0.5 for the ball and Cp = 1.0 for the sled. A larger value for this constantcould be chosen to model a much more irregular object, up to a value of 2. The followingequation is what is used to apply the air resistance: Cp r 2 v(t ) v(t ) Fairresis tan ce = 2 r v(t ) 2Planetary Motion. While every effort has been made to model the actual motion of the planetarybodies accurately, the focus of the simulation is not numerical prediction for the past or future.The equations of motion of the planetary bodies were all solved as two body systems. Thesystem was set up with six coupled inverse square force attraction differential equations whichwere solved using the Runge Kutta Fehlberg Forth-Fifth order (RKF45) numerical algorithm.With these equations we individually defined the motion of each of the eight planets and Plutoaround the Sun, without considering the multiple body interactions. We also modeled Halley’sComet and followed the same basic method of two body attractions to model each of the moonswith their respective planetary body. Planetary data was generated and obtained from manydifferent sources, and starting positions of the objects in their orbits is from actual data of thelocations of all celestial bodies on January 1, 2006. The orbits were all taken to be aligned withthe perihelion and aphelion of the orbits on the x axis, although inclined with respect to theecliptic at the reported values. Due to the limitations on the RKF45 numerical solutions, we dolose some precision in our simulation; the orbits are appropriate approximations of the actual 10
  13. 13. orbits, while most of the starting positions are accurate. Since we only use multiple two bodyproblems to solve for the orbit of each planetary object, we lose any of the effects of theinteractions that each planet or moon has on each other. Specifically, the motion of the moons ofJupiter is over generalized as a result of not considering the multiple-body interactions that existin reality due to their close orbits and similar masses.The planetary graphics are images of the actual planets, where available, and the shadows in theprogram are generated using masks to model the illuminated portions of each planet. Atmospherecolors have been generated by considering the atmospheric conditions on each planet, but are notscientifically accurate. The sizes of the graphics were determined by considering the pixel ratiosfor the astronomical scale, but are not completely consistent, to allow the viewer to see some ofthe smaller moons and planets, when in reality they would not be visible.The top object view was created using a rotation matrix to maintain the location of the sun on thepositive y-axis, with the planet and moon orbiting around the center of mass of the two-bodysystem. As the planet orbits around the Sun, the coordinate system rotates correspondingly toleave the Sun in the same location. Therefore, when the viewer enters the inside object view withthe default angle of 0 degrees, it is important to realize that the viewer is facing away from theSun and can only rotate around the planet by clicking the Angle Rotation button. The planetaryobject does not automatically spin on its axis and so the view remains radially away from theSun until the rotation angle is changed. It is also important to keep in mind that the rotationaround the planet does not occur on its rotation axis but in the plane of the solar system. Due tothese assumptions and limitations, there is an eclipse every month, where in reality the orbits donot follow a perfect model so eclipses are significantly less frequent.When the user changes elements of the orbits in the Parameters Palette, the planetary orbits arerecalculated and the planets are started at the perihelion point, there is no attempt made tomodify actual initial conditions to accommodate for the changed orbital parameters. 11
  14. 14. Figure 4. The virtual mechanics laboratory. Each of the different parts of the main laboratory are labeled. See below for more details.Laboratory ViewOverviewThe Laboratory View for the mechanics simulation is essentially a navigation tool to otherlocations within the virtual laboratory. The essential elements of this view (shown in Figure 4)are labeled and their purpose is described as follows starting from the lower right-hand corner ofthe laboratory and proceeding clockwise:• Laboratory Table. The various objects required for an experiment are placed on the tray on the laboratory table while in the Stockroom View. Clicking on the table or on the camera above takes the user to the Experimental View where the actual experiment is performed. Note that the laboratory table is depicted as a computer window that is meant to represent a virtual 2D environment where the various experiments can take place in the absence of other outside forces. 12
