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I've only formally learned as far as college level physics 1, but I don't understand potential energy. I get it in the equations, such as when the ball is just about to drop over the ramp its filled with potential energy, but what determines that it IS potential. The ball isn't moving yet, it's on a flat surface, and honestly probably won't fall unless its pushed. So how does a ball atop a ramp have potential energy, but one sitting flat on the ground doesn't? And since the entire earth is moving, how does it ever have 0 kinetic energy? Is this just one of those arbitrary things that's taught to get a grasp on concepts or is it used eternally through classical physics to the level of practiced physicists?

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  • $\begingroup$ Physics determines how the potential energy of a system can be calculated so that the energy might be stored or put to use. $\endgroup$
    – user245539
    Apr 15, 2020 at 13:26

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At a very high level, potential energy is the energy that's available to cause motion, but it isn't energy that is actually associated with motion (i.e. kinetic energy). Potential energy can only convert into kinetic energy (i.e. motion) when there is a gradient of potential energy, and the object will want to move from high potential energy to low potential energy -- in the process, it will convert the change in potential energy into kinetic energy.

So with that high level overview, let's consider your specific examples. When a ball is at the top of a ramp, it has some amount of potential energy. If the ball were sitting at the bottom of the ramp, it would have some other, lower amount of potential energy. And so there is a gradient of potential energy -- it is high at the top, low at the bottom, and so the ball moves from high to low (rolls down the ramp). And as it moves down the ramp, little by little, it's potential energy decreases and converts to kinetic energy.

The ball sitting on a flat ground has no gradients in potential energy. If it moves left or right, it still has the same amount of potential energy it did before. So there's no gradient, and no conversion of potential to kinetic energy.

Now, an important and subtle point here -- gradients of potential energy are what matter. Not the "total amount" of it. So, for convenience, we often take the bottom of the system in your examples to have zero potential energy. But we can add any arbitrary number to the whole field and the gradient is the same. Meaning, if the bottom of the ramp is $P = 0$ and the top is $P = 10$, then the ball behaves the exact same as if we said the bottom is $P = 1000$ and the top is $P = 1010$. Or -1000 and -990.

To your next question, kinetic energy and why it is zero if the Earth is still moving. First, it's important to recognize than when we work example problems, we usually work on an isolated system. Meaning, we ignore things that have a minimal impact on our problem. So, for a ball rolling down a ramp, the spin of the Earth and the movement of Earth through space don't matter really, for a small enough ball and ramp, so we don't have to worry about it.

But another, more subtle point, is that kinetic energy depends on your reference frame. So, a ball on a ramp sitting motionless on the floor has zero kinetic energy in the reference frame of the floor. Even if that floor is on a high speed train. But, somebody outside the train would see the ball and ramp go past them very quickly and so in their view, the ball has a lot of kinetic energy.

At the end of the day, the specific values of energy are rarely important. It's always the gradients of energy (in either time or space) that are really important, and those are preserved when we add constants to the fields (to use other words, for inertial motion).

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  • $\begingroup$ Ok, so PE and KE are system relative, not a universal value. I'm very bad at abstracts and that was never explained to me, I'm assuming because they figured it was implied $\endgroup$ Apr 15, 2020 at 13:22
  • $\begingroup$ @TheBasementNerd I recall it not being made terribly clear to me when I was learning classical mechanics either at the high school/AP/college intro level. It's usually just kind of implied when they tell you to calculate potential energy as $g \Delta h$ -- implicit in that is that potential energy is 0 at the bottom of whatever you're looking at. $\endgroup$
    – tpg2114
    Apr 15, 2020 at 13:23
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These are actually more than one question.

First for the potential energy: Generally when speaking about potential energy (and therefore also total energy), only energy-differences are meaningful. So when you say that a ball lying on the floor has no potential energy, this means that you define where the zero is. In this example the "nicest" definition might be defining the zero to be at the center of the earth, but the you would have to calculate with very big numbers, which is not so nice. So independent of where you define the zero to be, the physics remain the same. With the zero being defined at your floor, a hole in your floor must have negative potential energy, which sounds weird, but isn't forbidden or anything.

Next kinetic energy: Kinetic energy depends on the frame of reference. If this doesn't mean anything to you, you should read up on this concept. In your frame of reference a ball lying on the floor doesn't have kinetic energy, but in the frame of reference of the sun it does have a lot of it. The amazing thing is, that as long as you are in an so-called inertial frame which isn't being accelerated with respect to other inertial frames (kinda bad definition, but stick with me for the moment), the physics remain the same. Technically your frame of reference is NOT an inertial frame, because you are being accelerated by the earth spinning and so on (see Coriolis "force" / virtual forces). But for most experiments you can approximate it as being inertial because the effect of the earth spinning is way smaller than most things you can measure.

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  • $\begingroup$ So its just that PE and KE are based in the frame of reference and system, not as universal or measurable values that anyone can get the same reading of. They're used to measure stuff in a system, not determine a value about an object like mass or electrical conductivity $\endgroup$ Apr 15, 2020 at 13:24
  • $\begingroup$ Only energy differences are physical (and to compare measurements you have to take them in the same frame or transform them to the same frame). This is similar to voltage which is always compared to the ground, while the total electrical potential is also not physical. This concept is called gauge freedom (there is a lot more to it, but this is the basics). $\endgroup$
    – paleonix
    Apr 15, 2020 at 13:30

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