Illustration 1.1: Static Text Images Versus Physlet Animations
Illustration 1.1 describes how to use Physlets. First of all, a Physlet is a Physics (Java) Applet. We use Physlets to animate physical phenomena and to ask questions regarding the phenomena. Sometimes you will need to collect data from the Physlet animation and perform calculations in order to answer the questions. Sometimes simply viewing the animation will be enough.
Image from Isaac Newton's Principia (1687).
The Physlet animations presented in Physlet® Physics 2E will be similar to the static images in your textbook. There are differences that need to be examined, however, because we will be making extensive use of these types of animations throughout Physlet® Physics 2E. First consider the image taken from Sir Isaac Newton's Principia. It is a static image depicting possible orbits of an object around Earth. We are supposed to imagine objects thrown from the mountain top with different initial velocities and imagine where they would land. (We are also supposed to imagine that for just the right conditions objects could orbit in the circles farther out from the center of Earth.)
Please wait for the animation to completely load.
Now consider the Physlet animation of a similar situation. The animation shows 10 identical balls about to be thrown off a mountain top. The initial positions of the balls are identical, but they have different initial velocities. Restart.
Press play to begin the animation. Note that the VCR-type buttons beneath the animation control the animation much like buttons on a VCR, CD, or DVD player. Specifically,
- play starts the animation and continues it until either the animation is over or is stopped.
- pause pauses the animation. Press play to resume the animation.
- « step steps the animation backward in time by one time step (the size of the time step varies with the animation). In this animation, there is no "<<step" button.
- step » steps the animation forward in time by one time step.
- reset resets the animation time to the initial time. Press play to start the animation from the beginning.
Make sure you understand what these buttons do, since you will need to use them throughout the rest of the book when you interact with the Physlets on ComPADRE.
In addition to these buttons, there are hyperlinks on the page that control which animation is played. For example, on this page, Restart reinitializes the applet to the way it was when the page was loaded. On other pages there will often be a choice of which animation to play, but Restart always gets you back to the initial condition the animation was in when the page loaded.
So what is so neat about this animation compared to the static image? Plenty. Most of what you will study in physics is related to objects in motion. It is difficult to understand the details of the motion of an object if you are trying to describe it with a static picture. Since the examples in this book are interactive animations, you can actually see the details of the motion as the objects undergo their motions.
Restart (or reset) the animation and play it again. What do you notice about the motion of the balls? Specifically, what can you say about the motion of the balls that have orbits inside of the red ball? What can you say about the motion of the balls that have orbits outside of the red ball? First, all of the orbits are squashed circles (called ellipses) except for the red ball that moves in a circle. Second, all of the balls—except the red one—change speed throughout their orbits. The inner balls travel faster near the bottom of the screen as opposed to the top, while the outer balls travel slower at the bottom of the screen as opposed to the top. (Note that we are choosing to show the complete orbits of the balls, even the ones that would have hit Earth. We do this to compare all of the orbits.)
This is not something that is obvious from Newton's drawing from the Principia, but it is made clear by the animation. This effect is even easier to see with only three balls. Ghost images of the balls are placed at equal time intervals to further display this effect when you click only three balls. Don't forget to press play after selecting the hyperlink!
In the natural sciences, simulations are almost always deterministic. By deterministic, we mean that the simulation evolves in time according to a predefined mathematical model. The models we have built for this text may or may not represent physical reality. In fact, we will often present multiple models and ask you to determine which model is in agreement with experiment. Do not assume that every simulation obeys the laws of physics.
It is important not to confuse deterministic with predictable. Simulations that depend on random numbers, contain large numbers of parameters, or exhibit chaos are often not predictable in the sense that the exact behavior may depend on infinitesimal changes of initial conditions. However, even if the details of the dynamics cannot be determined, the model may still give useful information about the types of behavior that can occur.