However, for the Earth-car system as a whole, the total energy remains constant. This is what we call “energy conservation.” Therefore, as OR decreases, the vehicle must gain another type of energy. This is the kinetic energy (K.E.), which depends on the mass and the speed (v).
When the vehicle hits the ground, its potential energy is zero and it moves with a certain kinetic energy. It then goes up the curve and the opposite happens: its speed decreases and its potential energy increases. For simplicity, let’s consider three key points of this track: point 1 is at the top of the track, 2 is at the bottom, and the third is the top of the loop. As we just mentioned, the total energy at the three points is the same, so we can write the following:
You can see that the middle point doesn’t matter. Yes, all that potential energy from the initial position is converted to kinetic energy at the bottom, but then this energy is simply converted back into the same amount of potential energy. So for a 4 meter high loop, you would have to start the car at a height of 4 meters. Which is a terrible idea; The vehicle will reach the top of the loop, but since the kinetic energy is reduced to zero at this point, it will not go any further, it will simply fall.
Keep moving
If you want to go all the way around, the car will have to preserve its speed at the top. At what speed exactly? Suppose the loop is a perfect circle with radius R. We have to consider the forces acting on it at the top of the loop. Let’s see it in this diagram:
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