  15. 15. • Bell. The bell located on the experiment table is used to access Help. Help can also be found in the Pull-Down TV.• Lab Book. The lab book is used to record procedures and observations while performing experiments in the virtual laboratory. Data from the experiments can also be saved as links in the lab book where it can then be copied and pasted into an external spreadsheet program for further analysis. See the Lab Book section below for further explanation.• Stockroom. Clicking on the stockroom window brings the user to the Stockroom View. While at the stockroom, objects, gravity, frictions, forces, or planets can be selected and placed on the Transfer Tray. The clipboard hanging in the stockroom can also be clicked to select preset experiments or accept an assignment.• Pull-Down TV. In the upper right-hand corner of the laboratory is a small handle that, when clicked, pulls down a TV that can display information in two different modes. In assignment mode, the TV displays the assignment text for the accepted assignment. This is intended to allow easy reference to the assignment instructions while performing the work in the virtual laboratory. When an assignment has not been accepted, the assignment mode is left blank. In the help mode, the TV lists the help menu for the laboratory.• Camera. By clicking on the LCD display on the camera, users can access the Experiment View of the mechanics laboratory where the experiments are performed.• Exit. The exit button allows users to return the general laboratory.• Return Items. The Return Items option allows users to return all items from the Transfer Tray to the Stockroom without having to go to the stockroom.Pull-Down TVIn the upper right-hand corner of the laboratory is a small handle, which when clicked, pullsdown a TV and can display information in two different modes:Help. In help mode, the table of contents for the laboratory help is listed on the TV. Clicking asubject listed in the table of contents brings up the help window.Assignments. In assignment mode, the TV displays the assignment text for the currentlyaccepted assignment. This is intended to allow easy reference to the assignment whileperforming the work in the virtual laboratory. When an assignment has not been accepted, theassignment mode is left blank. 13
  16. 16. Figure 5. The mechanics stockroom. The equipment used for performing various experiments in the laboratory is divided into gravity, frictions, forces, the ramp, objects, and the planets. An item is selected by clicking and dragging the item down to the Transfer Tray on the laboratory table.StockroomOverviewThe stockroom (shown in Figure 5) is used to select and place items on the Transfer Tray for aparticular experiment that will be carried out on the virtual laboratory table. The essentialfeatures of the stockroom are described in the following list.• Transfer Tray. Items needed for a particular experiment are double clicked or dragged and dropped to the Transfer Tray. After returning to the Laboratory View and then going to the Experiment View, these items will be available for placement in the motion area of the laboratory table.• Bell. As in most stockrooms, the bell is used to access Help for the stockroom. 14
  17. 17. • Lab Book. The lab book is used to record procedures and observations while performing experiments in the virtual laboratory. Data from the experiments can also be saved as links in the lab book where it can then be copied and pasted into an external spreadsheet program for further analysis. See the Lab Book section below for further explanation.• Return to Lab Arrow. Clicking the Return to Lab arrow returns the user to the laboratory. Any items that are on Transfer Tray will be available in the Experiment View for creating experiments. Items on the Transfer Tray do not necessarily have to be placed in the motion area. Instead, the Transfer Tray can be used as a temporary storage location while investigating different experimental configurations.• Return Items. The Return Items option allows users to return all items from the Transfer Tray to the Stockroom without having to go to the stockroom.• Clipboard. Clicking the clipboard gives access to 15 fundamental experiments that are already predefined and ready to run. Be aware that access to these preset experiments can be turned off by the instructor. The clipboard also gives access to assignments given by the instructor.Available ItemsItems available for the various experiments that can be performed in the virtual mechanicslaboratory are described below.Solar SystemThe planetary bodies in the solar systemare available for users to observe planetarymotion from various perspectives and toobserve the motion of the moons aroundthe planets. Planets can be selected individually or all at once using the All Objects button.Objects• Ball. The ball is used in projectile motion and ramp experiments. It can be made of several different materials to study the effect of rolling friction on ramp motion. Air friction and rolling friction can be applied simultaneously, and all gravities can be applied to the ball.• Bucket of Balls. The bucket of balls is used in billiard ball type experiments. The effect of rolling friction can be studied as well as conservation of momentum. Users can choose up to fifteen balls at once, but this is done in the Experiment View. 15
