5 ms·

There's a bunch of half-answers in this thread. > Generally speaking, when we lift matter high above, we get some of the used energy back when it falls back do

There's a bunch of half-answers in this thread. > Generally speaking, when we lift matter high above, we get some of the used energy back when it falls back down. > Where is the energy stored in the meantime? Potential energy in a gravity well is negative. The "zero" point is the limit when you get far away from all gravitational bodies. The better question is: Where does the kinetic energy come from when you descend down the gravity well in the first place? The answer is mass. All potential energy is ultimately realized as a change in mass, equal to the famous `mass_difference * speed_of_light^2`. As the body falls down the gravity well, it gains kinetic energy and loses mass. When atoms bind together in an exothermic reaction, their final state is bound more tightly than their initial state. They released some energy in the form of molecular-scale kinetic energy (ie, heat), and they have lost mass. When atoms change configuration in an endothermic reaction, their final state is bound less tightly than their initial state. Some energy was required to push them up to that higher-energy state (sometimes in the form of heat), and they have gained mass. When light nuclei fuse together, their final state is more tightly bound than their initial state. They released some energy in the form of atomic-scale kinetic energy (ie, heat) and a photon, and they have lost mass. Ironically, when very heavy nuclei have fissioned, their final state is more tightly bound than their initial state. They released some energy in the form of atomic-scale kinetic energy (ie, heat) and photons, and they have lost mass. When a spring is compressed, the molecules within the elastic material are stretched apart from one another such that their final state is less tightly bound than their initial state, and the spring has gained mass.

saagarjha 6y ago
> Potential energy in a gravity well is negative. The "zero" point is the limit when you get far away from all gravitational bodies. Like all potential energies, its definition is relative and its zero point convention. > As the body falls down the gravity well, it gains kinetic energy and loses mass. So you’re a saying that hydrogen lower in a gravity well will fuse worse?
- brandmeyer 6y ago
  > Like all potential energies, its definition is relative and its zero point convention. Turns out that this one does have a unique definition because the limit exists, and because the sum of kinetic energy and rest mass determines the gravitational influence of a body. > > As the body falls down the gravity well, it gains kinetic energy and loses mass. > So you’re a saying that hydrogen lower in a gravity well will fuse worse? No. The processes are orthogonal to each other. Forget for the moment that its the release of kinetic energy by dropping down the gravity well that makes the subsequent fusion possible at all. Whether you fused first and then dropped down the well, or dropped down the well first and then fused, the final state is the same.
  - saagarjha 6y ago
    > the sum of kinetic energy and rest mass determines the gravitational influence of a body No, I’m pretty sure it’s just rest mass. The gravitational force doesn’t change based on your kinetic energy. > Whether you fused first and then dropped down the well, or dropped down the well first and then fused, the final state is the same. Except the problem is that fusion only converts some fraction of mass into energy (while in your hypothesis potential energy is directly converted to mass), so in your case it would actually matter whether the fusing happened before or after falling in because lower in the gravity well, the mass would be less and you’d get less energy from the fusion.
    - cuspycode 6y ago
      > No, I’m pretty sure it’s just rest mass. The gravitational force doesn’t change based on your kinetic energy. The energy-momentum tensor (a.k.a. stress-energy tensor) is what determines spacetime curvature, and it depends on both rest mass, kinetic energy, momentum, pressure, and shear stress.
    - Xcelerate 6y ago
      > The gravitational force doesn’t change based on your kinetic energy. This is not correct. Gravity is a function of everything that has energy (see the stress energy tensor). It’s a very unusual “force” in this regard. This leads to interesting situations like a perfectly mirrored box of light (if you could have such a thing) weighing more on a scale than a box without light in it. Also, a spinning cue ball or a compressed spring weigh more than a stationary ball and an uncompressed spring. Granted, these differences are so small as to be undetectable by any equipment we could ever build, but it’s still interesting to think about.
TeMPOraL 6y ago
> When a spring is compressed, the molecules within the elastic material are stretched apart from one another such that their final state is less tightly bound than their initial state, and the spring has gained mass. Wait, isn't this the other way around? Why would molecules be less tightly bound when a string is compressed? They're all being pushed closer together.
- jiveturkey 6y ago
  I only looked this up based on the comment, and I am not versed in this, beyond standard undergrad physics an eon ago. Reader beware. The GP is wrong; it's not because molecules are closer or further apart, it's because we have introduced potential energy into the spring. The spring would gain mass regardless if it is compressed (molecules closer together?) or extended (molecules further apart?). I used question marks there because a coil spring is a wound wire. The coil-to-coil proximity is not happening at a molecular level and is irrelevant. It is the stretching of the bonds in the [circular] direction of the winding where they get closer/further. Being helical, when deformed one side is in tension and one side in compression, so there's a net zero molecular proximity. So I'm not convinced that spring compression is molecules getting closer, and that spring extension is molecules getting further. There's also a torsion spring, which is a bar with the ends fixed in place, that is twisted axially for the spring effect. Often used in formula car applications, but widely elsewhere as well. Here it is clear to see that compression and extension have the exact same effect, and that "closer" and "further" both occur. The introduced potential energy is equivalent to mass, hence the spring has gained mass (and the compressing/extending object has lost mass). https://www.physicsforums.com/threads/a-compressed-spring-has-more-mass.585199/ https://www.physicsforums.com/threads/a-compressed-spring-ha...
  - brandmeyer 6y ago
    I agree that picking compression specifically was misleading. > The GP is wrong; it's not because molecules are closer or further apart, it's because we have introduced potential energy into the spring. The structure of the electron orbitals leads to a preferred bond length. So, pushing them closer or farther apart from that preferred bond length introduces potential energy into the spring. Its just that either direction is "up" the potential energy well.

