2. Table of Contents
Overview ..................................................................................................................1
The 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
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3. Overview
Welcome to Virtual Physics: Mechanics, a realistic and sophisticated simulation of mechanics
and planetary motion experiments. In this virtual laboratory, students are free to setup and
perform 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 main
focus of the mechanics laboratory is to allow students the ability to explore and discover, in a
safe and level-appropriate setting, the concepts and ideas that are important in the study of
Newtonian mechanics.
The purpose of the mechanics laboratory is to allow students the ability to experiment with and
understand the concepts of forces, frictions, acceleration, and collisions and their effect on the
motion of objects under controlled conditions. A partial list of the experiments performed in the
mechanics laboratory include projectile motion in uniform or radial gravity, ramp motion in
uniform or radial gravity, the collision of multiple balls with elastic or inelastic collisions, a
falling rod, and the motion of planetary objects in the solar system viewed from various
perspectives. The laboratory allows complete control of nearly all parameters defining the
experiments including forces, gravity, frictions, mass, size, and direction. The difficulty level of
these experiments ranges from basic to sophisticated, depending on the level of the class and the
purpose for performing the experiments.
The set of Virtual ChemLab and Virtual Physics simulations are available in a network version, a
single user or student version, or a CD-Only version. In the network version (a typical computer
lab installation) electronic assignments and notebook submissions are handled directly through
the local area network or via the web through the web connectivity option. In the single user or
student 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 or
assignments written by an instructor. However, a student version can be enabled to use the web
connectivity option, which allows the exchange of electronic assignments and notebook results
using a regular internet connection. In the CD-Only version, the simulations can be run directly
off the CD without having to be installed on a hard drive. The CD-Only version comes packaged
only with textbooks and cannot be enabled to use electronic assignments. The CD-Only version
is designed explicitly to use workbooks that are included with the text. For increased speed the
contents 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-enabled
version of Virtual Physics. While reading through the users guide, keep in mind that a student
version and CD-Only version of the software are almost identical to a network version except for
two main differences. (1) In both student and CD-Only versions, the hallway contains an
electronic workbook from which students select experiments that correspond to assignments in
their accompanying “real” workbooks. Details on using the electronic workbook are given in the
Getting Started section of the “real” workbook. (2) In the CD-Only version, no electronic
assignments 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 assignments
from the instructor via the internet by accessing the simulations through the card reader and
providing a user name, password, and URL address. Details on accessing electronic assignments
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4. are found in the Accessing Virtual ChemLab, Accessing Virtual Physics, Accessing VES, or
Accessing VPS user guide found on the CD.
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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 Start
From the hallway (Figure 1), click on the Physical Science Laboratory door and using the card
reader (Figure 2) enter your user name, password, and (for web connections) the URL address
for your Y Science server. These will be provided by your instructor. If you do not know this
information contact your instructor. If you do not need to receive electronic assignments, click
on the Guest button on the card reader to gain access to the laboratory. If your version contains
an electronic workbook on a table in the hallway, you can enter the physical science laboratory
by clicking on the electronic workbook and selecting an assignment. Details on accessing the
virtual laboratory are found in the Accessing VPS user guide found on the CD.
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6. Once in the laboratory (shown in Figure
3), you will find nine different
laboratory benches that represent nine
different physical science laboratories.
Mousing over each of these laboratory
benches pops up the name of the
selected laboratory. To access the
mechanics laboratory, click on the first
table on the left. On the far right-hand
side of the room there is a chalkboard
used to display messages from the
instructor or display a summary of
assignments. If one or more messages
are available from the instructor, the text
“Messages” will be displayed repeatedly
on the chalkboard. Clicking on the Figure 2. The card reader where you enter your
chalkboard will bring up a larger image user name, password, and for web
of the chalkboard where messages and connections the URL address of your
assignments 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 stockroom
window. 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.
