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Illustration 7.2: Representations of Energy
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There are many different ways to represent motion (as we have already seen). The same is true for energy. For example we can represent an object's kinetic energy using a graph of kinetic energy vs. time, a bar chart of kinetic energy that changes with time, or as a value in a table that changes with time (position is given in meters, time is given in seconds, and energy on the bar graph is given in joules). All three representations give us the same information, just in different forms. So why might we want to use a different representation? Well, it depends on what concept we are trying to illustrate and which representation gets to the heart of that concept. The collision occurs at a distance due to magnets on the front of each cart that allow the carts to collide without touching. Restart.
The graph shows us an instant-by-instant accounting of the kinetic energy of each cart. This is important if we wish to analyze every detail of the kinetic energy of the carts involved in the collision. Usually we are interested in whether or not energy is conserved in a given collision. In this case a graph gives this information, but it also gives us much more information. Notice that during the collision (kinetic) energy appears to be missing! This energy must be accounted for, so where is it? It is temporarily stored by the magnets attached to the carts. If there was a spring in between the carts, the energy would have been temporarily stored there instead. This energy is then transferred back to the carts by the end of the collision. This is why we compare the kinetic energies before the collision to those after the collision and often do not attempt to analyze the details of the collision itself.
Another way to answer the question of energy conservation, therefore, is with the bar chart (it is color coded) or with a table (the values are labeled). We simply compare the values—either the size of the bars or the values from the table—from before and after the collision. Are they the same? If yes, the energy, specifically the kinetic energy, of the two-cart system is conserved.