What is mass of a spring?

Question

If we take a spring of mass M and compress it, it's energy
will increase by ΔE = 1/2 kx², and, accordingly, its mass
will inrease by ΔM = ΔE/c² = 1/2 k(x/c)². What this new
mass ΔM consist of?

Answer 1

Since you're posing a relativistic question, I would prefer to examine this question in clearer relativistic terms, and restate the problem in a different way. Imagine that we have a frictionless sled of mass M on rails and at rest. Then the total energy of the sled is

E = Mc²

Suppose it expends a certain mass m converted entirely into energy, used to propel the sled with 100% efficiency. Then the total energy of the sled is now

E = (M-m)c² /√(1-(v/c)²) = Mc²

since total energy is conserved. Adding mc² to both sides and rearranging, we have:

(M-m)c² /√(1-(v/c)²) - (M-m)c² = mc²

The term on the left is the expression for the relativistic kinetic energy for a mass of (M-m) moving at speed v, while the term on the right is the energy converted from mass m. It got converted into kinetic energy.

Going back to the original problem, if work is done to a spring with no change in internal heat, then the higher potential energy it then has will result in a heavier mass by ΔM = ΔE/c² = 1/2 k(x/c)². Releasing this potential energy will result in a conversion of this mass into some other form of energy such as kinetic energy, as with the example given above. There are numerous instances where increased potential energy in the form of electron orbitals or binding energies in nuclei or even Van der Vaal forces does result in a greater mass, which is lost upon losing such potential energy.

Answer 2

I don't understand the question? Everything you wrote is correct. The mass increases by that amount when you squish it. It's a very small mass of course. So what's the question? Are you bothered by the idea of the electrostatic energy added by stretching the metal being massive? When you get to smaller and smaller elementary particles, you become more comfortable with this sort of thing. For many baryons, the component quarks are only a tiny fraction of the barion mass. The rest is binding energy. It only seems wierd at first until you drop your preconception of mass as something more tangible than potential energy.

Answer 3

i've got self belief you're pertaining to the pendulum type of a ball on a spring putting from a standing pole. To calculate its era is 2pi circumstances the sq. root of L/g. *L is the size ang g is the acceleration of gravity. i do no longer understand what you're asking in the different 2 questions. A node is a table sure portion of a wave.

Answer 4

E = mc² is an expression showing the amount of energy inherent in a given quantity of mass.

½kx² is an amount of energy added to the mass by virtue of its elastic properties while maintaining the exact same mass.

Your bookkeeping fails in your second equation.

Answer 5

compressing a spring will not increase it's mass - perhaps you are referring to the potential energy - but unless you increase the material content of the spring the mass will remain constant