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7. Start a mechanics experiment by selecting an object and then choosing a gravity, friction, and/or
force to act upon the selected object. Begin a planetary motion experiment by selecting some or
all of the planetary objects. Select items by double clicking on the item or by clicking and
dragging the item down to the tray. Clicking on the green Return to Lab arrow will return you to
the 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 you
to the Experiment View. Set up an experiment by dragging the desired items to the motion area
and clicking on the Start button. An experiment can also be started by clicking on the Force
button if a force is placed on the object. Important areas in the Experiment View include the
Cartesian or polar coordinate system buttons, the Parameters Palette for controlling the
experimental variables, the Units buttons, time control, data recording, and the data display. The
Clear and Reset buttons are useful for performing multiple experiments and systematically
changing variables.
Other important items in the laboratory include the pull-down TV in the upper right-hand corner
where Help and assignment instructions are accessed. Access the electronic lab book by clicking
on 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 data
from the experiments can be saved to the lab book by clicking on the Record button located in
the Experiment View. This data is saved in the form of links that can be opened and then copied
and pasted into a spreadsheet program for further calculations and graphing. The physical
science laboratory is accessed by clicking on the exit sign.
The Simulation
Overview
The primary purpose of the mechanics simulation is to provide students a realistic environment
where they can explore and better understand the concepts in Newtonian mechanics using
fundamental mechanics methods. In Virtual Physics: Mechanics, experiments are performed in a
framework consistent with the other Virtual ChemLab simulations; that is, students are put into a
virtual environment where they are free to choose their objects and equipment, build a
conceptual experiment of their own design, and then experience the resulting consequences. The
focus in the mechanics simulation is to allow students the flexibility to perform many
fundamental experiments to teach the basic concepts of Newton’s laws and planetary motion that
are easier to model in a simulated situation rather than a real laboratory. The ability to control the
frictions, forces, and physical parameters of motion allows students the ability to easily use
equipment that can be found in most instructional laboratories and some equipment that would
be less readily available. Students are able to measure speeds and distances, describe the motion
of objects using graphs, interpret data, understand our solar system, and gain a foundation for
concepts in physics. These results can then be used to validate Newton’s laws; demonstrate the
interplay between force and motion; calculate conservation of momentum; and study the
intricacies of the solar system under variable initial conditions and parameters.
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8. Simulation Principles and Features
The important principles and features forming the foundation of the mechanics simulation are
listed below. There are five different types of experiments within the mechanics simulation: Free
Motion, Ramp Motion, Billiards Ball Motion, Falling Rod Rotational Motion, and Planetary
Motion. Each experiment operates within the general framework of the lab and many of the same
objects 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 in
basic projectile motion. The effects of air resistance, continuous or impact forces, and gravity
can be studied and data can be saved for later graphical and numerical analysis. The experiments
allow students complete control over the forces acting on objects in motion, which allows them
to understand the ideal and real behavior behind Newton’s Laws. Within these experiments the
student can choose either a ball or sled and watch how it moves through the air when different
forces are applied, in the presence of air resistance, and with a variety of types of gravity. The
basic principles of projectile motion can easily be studied by examining the trajectories both
qualitatively and quantitatively. Orbital motion is also simple to simulate by choosing a radial
gravity field or gravity sink and then studying the initial velocities or forces that would be
necessary to put an object into orbit around the origin. The principles of angular velocity and
acceleration can be examined by studying the motion in polar coordinates. These simulations are
useful to study kinematics by teaching about free falls with constant acceleration, the affects of
the initial angle of velocity to determine the range and components of velocity, the concept of
terminal velocity, and the principle of what variables affect the speed of an object falling through
the air.
Ramp Motion. Planar motion is the focus of motion experiments on an inclined plane. Motion
without slipping and with slipping is presented so students can investigate the effects of surface
friction on the motion of an object. Rotational velocity and angular acceleration are displayed to
teach 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. All
mechanics experiments allow students to record data from the equations of motion for later
graphical and numerical analysis, which in the case of ramp motion is very useful because of the
difficulty of obtaining real life data without complex equipment. Ramp experiments can be set
up with either uniform downward gravity or a radial gravity source within the ramp. Traditional
ramp experiments can be set up with uniform downward gravity and a ball set on the ramp. By
choosing the materials of the ball and ramp, the kinetic and static coefficients of friction are set
and air resistance and forces can then be applied to enhance the experiment. The radial gravity
source can be used to teach oscillating motion with or without damping. The radial gravity is set
inside of the ramp and the chosen object can be observed oscillating up and down the ramp over
the point sink.