saagarjha 6y ago

> Potential energy in a gravity well is negative. The "zero" point is the limit when you get far away from all gravitational bodies. Like all potential energies, its definition is relative and its zero point convention. > As the body falls down the gravity well, it gains kinetic energy and loses mass. So you’re a saying that hydrogen lower in a gravity well will fuse worse?

brandmeyer 6y ago
> Like all potential energies, its definition is relative and its zero point convention. Turns out that this one does have a unique definition because the limit exists, and because the sum of kinetic energy and rest mass determines the gravitational influence of a body. > > As the body falls down the gravity well, it gains kinetic energy and loses mass. > So you’re a saying that hydrogen lower in a gravity well will fuse worse? No. The processes are orthogonal to each other. Forget for the moment that its the release of kinetic energy by dropping down the gravity well that makes the subsequent fusion possible at all. Whether you fused first and then dropped down the well, or dropped down the well first and then fused, the final state is the same.
- saagarjha 6y ago
  > the sum of kinetic energy and rest mass determines the gravitational influence of a body No, I’m pretty sure it’s just rest mass. The gravitational force doesn’t change based on your kinetic energy. > Whether you fused first and then dropped down the well, or dropped down the well first and then fused, the final state is the same. Except the problem is that fusion only converts some fraction of mass into energy (while in your hypothesis potential energy is directly converted to mass), so in your case it would actually matter whether the fusing happened before or after falling in because lower in the gravity well, the mass would be less and you’d get less energy from the fusion.
  - cuspycode 6y ago
    > No, I’m pretty sure it’s just rest mass. The gravitational force doesn’t change based on your kinetic energy. The energy-momentum tensor (a.k.a. stress-energy tensor) is what determines spacetime curvature, and it depends on both rest mass, kinetic energy, momentum, pressure, and shear stress.
  - Xcelerate 6y ago
    > The gravitational force doesn’t change based on your kinetic energy. This is not correct. Gravity is a function of everything that has energy (see the stress energy tensor). It’s a very unusual “force” in this regard. This leads to interesting situations like a perfectly mirrored box of light (if you could have such a thing) weighing more on a scale than a box without light in it. Also, a spinning cue ball or a compressed spring weigh more than a stationary ball and an uncompressed spring. Granted, these differences are so small as to be undetectable by any equipment we could ever build, but it’s still interesting to think about.

TeMPOraL 6y ago

> When a spring is compressed, the molecules within the elastic material are stretched apart from one another such that their final state is less tightly bound than their initial state, and the spring has gained mass. Wait, isn't this the other way around? Why would molecules be less tightly bound when a string is compressed? They're all being pushed closer together.

jiveturkey 6y ago
I only looked this up based on the comment, and I am not versed in this, beyond standard undergrad physics an eon ago. Reader beware. The GP is wrong; it's not because molecules are closer or further apart, it's because we have introduced potential energy into the spring. The spring would gain mass regardless if it is compressed (molecules closer together?) or extended (molecules further apart?). I used question marks there because a coil spring is a wound wire. The coil-to-coil proximity is not happening at a molecular level and is irrelevant. It is the stretching of the bonds in the [circular] direction of the winding where they get closer/further. Being helical, when deformed one side is in tension and one side in compression, so there's a net zero molecular proximity. So I'm not convinced that spring compression is molecules getting closer, and that spring extension is molecules getting further. There's also a torsion spring, which is a bar with the ends fixed in place, that is twisted axially for the spring effect. Often used in formula car applications, but widely elsewhere as well. Here it is clear to see that compression and extension have the exact same effect, and that "closer" and "further" both occur. The introduced potential energy is equivalent to mass, hence the spring has gained mass (and the compressing/extending object has lost mass). https://www.physicsforums.com/threads/a-compressed-spring-has-more-mass.585199/ https://www.physicsforums.com/threads/a-compressed-spring-ha...
- brandmeyer 6y ago
  I agree that picking compression specifically was misleading. > The GP is wrong; it's not because molecules are closer or further apart, it's because we have introduced potential energy into the spring. The structure of the electron orbitals leads to a preferred bond length. So, pushing them closer or farther apart from that preferred bond length introduces potential energy into the spring. Its just that either direction is "up" the potential energy well.