  18. 18. • Sled. The sled is used in projectile motion experiments and on the ramp. It can be made of several different materials to study the effect of sliding friction on ramp motion. Air friction and sliding friction can be applied simultaneously, and all gravities can be applied to the sled.• Rod. The rod is used in a falling-chimney experiment to demonstrate the constrained motion of a falling rod. The material and length of the rod can be chosen which could cause the rod to break under certain circumstances. Only downward gravity can be used with the rod.RampThe ramp is a surface with an adjustable angle of inclination used to studythe motion of a ball or sled as they move down the ramp. Users can choosethe material on the surface of the ramp to control the magnitude of rollingand sliding friction. Uniform downward or radial gravity can be used withthe ramp.Frictions• Air Friction. Air friction simulates the effect of air resistance on the motion of the ball or sled. Air friction can be used in projectile motion and ramp motion experiments.• Rolling Friction. Rolling friction simulates the frictional forces associated with a ball as it slides down a ramp and starts to roll. Different materials can be chosen for the object and ramp to define the magnitude of the friction. Rolling friction is used in ramp motion and billiard ball motion experiments.• Sliding Friction. Sliding friction simulates the frictional forces associated with an object sliding across a surface. Different materials can be chosen for the object and ramp to define the magnitude of the friction. Sliding friction is used with the sled in ramp motion experiments.Forces• Rocket. The rocket can be attached to the ball or sled and can be fired for set time intervals or indefinitely. The magnitude of the force can be adjusted, and the rocket can be attached at various angles to the ball and sled.• Plunger. The plunger is used to impart a short duration force or impact on a ball or sled. The magnitude of the impact can be adjusted, and the plunger can be attached at various angles to the ball, sled, or a ball in the bucket of balls. 16
  19. 19. Gravities• Upward Gravity. The upward gravity is used to apply gravity in an upward direction. The strength of the gravity can be adjusted. Although the motion area appears vertical when viewed from the monitor, gravitational forces must be applied explicitly.• Downward Gravity. The downward gravity is used to apply gravity in a downward direction similar to what would be experienced on a planet or moon. The strength of the gravity can be adjusted.• Right Gravity. The right gravity is used to apply gravity in a rightward direction. The strength of the gravity can be adjusted.• Left Gravity. The left gravity is used to apply gravity in a leftward direction. The strength of the gravity can be adjusted.• Radial Gravity. Radial gravity simulates a gravitational sink or the gravity experienced as objects are attracted to a central force field. This gravity is similar to the gravitational field associated with large bodies such as planets and moons.Allowable CombinationsOnly certain combinations of the stockroom items can be selected from the stockroom. The focalobject is the object that will be in motion, and the allowed objects are forces and frictions thatcan be applied to the focal object. These combinations are as follows. Focal Object Allowed Objects None , or , , , , , 17
  20. 20. , or , , ,Preset ExperimentsWhen allowed by the instructor, the clipboard gives access to a list of 15 mechanics experimentsthat are predefined and ready to run. To select one of these experiments, click on the clipboardand then click on the desired experiment. The appropriate objects, forces, gravities, or planetswill be automatically selected and placed in the Transfer Tray or you will be broughtautomatically to the Experiment View. If, after having selected the preset experiment from theclipboard, the objects in the Transfer Tray are touched or moved before returning to thelaboratory, the preset nature of the experiment will be turned off and the experiment will have tobe setup manually in the laboratory.The following point should be kept in mind: The 15 preset experiments that are included with theinstallation cover many of the fundamental mechanics experiments that demonstrate importantconcepts. These preset experiments are only a small set of the large number of experiments thatcan be designed and implemented in this simulation.AssignmentsBelow the preset experiments on the clipboard, the next available mechanics assignment that hasbeen released by the instructor will be listed. The information given in this assignment area is theassignment number, the title of the assignment, the due date, and the points possible.Mechanics assignments as whole can be quite different depending on the level of the class andthe specific experiment that will be performed. But in general, a mechanics assignment consistsof a description of an experiment and a series of instructions that must be performed in thelaboratory. In some assignments, the experiment will already be predefined and automatically setup in the laboratory requiring some simple observations. Other assignments could be verygeneral and could involve designing an experiment, making quantitative measurements,performing calculations, and writing conclusions.An assignment is accepted by clicking on Accept below the assignment information area wherethe text of the assignment (the description and instructions) is then placed on the clipboard forreview. Clicking on Procee d wit h Assi g nme nt places the laboratory in assignment mode andplaces any experimental equipment that was predefined as part of the assignment on the TransferTray. Not all assignments will have predefined experiments. If equipment is not automatically 18