Billiard Balls Motion. The purpose of the billiard balls experiments (or what we call “Bucket of
Balls”) is to teach conservation of momentum principles and to show the effect of table friction
on the motion of balls. Traditional air tracks or frictionless surfaces are modeled to show
perfectly elastic collisions and momentum transfers. Inelastic properties, table friction, the
influence of gravity, and impact forces can also be simulated to expand the functionality. The
most fundamental conservation principles can be shown with one dimensional motion but two
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9. dimensional motion is instructional to shown the expected angle bouncing and collision
predictions for multiple balls set up on a table with four walls. Experiments can be set up with up
to 15 balls and a plunger can be set to impact any of them to set the collisions in motion. The
location, velocity, and momentum of each ball can be tracked and recorded to further instruct
students in the mathematical predictions of conservation equations.
Falling Rod Motion. This experiment is a simulation of a traditional physics problem of a falling
chimney. A rigid rod is constrained to rotate at constant angular velocity. However, by varying
the length of rod, the angular acceleration is determined, so longer rods have slower rotational
acceleration. The speed of the tip of the rod can reach extremely large speeds as a result of the
rotational velocity addition and can actually fall faster than would be predicted in free fall
motion. Various materials for the rod can be chosen to simulate the tensile strength and material
density so the rod will snap and break at various points as the material strains to reach the rigid
rod predicted speeds. The simulation is instructional to teach about the strength of different
materials and the effects of length on angular velocity. The position and velocity of the tip of the
rod are recorded to further model and analyze the motion.
Planetary Motion. This simulation includes many different experiments to qualitatively model
the motion of planetary bodies within the solar system. Students can observe the motion of
planetary objects in the solar system from above and from a side view to learn about, for
example, the inclined orbit of Pluto. They can also zoom down above an object to watch it and
its 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 system
and watch the object’s moons and other planetary bodies move in the sky. The experiments are
useful 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 explore
and observe the solar system from different points of view. It is a useful tool to allow students to
see the whole scheme of the solar system, but also to show them individual orbital characteristics
and specific planetary facts. This simulation is a qualitative teaching tool and a model of the
solar system and not meant to be an exact quantitative representation.
Simulation Assumptions and Equations
Free Motion. Basic Newtonian force equations were used to model the motion of the objects
within 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 derivative
equations were manipulated into four first order equations and then integrated through RKF45 to
find the position and the velocity equations of motion of the objects. The assumptions and
generalizations 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.
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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 are
common to multiple experiments.
Ramp Motion. Newtonian force equations were used as the equations of motion for simulating
the ramp motion experiments. All force equations were solved using a Runge Kutta Fehlberg
Forth-Fifth (RKF45) numerical method to solve the differential equations. The one second
derivative equation was manipulated into two first order equations and then integrated through
RKF45 to find the position and the velocity equations of motion of the objects. The friction force
is a linear force dependent only on the coefficient of kinetic friction and the force of gravity. The
friction can be strong enough that the initial conditions of the ball do not permit it to overcome
the static friction barrier, but once the object starts moving, the frictional force is constant and is
not 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
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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 are
common to multiple experiments.
Billiard Balls Motion. These balls are similar to the single ball in that they are all treated as point
masses with a defined radius. The material of the balls can be chosen to set the friction
coefficient with the table. When the rolling friction icon is applied, it essentially applies a sliding
friction 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 the
conservation of momentum between collisions of similar masses or different masses. The balls
are constrained to the y = 0 line. When rolling friction is turned on then there is a normal gravity
pulling the balls into the table. (This gravity is not shown.) However, uniform gravity in any of
the 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 solution
for the motion of the balls. We are able to integrate the equations because they are second order
separable equations that are easy to integrate explicitly. For collision purposes we take
conservation 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 2
This is simply m1 v1 + m2 v 2 = m1 v + m2 v and
1 2 + = +
2 2 2 2
respectively. Solving these equations we have two equations for v1 and v2 that are the resulting
velocities, and we can then solve for our coefficient of restitution, which can be found in many
books.
