Virtual Physics

Mechanics and Planetary Motion

Student Guide

Brigham Young University

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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

1

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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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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The Mechanics Laboratory

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.

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.

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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

chalkboard will bring up a larger image

of the chalkboard where messages and

assignments can be viewed. Messages

can be deleted by clicking on the eraser.

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.

Figure 2. The card reader where you enter your

user name, password, and for web

connections the URL address of your

Y Science server.

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.

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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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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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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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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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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.

This is simply m1 v1 + m2 v2 = m1 v1'+ m2 v2

' and 2222

2'

22

2'

11

2

22

2

11vmvmvmvm

+=+

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

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(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:

2

)()()(2

2

tan

tvtvrCtvrF

p

ceairresis =

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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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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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.

Figure 4. The virtual mechanics laboratory. Each of the different parts of the main

laboratory are labeled. See below for more details.

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• 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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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.

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.

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• 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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• 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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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 , , ,

, ,

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, 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 Proceed wit h Ass ignment 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

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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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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.

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.

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• 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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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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• 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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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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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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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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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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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.