  21. 21. placed on the stockroom counter, then the appropriate equipment for the experiment will have tobe selected from the stockroom and then brought out to the laboratory.When an assignment has been accepted, two changes are made to the operation of the laboratory.(1) Clicking on the Assignment button on the pull-down TV will display the text of theassignment. The assignment text on the TV is intended to be a reference while doing the work inthe laboratory and will be available as long as the assignment is out in the laboratory. (2) Afteran assignment has been accepted, a new section is created in the lab book (named with theassignment number) where only the notes and saved detector output associated with thatassignment can be recorded. Each assignment will have its own section, and these sections canonly be modified while the assignment is out in the laboratory. When the experimental work isfinished and the observations, results, and conclusions have been recorded in the lab book, theassignment is submitted for grading by clicking on the Report button in the lab book. Aftersubmitting an assignment, further editing in the assignment section is locked out.The laboratory can be put back into a normal “exploratory” mode by either reporting theassignment or clearing the laboratory by putting all the equipment back on the stockroomshelves. 19
  22. 22. Figure 6. The experiment view. Items selected from the stockroom are placed in the tray, which can then be dragged to the motion area for experiments. Various controls include the coordinate system, parameters palette, units, experiment control, time, recording, and the data area.Experiment ViewOverviewThe Experiment View is where the mechanics and planetary experiments are performed. Set upan experiment by dragging the selected objects to the motion area and positioning them asappropriate. The experiment is started by clicking on the Start button or if a Force is attached byclicking on the Force button. The essential features of the Experiment View (see Figure 10) aredescribed in order starting from the upper left hand corner of the lab and proceeding counter-clockwise.• Lab Book. The lab book is used to record procedures and observations while performing experiments in the virtual laboratory. Data from the experiments can be saved as links in the lab book and then copied from the lab book into an external spreadsheet program for further analysis. 20
  23. 23. • Bell. The bell is used to access the Help Menu.• Coordinate View Buttons. The Cartesian coordinate button switches the grid in the motion area to a standard x-y grid, and the data display is in Cartesian coordinates. When the Total button is also selected, the total speed and acceleration are displayed and are not divided up into the x and y components. The Polar coordinate button switches the grid to a polar coordinate system, and the data display contains r, , vr, , ar, , pr, and p . When the Total button is selected, the totals are displayed for r, , v, a, and p and are not divided up into r and components .• Parameters Palette. Open the Parameters Palette by clicking the Parameters button. It is used to change the various experimental variables. Variables can only be changed before starting an experiment or when an experiment is paused and not while an experiment is in progress. More details on using the Parameters Palette are given below.• Units Control. The desired units for time, position, mass, and force can be set using this menu. A desired unit is selected by repeatedly clicking on the appropriate button until the unit is displayed. All data displayed in the Data Area, saved to the lab book, or displayed in the Parameters Palette will reflect the unit that was chosen.• Experimental Control Panel. The Experiment Control panel is used to start and stop the experiment or apply the force that has been attached to the focal object. When there is an initial velocity set for an object in the experiment, clicking Start will apply that initial velocity. If the plunger or rocket is attached to the object, clicking the Force button will start the experiment by applying the force. If a plunger is attached, it can only be hit once. Rockets can be used repeatedly by clicking the Force button each time. The magnitude of the force applied by the rocket or plunger, and the duration of the firing can be set in the Parameters Palette. The Clear button returns the items to the Transfer Tray and resets values to their default initial conditions. The Reset button leaves the items in the motion area, but resets the experimental variables back to their state before the most recent experiment.• Time Control . This menu is used to display the time elapsed since starting the experiment. The time can be modified to elapse faster or slower than actual time by clicking on the + or – buttons and can be adjusted at any point during the experiment. During Planetary experiments, the elapsed time of the experiment is replaced with the absolute time (representing the 21