In order to do this for two dimensions we examined the angle of the collisions. Since in one
dimension the balls hit at exactly the center of mass (direct collisions), it is easy to see that the
resulting velocities will only be in the same direction as the initial. However for two dimensions
this is not the case. We determined the resultant angles and velocities by considering the center
of the balls and the radius and determining the time of collision and then using projection
geometry on two lines, one connecting the two centers and the other is at the point of impact
perpendicular to the first line. From here we project the velocities onto this new respective axis
and 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 and
angular velocity of the rod. The equations were solved using a Runge Kutta Fehlberg Forth-Fifth
9
12. (RKF45) numerical method to solve the differential equations. This gave the angle of the rod
over time. Then we calculated the tensile force on the leading and trailing edge of the rod to
determine 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 as
it falls due to tensile stress. We have not accounted for sheer strain, cracking, or other
imperfections 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 air
resistance 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 set
time period or indefinitely. The impulse force (plunger) hits the object with a chosen magnitude
for a short period (default 0.05 seconds) of time thus giving the object an almost instantaneous
initial velocity. The assumptions are those of a perfect rocket force with no flaws in ignition and
an exact central hit from the plunger to prevent spin.
Frictions. A friction is considered something that opposes an object’s motion. In these
simulations there are three types of frictions available. Some depend on the speed of the moving
object and others depend on the surface area of the object. The rolling and sliding friction were
described previously under ramp motion. For air friction, we have combined linear and quadratic
air resistance terms to create a general air resistance. Linear air resistance is modeled
proportional to the velocity, radius, and a constant generally agreed to be = 0.000155. The
quadratic air resistance term is proportional to the cross sectional area of the object, the air
density at the chosen altitude, the square of the velocity and a constant describing the irregularity
of the surface Cp = 0.5 for the ball and Cp = 1.0 for the sled. A larger value for this constant
could be chosen to model a much more irregular object, up to a value of 2. The following
equation is what is used to apply the air resistance:
Cp r 2 v(t ) v(t )
Fairresis tan ce = 2 r v(t )
2
Planetary Motion. While every effort has been made to model the actual motion of the planetary
bodies 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. The
system was set up with six coupled inverse square force attraction differential equations which
were 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 Pluto
around the Sun, without considering the multiple body interactions. We also modeled Halley’s
Comet and followed the same basic method of two body attractions to model each of the moons
with their respective planetary body. Planetary data was generated and obtained from many
different sources, and starting positions of the objects in their orbits is from actual data of the
locations of all celestial bodies on January 1, 2006. The orbits were all taken to be aligned with
the perihelion and aphelion of the orbits on the x axis, although inclined with respect to the
ecliptic at the reported values. Due to the limitations on the RKF45 numerical solutions, we do
lose some precision in our simulation; the orbits are appropriate approximations of the actual
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13. orbits, while most of the starting positions are accurate. Since we only use multiple two body
problems to solve for the orbit of each planetary object, we lose any of the effects of the
interactions that each planet or moon has on each other. Specifically, the motion of the moons of
Jupiter is over generalized as a result of not considering the multiple-body interactions that exist
in reality due to their close orbits and similar masses.
The planetary graphics are images of the actual planets, where available, and the shadows in the
program are generated using masks to model the illuminated portions of each planet. Atmosphere
colors have been generated by considering the atmospheric conditions on each planet, but are not
scientifically accurate. The sizes of the graphics were determined by considering the pixel ratios
for the astronomical scale, but are not completely consistent, to allow the viewer to see some of
the 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 the
positive y-axis, with the planet and moon orbiting around the center of mass of the two-body
system. As the planet orbits around the Sun, the coordinate system rotates correspondingly to
leave the Sun in the same location. Therefore, when the viewer enters the inside object view with
the default angle of 0 degrees, it is important to realize that the viewer is facing away from the
Sun and can only rotate around the planet by clicking the Angle Rotation button. The planetary
object does not automatically spin on its axis and so the view remains radially away from the
Sun until the rotation angle is changed. It is also important to keep in mind that the rotation
around the planet does not occur on its rotation axis but in the plane of the solar system. Due to
these assumptions and limitations, there is an eclipse every month, where in reality the orbits do
not 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 are
recalculated and the planets are started at the perihelion point, there is no attempt made to
modify actual initial conditions to accommodate for the changed orbital parameters.
