My physics is pretty rusty so fill me in here. From what I understand, if I roll a boulder up a hill to a cliff edge I have to exert energy to do so. And according to the laws of thermodynamics, energy cannot be created or destroyed, so the energy I exerted is transfered to the boulder as potential energy. If I roll the boulder off the cliff and it smacks into the ground below, the potential energy is converted into kinetic energy.
I just don’t get why the potential energy is created. How does the energy from my rolling become potential energy? Does the boulder show any measurable change? Isn’t this purely theoretical? How exactly do physicists prove it exists other than showing it makes their equations balance on paper?
What changes is “h”. That is the height difference from where the boulder started to where it ended. If h is positive, it has more potential energy.
Lets say that you and the boulder are standing on solid level ground, you both have the same potential energy and the boulder poses no danger in crushing you. Now, you pick the boulder up with a crane and raise it 20’ above your head. The boulder now has the potential to exert enough energy to crush you.
In the above example, suppose I am 5’ tall. The boulder has 15’ of potential energy, because it can fall 15’, right?
Now suppose I move out of the way of the boulder. It now has a full 20’ of potential energy, right? Where did the extra energy come from?
Further: Suppose I was standing on a board of some kind, which I move out of the way to reveal a hole which is one mile deep. The tiny expenditure of energy which I used to move the board has given that boulder a LOT more potential energy, almost for free!
I think I’m misunderstanding something. Someone, please educate me!
You have to describe potential energy relative to a datum. In my example, the datum was the floor that both you and the boulder were standing on.
RE: your question about 15’ vs 20’ of PE. If you raise the boulder 20’ from the established datum, it has 20’ of PE. If it gets dropped on your head and somehow sits there without crushing you, it has used up 15’ of PE, but still has 5’ of PE since if it were to roll off your head, it would still fall 5’.
I missed the other part. If you use the floor as a datum, if you revealed a hole 1 mile deep, and if the boulder were to fall the one mile, the boulder would now have -5280’ of PE because that’s how much energy it would take to get the boulder back to where it started.
Gravity is not the only way of storing potential energy. Whereas gravity stores a potential energy based on a change in height, a spring stores potential energy based on a change in length.
If I may try to interpret the OP, I think the issue not how to calculate PE, but whether a boulder could somehow be measured to be more “energetic” by virtue of it being higher up. As far as I know there’s no test you could do on a rock to figure its potential energy without checking its height above the ground, or measuring how hard it was to get up there. It’s not like there’s extra energy packets zipping around within it.
But then again, it has to be more than just some bookkeeping trick nature does to keep conservation of energy working.
It might help more to think of the potential energy stored in, say, a stretched rubber band. All those molecular bonds would like to be in their natural state, but they’re instead stretched out. In a way, the potential energy is stored in all those bonds.
Better physicists will surely be along soon to correct me
Like I said, potential energy means nothing without a starting point. You have to work to store PE.
W=F*D
Whether it is the force to push a boulder some distance up a hill or the force to compress a spring some distance, once the work is done, it is stored as PE. Now if you let go of the spring or allow the boulder to roll back down the hill you get all that work back. Of course in the real world, you have to subtract things out like friction and air resistance.
No, the boulder shows no locally-measurable change merely from gaining gravitational potential energy.
You can think of potential energy as a bookkeeping device. It’s a very useful bookkeeping device, because conservation of energy is a very powerful constraint on physical systems (and patent law). Physicists love conservation laws, and adding a somewhat mysterious but easily-calculated number to keep something conserved is a price worth paying.
But whenever physicists see a bookkeeping device or happy coincidence like this, something gnaws at their souls. They are compelled to try to find some deeper explanation, some theory or interpretation that turns the trick into a natural consequence of some physical effect. In the case of gravitational (and electromagnetic) potential energies, their explanation was that the energy is stored nonlocally in the fields. Moving a boulder uphill forces the gravitational field into a higher-energy state, just like stretching a rubber band; and what brings the boulder back downhill is this higher-energy state relaxing back to a less-stretched-out condition.
Then, of course, physicists turn their attentions to this mysterious “field,” which they initially thought of as just a bookkeeping device for understanding how the forces change with position. You can write down “classical field equations” (Maxwell’s equations for EM; Einstein’s equations for gravity) describing the properties of this field, but what is it, really? Where does it live, and how does it propagate? In the case of electromagnetism, physicists discovered that it was quantized. The field had certain indivisible properties–“quanta”–and understanding their properties led to the theory of quantum electrodynamics. So now they think they understand electromagnetic potential energy–it’s the energy in the electromagnetic field–and they understand the electromagnetic field–it’s a bunch of these “quanta” behaving according to laws they can write down; and they can sleep at night.
Until they start thinking about gravity. It’s a natural guess that gravity, which classically looks so much like electromagnetism (long-range inverse-square forces), should follow the same path. But quantizing gravity turns out to be more difficult, both theoretically (Einstein’s equations are nonlinear, for example, while Maxwell’s equations are linear) and empirically (gravity is such a weak force (not to be confused with the Weak Force) that it is difficult to explore experimentally).
Drewbert: Your post seems to describe the same question I had. The answer is that the “bookkeeping trick” is Brewha’s requirement that “potential energy means nothing without a starting point”.
Thanks all! This has been annoying me for only 40 years or so.
Another way of looking at it, is that in (almost) all areas of physics, energy itself doesn’t matter. It’s only changes in energy that matter. If a 1 kg rock falls 1 meter in Earth’s gravity, it loses 9.8 Joules of potential energy. It could have gone from 9.8 J to 0 J, or from 10009.8 J to 10000 J, or from -17.3 J to -27.2 J, depending on what you call “zero”, but in all cases, the change was 9.8 J.
Of course there is a change. It increases in mass. E=mc[sup]2[/sup]. Note that for everyday objects, the change is too small percentagewise to be measured using the usual techniques. But for subatomic particles changing position in a field, it can be.
