Based on what you have learned from the previous two tutorials, how would you arrange the magnets to create the following potential energy diagram?
In general, when we work on a certain task, we always prefer to have as much information (data) available as possible. In the example with the car, to analyze completely its behavior, you will need an additional piece of information - the total energy of the car. The total energy (potential + kinetic) is often represented by a horizontal line added either to the kinetic or potential energy diagrams. From now on we will draw the total energy as a line relative to the potential energy diagram, as shown below in Figure 2.
Why should we draw the total energy as a flat line, while the potential energy changes in situations where we ignore friction?
Consider a car which has the total energy indicated in Figure 2. It is approaching from the right a set of magnets which have the potential energy represented by the solid curve. See Figure 3.
What is the value of the kinetic energy:
a) at distance of x = 12 m; b) at point A, where the potential energy and total energy are equal; and
c) at distance of x = 8 m.
Notice that in the shaded region (x = 8m, for example) the kinetic energy that we calculate is negative. This result is a difficulty. The mass of the car is always positive, as well as its squared velocity. Thus, kinetic energy cannot be negative. A negative kinetic energy has no physical meaning! For a negative kinetic energy to exist, it has to be associated with negative mass or negative (velocity)2. Neither of these is physically possible. The only other option is that the car cannot go in regions where we calculate a negative kinetic energy.
Therefore, it is not physically possible for the car to get to the LEFT of point A. When the car approaches point A from the right, it will stop and turn back in the opposite direction.