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14. Figure 4. The virtual mechanics laboratory. Each of the different parts of the main
laboratory are labeled. See below for more details.
Laboratory View
Overview
The Laboratory View for the mechanics simulation is essentially a navigation tool to other
locations 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 of
the 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.
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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 TV
In the upper right-hand corner of the laboratory is a small handle, which when clicked, pulls
down 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 a
subject listed in the table of contents brings up the help window.
Assignments. In assignment mode, the TV displays the assignment text for the currently
accepted assignment. This is intended to allow easy reference to the assignment while
performing the work in the virtual laboratory. When an assignment has not been accepted, the
assignment mode is left blank.
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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.
Stockroom
Overview
The stockroom (shown in Figure 5) is used to select and place items on the Transfer Tray for a
particular experiment that will be carried out on the virtual laboratory table. The essential
features 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.
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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 Items
Items available for the various experiments that can be performed in the virtual mechanics
laboratory are described below.
Solar System
The planetary bodies in the solar system
are available for users to observe planetary
motion from various perspectives and to
observe the motion of the moons around
the 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.
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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.
Ramp
The ramp is a surface with an adjustable angle of inclination used to study
the motion of a ball or sled as they move down the ramp. Users can choose
the material on the surface of the ramp to control the magnitude of rolling
and sliding friction. Uniform downward or radial gravity can be used with
the 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.
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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 Combinations
Only certain combinations of the stockroom items can be selected from the stockroom. The focal
object is the object that will be in motion, and the allowed objects are forces and frictions that
can be applied to the focal object. These combinations are as follows.
Focal Object Allowed Objects
None
, or , , ,
, ,
17
20. , or , , ,
Preset Experiments
When allowed by the instructor, the clipboard gives access to a list of 15 mechanics experiments
that are predefined and ready to run. To select one of these experiments, click on the clipboard
and then click on the desired experiment. The appropriate objects, forces, gravities, or planets
will be automatically selected and placed in the Transfer Tray or you will be brought
automatically to the Experiment View. If, after having selected the preset experiment from the
clipboard, the objects in the Transfer Tray are touched or moved before returning to the
laboratory, the preset nature of the experiment will be turned off and the experiment will have to
be setup manually in the laboratory.
The following point should be kept in mind: The 15 preset experiments that are included with the
installation cover many of the fundamental mechanics experiments that demonstrate important
concepts. These preset experiments are only a small set of the large number of experiments that
can be designed and implemented in this simulation.
Assignments
Below the preset experiments on the clipboard, the next available mechanics assignment that has
been released by the instructor will be listed. The information given in this assignment area is the
assignment 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 and
the specific experiment that will be performed. But in general, a mechanics assignment consists
of a description of an experiment and a series of instructions that must be performed in the
laboratory. In some assignments, the experiment will already be predefined and automatically set
up in the laboratory requiring some simple observations. Other assignments could be very
general 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 where
the text of the assignment (the description and instructions) is then placed on the clipboard for
review. Clicking on Procee d wit h Assi g nme nt places the laboratory in assignment mode and
places any experimental equipment that was predefined as part of the assignment on the Transfer
Tray. Not all assignments will have predefined experiments. If equipment is not automatically
18
21. placed on the stockroom counter, then the appropriate equipment for the experiment will have to
be 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 the
assignment. The assignment text on the TV is intended to be a reference while doing the work in
the laboratory and will be available as long as the assignment is out in the laboratory. (2) After
an assignment has been accepted, a new section is created in the lab book (named with the
assignment number) where only the notes and saved detector output associated with that
assignment can be recorded. Each assignment will have its own section, and these sections can
only be modified while the assignment is out in the laboratory. When the experimental work is
finished and the observations, results, and conclusions have been recorded in the lab book, the
assignment is submitted for grading by clicking on the Report button in the lab book. After
submitting 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 the
assignment or clearing the laboratory by putting all the equipment back on the stockroom
shelves.