  24. 24. indicated position of the planets) with the format yyyy:ddd where yyyy is the year and ddd is the specified day of the year. (Note that the last day of the year is actually 1.25 days long.) The Acceleration value is the amount of time the simulation advances at approximately 10 second intervals when the planets are in motion and has values of 1 day, 10 days, …, up to 100 years. Above the current year and date arrows are used to advance time manually forward or backward at the specified acceleration.• Recording. Recording is used to save the selected data in the display area to the lab book for later analysis. Data is saved as links and can be accessed by clicking on the data link. The variables that will be recorded are selected by clicking the Check All button or by selecting the individual boxes above the variables in the Data Display area. Click the Record button either before starting the experiment to collect all of the data or at any period during the experiment to collect a certain range of data. The saving process will continue automatically until the Pause button is clicked or the experiment stops. Recording can also be stopped by clicking on the Stop button. If the data set becomes too large, then new links will be automatically created. The lab book must be open for data to be saved. Note that the Acceleration rate governs the density of points saved to the lab book. At the default rate, several data points are collected per second.• Current Data Display. The current position, velocity, acceleration, and momentum components are displayed in this area. The data is displayed in the coordinate system specified by the Coordinate View buttons. The check boxes above each column are used to select the data that will be saved during recording.• Tracking. For billiard ball experiments or for planetary motion, the data for the individual balls or planets or moons that should be displayed in the Data Display is selected by scrolling through the tracking list. The arrows are used to scroll through the list.• Zoom Out. The Zoom Out button is used to return to the Laboratory View. All experiments that are in motion will stay in motion and the user can return to the Experiment View. Items cannot be selected in the stockroom while an experiment is in progress, however.• Return Items. This button is used to return all items to the stockroom and it automatically returns the user to the Laboratory view. 22
  25. 25. • Planetary Control. During planetary experiments, the Planetary Control buttons are used to control the various views or perspectives of the solar system and planet-moon systems. These buttons control, from top to bottom, (1) the normal size or large size for the planets and moons for easier viewing, (2) the top view or side (parallel) view of the solar system, (3) view the planet-moon system indicated in the Tracking box, (4) go to the inside view for the planetary object and view the solar system from the surface of the object, and (5) rotate around the surface of the object in 15° increments. An additional button available in the solar system view (not shown) is the Trails button which allows the past position of the planetary objects to be tracked forming a trail.• Transfer Tray. Items selected in the Stockroom are put on the Transfer Tray at the top of the laboratory table. After entering the Experiment View, those items can be dragged down into the motion area to setup experiments or dragged from the motion area back to the tray to change experiments. Clicking the Clear button returns all items back to the Transfer Tray from the motion area.Controlling TimeThe Time Control area is used to display the time elapsed since starting theexperiment. The time can be modified to elapse faster or slower than actualtime by clicking on the + or – buttons and can be adjusted at any pointduring the experiment. During Planetary experiments, the elapsed time ofthe experiment is replaced with the absolute time (representing the indicatedposition of the planets) with the format yyyy:ddd where yyyy is the year andddd is the specified day of the year. The Acceleration value is the amount oftime the simulation advances at approximately 10 second intervals when theplanets are in motion and has values of 1 day, 10 days, …, up to 100 years.Above the current year and date arrows are used to advance time manuallyforward or backward at the specified acceleration.Saving DataRecording is used to save the selected data in the display area to the lab book forlater analysis. Data is saved as links and can be accessed by clicking on the datalink. The variables that will be recorded are selected by clicking the Check Allbutton or by selecting the individual boxes above the variables in the DataDisplay area. Click the Record button either before starting the experiment tocollect all of the data or at any period during the experiment to collect a certainrange of data. The saving process will continue automatically until the Pause button is clicked orthe experiment stops. Recording can also be stopped by clicking on the Stop button. If the data 23
