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Illustration 1.2: Animations, Units, and Measurement

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Most physics problems are idealizations of actual physical situations. In many physics problems, moving objects are set into motion before the problem even starts. This allows the problem to focus on one particular concept. Physlet animations are no different. The animations depict only a short period of time in the "life" of an object. Sometimes the objects start at rest, and when you press play they begin their movement. Other times, the object is already moving, even before you press play, and pressing play just starts the animation. Look for visual clues as to whether the object starts at rest or is already moving when the animation begins. Both animations on this page (Animation 1 and Animation 2; do not forget to press play) depict objects that are already moving when the animation starts (at t = 0). (Likewise, when the animation is over and you see the "End of Animation" message, the animation is over, but the motion of the object could continue. This continuing motion is just not depicted.)

Units are important to physicists. However, computer simulations store numbers and these numbers do not have units. Calculations are performed just as they are on a pocket calculator. Restart. This can cause confusion since the time and distance units shown on the computer display do not have an a priori relationship to the real world. In other words, we can assign the relationship to be anything we want it to be. In Animation 1, for example, the part of the animation that models the motion of an electron might define the distance unit to be 10-9 m, i.e., a nanometer, and the time unit to be 10-6 s, i.e., a μs. Another part of the animation, depicting a person walking, might define position given in meters and time given in seconds (the MKS system of units). Still another part of the animation depicts a star and might define position units to be 108 meters and time to be Earth years. In general, you should look for the units specified in the problem (whether from your text or from Physlet® Physics): On the Physlet Physics CD all units are given in boldface in the statement of the problem. The units for Animation 2 are given in the following paragraph.

Although computer simulations allow precise control of parameters, their resolution is not infinite. The numbers used to calculate the position and velocity of a particle have finite precision, and the algorithm updates these values at discrete times. Consequently, data is only available on the screen at certain predefined intervals. Whenever this data is presented on screen as a numeric value, it is correct to within the last digit shown. Start Animation 2 and follow the procedures below to make position measurements (position is given in meters and time is given in seconds).

Some problems require that you click-drag the mouse inside the animation to make measurements. Try it. Place the cursor in the animation and left-click and hold down the mouse button. Now drag the mouse around to see the x and y coordinates of the mouse change in the lower left-hand corner of the animation. Notice the way the coordinates change. As you drag the mouse around can you find the origin of coordinates? This is an easy question in these animations because the coordinate axes are shown. However, the coordinate axes will not always be shown. You can always find the origin of coordinates by click-dragging the mouse.

In addition, these measurements cannot be more accurate than one screen pixel. This means that depending on how you measure the position of an object you may get a slightly different answer than another student in your class.

For example, where is the man in Animation 2 at t = 10 s? You could get anywhere between 19.4 meters and 20.3 meters depending on whether you are measuring the position of the man from his front, back, or center. In order to make good measurements you must be consistent.

You also must be careful to choose a problem-solving approach that does not depend critically on the difference between two numbers that are almost equal. It may not be possible to extract certain types of information from an animation if the changes in the relevant parameters are too small.

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