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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 View
Overview
The Experiment View is where the mechanics and planetary experiments are performed. Set up
an experiment by dragging the selected objects to the motion area and positioning them as
appropriate. The experiment is started by clicking on the Start button or if a Force is attached by
clicking on the Force button. The essential features of the Experiment View (see Figure 10) are
described 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.
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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
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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.
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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 Time
The Time Control area 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 indicated
position of the planets) with the format yyyy:ddd where yyyy is the year and
ddd is the specified day of the year. 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.
Saving Data
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
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26. 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.
Parameters Palette
The Parameters Palette gives the user control over specific
settings for objects and other variables in the experiment such as
the 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 for
those items that have been selected from the stockroom and
placed on the Transfer Tray. The buttons at the top of the palette
can be used for easy navigation to each group.
Nearly every variable in the palette can be changed or updated using a slider to change variables
from their minimum to maximum settings or by entering a number directly into the text box. It
should 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°. Units
for 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 the
palette.
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.
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27. Bucket of Balls
Selecting the material controls the friction coefficient for each
ball. All of the balls are made of the same material. The diameter,
mass, and initial velocity can also be selected for each ball
separately or these variables can be forced to be the same by
checking the option box. The elasticity of the collisions can also
be controlled from zero (perfectly inelastic collisions) to one
(perfectly elastic collisions).
Sled
Selecting the material controls the friction coefficient of the sled.
The mass; length, width, and height of the sled; and the initial
velocity can also be selected.
Rod
Selecting the material controls the tensile strength and density of
the rod, although these can each be entered independently. The
length and radius of the rod can also be chosen. Note that the
tensile strength controls when and where the rod will break as it
falls.
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28. Planetary Objects
The orbital variables for each planetary body are selected by
clicking on the appropriate object button. The parameters that can
be adjusted include the Sun mass (the same for each object) and
for each object the mass, axis length, orbital eccentricity, and the
orbit inclination. The moons that will be attached to the object can
also be selected. When the orbital parameters for an object are
changed from their default or actual values, the orbit will always
start at the perihelion.
Ramp
For the ramp, users can choose the length of the ramp and the
ramp inclination. Buttons for predefined inclinations are also
available. When a radial gravity source is applied to the ramp, the
offset of the gravity source from the surface of the ramp can be
chosen.
Air Friction
The air friction coefficient is calculated based on the air pressure
or altitude. Entering the air pressure calculates the corresponding
altitude and vise versa, however pressures greater than 1 atm
always produce altitudes of zero.
Rolling Friction
Users can enter the material of the object and surface or enter the
friction coefficient directly.
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29. Sliding Friction
Users can enter the material of the object and surface or enter the
friction coefficient directly.
Rocket
Users can define the force or magnitude of the rocket thrust and
the 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 be
fired for a definite time period or indefinitely.
Plunger
Users can define the force or magnitude of the impact and the
angle. Angles are measured from the x-axis where +x is 0°, + y is
90°, -x is 180°, and –y is 270°.
Gravity
The gravity can be defined by selecting the equivalent gravity of
one of the solar system bodies, entering the magnitude of g
directly, or by entering the number of earth g’s. The parameters
are the same regardless of the type of gravity selected.
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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 Book
The laboratory notebook is used to write and save experimental procedures and observations for
each student and to submit the results of assignments. Data from the mechanics laboratory can
also be saved to the lab book for later reference and more detailed analysis. The notebook is
organized by sections and pages. New pages can be created as needed for each section. The first
section is labeled Practice and is always the section that is available to the student anytime an
instructor assignment is not out in the laboratory. When an assignment is accepted for the first
time, a new section is created in the lab book (named with the assignment number) where only
the notes associated with that assignment can be recorded. Each assignment will have its own
section, 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 an
assignment has been submitted, an extra page is added to the end of the section where grading
information will be posted.
The lab book is launched by clicking once on the lab book located on the work table. Detailed
information on how to use the lab book is located in the Lab Book User Guide.
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