The Equilibrium and Elasticity section of the Physics_1 online course published by M. Casco Associates includes some mathematical models of real objects so that the reader may experiment with the ideas presented in the text. The equilibrium free-body models are displayed in a framework similar to the static equilibrium view of a ladder shown at the right. The ladder link will open the actual model so you can try out the controls I describe here.

The general layout of these models emulates a piece of graph paper, without the lines on it. The mouse cursor position is shown in the bottom margin in Cartesian coordinates (x,y). The vertical (y) extent of the coordinates system is set by values entered in the limit boxes in the left margin. The limit boxes in the bottom margin set the horizontal extent of the coordinate system. The model view shown is of an object representing a rigid beam that may stand in for a ladder leaned against a wall, a balanced beam supported in the middle or drawbridge supported at one end with an angled cable holding the other end up. The reaction forces they exert on the beam represent the supports and loads. In this model the aspect ratio is fixed at the normal computer screen 4 by 3, so that the object shape and angular relationships are preserved. Changing either vertical or horizontal coordinate system limits will automatically change the other limits to maintain the aspect ratio.

In the left margin of models there is a cluster of pan/zoom controls. Around the center of the cluster are buttons for shifting the view window up, down, left, or right. Each click on one of these buttons shifts the view window by 1/2 its extent. Changing the coordinate system limits does this shifting. In the center of the cluster are three buttons for zooming. The F (farther) button zooms out by expanding the coordinate system limits 25%. The N (nearer) button zooms in by shrinking the coordinate system limits by 20%. The differences in percent make the F and N buttons undo one another's action. The B (back) button restores the pre-set coordinate limits, restoring the original image size.

The colors displayed on the models are mainly taken from your computers color scheme. The margin color is taken from the background color of your desktop. The drawing area color is your window background color. The drawing area is outlined in the color of your system information background. The text color for text in the margins is your windows text color. The object and vector colors are set by the model drawing algorithms.

Since these models change state between the model setup and model output, there is a button labeled Action, to start the model running. The model output is displayed as a free-body equilibrium diagram, the Action button calculates equilibrium for the system as defined in the setup and shows, as vectors, the equilibrium forces. A Clear button is provided to reset the model to the conditions prior to the most recent run or if you choose, clear the entire setup so you may create a model of your own design.

To add a vector to the free-body diagram, click the Vector button. . This opens the vector setup dialog box, shown at the left. You may elect to enter the vector components as rectangular or polar coordinates. If coordinates are already entered, they may be converted to the other type by changing this choice. Enter the vector label in the text field provided. You may label the vector anything you want. If you leave the label blank the model will automatically label the vector "vector = i*[x component] + j*[y component]". If you enter a label with i* as the last two characters, the model will append i*[x component] + j*[y component] to the label you provided. The label will be written in the top left quadrant of the drawing area, listed from top to bottom in the order in which the vectors are added to the model. The color of the vector and its label is determined by its position in the list. If you have an unusual window background color, the visibility of some vectors may be limited.

The direction of all vectors is set by the components you enter. The magnitude may be selected as fixed or variable. For fixed vectors, the magnitude is set by your vector's components. For variable vectors, the initial magnitude comes from the components. The final magnitude is calculated when the Action button is clicked, and reflects the equilibrium condition. The attachment point may be fixed at either end or in the middle of the object, made movable or fixed at a specified percent position. The ends are designated by color because the object angle might be set anywhere so that left and right lose their significance. Movable vectors are initially set at the "% along object" entered in that text field.

The vector will fall into one of four classifications with regard to the sort of force it represents. The classification is used internally by the equilibrium calculation algorithms to enforce some physical constraints on the equilibrium solution.

Certain choices will automatically lock out incompatible other choices. Also when the Vector button invokes the vector setup dialog, the Delete button is disabled. Another way to use the vector setup dialog is to edit existing vectors. Click the mouse on any of the vector labels to call the dialog for this purpose. In this event, you may delete the selected vector as well as make any other changes as described above.

The angle of the beam, ladder or bridge in the different versions of this model may be changed in two ways. Either the new angle may be entered in the angle text field in the top margin or you may click on the object and drag it to a new angle. The angle text field is updated with the angle to which the object is dragged. The object likes to be dragged by the green end. If you click on the other end, the green end flips to the cursor position when you start dragging.