  26. 26. set becomes too large, then new links will be automatically created. The lab book must be openfor data to be saved. Note that the Acceleration rate governs the density of points saved to the labbook. At the default rate, several data points are collected per second.Parameters PaletteThe Parameters Palette gives the user control over specificsettings for objects and other variables in the experiment such asthe magnitude of gravity, ball material, or the slope of the ramp.The parameters are divided into six groups that include objects,the ramp, frictions, forces, gravity, and the motion area scaling.Each is context sensitive and only contains the parameters forthose items that have been selected from the stockroom andplaced on the Transfer Tray. The buttons at the top of the palettecan be used for easy navigation to each group.Nearly every variable in the palette can be changed or updated using a slider to change variablesfrom their minimum to maximum settings or by entering a number directly into the text box. Itshould be noted that initial velocities are entered as a total velocity and a direction or angle.Angles are measured from the x-axis where +x is 0°, + y is 90°, -x is 180°, and –y is 270°. Unitsfor the variables correspond to the units defined in the Units area.Given below is a brief description of the variables that can be adjusted for each item listed in thepalette. Ball Selecting the material controls the friction coefficient of the ball. The diameter, mass, and initial velocity can also be selected as well as the mass distribution as a uniform solid or ring. 24
  27. 27. Bucket of BallsSelecting the material controls the friction coefficient for eachball. All of the balls are made of the same material. The diameter,mass, and initial velocity can also be selected for each ballseparately or these variables can be forced to be the same bychecking the option box. The elasticity of the collisions can alsobe controlled from zero (perfectly inelastic collisions) to one(perfectly elastic collisions).SledSelecting the material controls the friction coefficient of the sled.The mass; length, width, and height of the sled; and the initialvelocity can also be selected.RodSelecting the material controls the tensile strength and density ofthe rod, although these can each be entered independently. Thelength and radius of the rod can also be chosen. Note that thetensile strength controls when and where the rod will break as itfalls. 25
  28. 28. Planetary ObjectsThe orbital variables for each planetary body are selected byclicking on the appropriate object button. The parameters that canbe adjusted include the Sun mass (the same for each object) andfor each object the mass, axis length, orbital eccentricity, and theorbit inclination. The moons that will be attached to the object canalso be selected. When the orbital parameters for an object arechanged from their default or actual values, the orbit will alwaysstart at the perihelion.RampFor the ramp, users can choose the length of the ramp and theramp inclination. Buttons for predefined inclinations are alsoavailable. When a radial gravity source is applied to the ramp, theoffset of the gravity source from the surface of the ramp can bechosen.Air FrictionThe air friction coefficient is calculated based on the air pressureor altitude. Entering the air pressure calculates the correspondingaltitude and vise versa, however pressures greater than 1 atmalways produce altitudes of zero.Rolling FrictionUsers can enter the material of the object and surface or enter thefriction coefficient directly. 26
  29. 29. Sliding FrictionUsers can enter the material of the object and surface or enter thefriction coefficient directly.RocketUsers can define the force or magnitude of the rocket thrust andthe angle of the force. Angles are measured from the x-axis where+x is 0°, + y is 90°, -x is 180°, and –y is 270°. The rocket can befired for a definite time period or indefinitely.PlungerUsers can define the force or magnitude of the impact and theangle. Angles are measured from the x-axis where +x is 0°, + y is90°, -x is 180°, and –y is 270°.GravityThe gravity can be defined by selecting the equivalent gravity ofone of the solar system bodies, entering the magnitude of gdirectly, or by entering the number of earth g’s. The parametersare the same regardless of the type of gravity selected. 27
  30. 30. Scaling The scale of the motion area is usually set automatically and changes as objects go past the edge of the area; however, the scale can be set manually and fixed or allowed to auto scale. Note that the motion area is not square, so in order to fix the aspect ratio the x- and y-axis values are constrained.Lab BookThe laboratory notebook is used to write and save experimental procedures and observations foreach student and to submit the results of assignments. Data from the mechanics laboratory canalso be saved to the lab book for later reference and more detailed analysis. The notebook isorganized by sections and pages. New pages can be created as needed for each section. The firstsection is labeled Practice and is always the section that is available to the student anytime aninstructor assignment is not out in the laboratory. When an assignment is accepted for the firsttime, a new section is created in the lab book (named with the assignment number) where onlythe notes associated with that assignment can be recorded. Each assignment will have its ownsection, and these sections can only be modified while the assignment is out in the laboratory.Once an assignment has been submitted for grading, no other modifications are allowed. After anassignment has been submitted, an extra page is added to the end of the section where gradinginformation will be posted.The lab book is launched by clicking once on the lab book located on the work table. Detailedinformation on how to use the lab book is located in the Lab Book User Guide. 28

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