Free body diagram tool 
 
   

This display is a 2 dimensional free body diagram tool. You may enter the effective mass of the particle, the initial position, the initial velocity, if any, and a series of force vectors. The program resolves the force vectors, calculates the accelerations and plots the trajectory of the particle. We are limited to forces that are constant over time at this stage. Later we will add the ability to deal with forces that may depend on time or some other parameter.

There are two different views on this display. One is the free body diagram, the other is the plot of positions vs. time. The display opens with the free body diagram view where you may enter values for the following parameters.
Effective mass (mass)
Initial x position (ix)
Initial y position (iy)
Initial velocity magnitude (|iv|)
Initial velocity angle (iv<)
Force magnitude (|f|)
Force angle (f<)
The space cell limits in this view are set automatically to accommodate the largest vector you enter and to maintain the space cell aspect ratio of w:h = 4:3.

The force magnitude and angle input pairs may be repeated for up to 10 different force vectors. Setting the initial velocity requires both magnitude and angle to be set. When that is done, a vector in gray shows the direction of the velocity. The x and y components of all vectors are displayed on the screen. You may edit a force vector already entered by clicking on the screen where the text describing the vector is located. In addition to the x and y position which are always shown, you may choose to plot the velocity components and speed. Check the appropriate check boxes. When the free body diagram is complete, click on the Plot button to display the time plot view.

In the time plot view you may change the amount of time displayed by entering a value in the horizontal limit input box. The vertical scale of the time plot is set automatically so the other space cell limits are locked in. By positioning the cursor you may pick off values of time, x position or y position in which you are interested. Clicking on FBD when the time plot is shown will toggle the free body diagram back up so you can review the parameters or add additional force vectors. The reset button restores all default values and sets up the free body diagram view.

As an example, on the free body diagram below enter an initial velocity magnitude of 10 meters per second at an angle of 45 degrees. Then enter a single force of 9.8 Newtons at an angle of -90 degrees. This represents a situation like the ball toss with both vertical and horizontal velocity. Find the maximum height to which the particle rises and the time at which that height is reached. We will work additional examples using the free body diagram later.

Web site contents Copyright James D Jones 2011, All rights reserved.