This display is a 2 dimensional free body diagram tool. You may enter the
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.