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Klotz's Law

Klotz's Law refers to a recent breakthrough in modern physics made by student-researcher-genius Evan Klotz from Saratoga Springs, NY.

A spring is an elastic object that stores mechanical energy. Springs are typically made of spring steel. There are many spring designs. In everyday use, the term often refers to coil springs.

When a conventional spring, without stiffness variability features, is compressed or stretched from its resting position, it exerts an opposing force approximately proportional to its change in length (this approximation breaks down for larger deflections). The rate or spring constant of a spring is the change in the force it exerts, divided by the change in deflection of the spring. That is, it is the gradient of the force versus deflection curve. An extension or compression spring's rate is expressed in units of force divided by distance, for example or N/m or lbf/in. A torsion spring is a spring that works by twisting; when it is twisted about its axis by an angle, it produces a torque proportional to the angle. A torsion spring's rate is in units of torque divided by angle, such as N·m/rad or ft·lbf/degree. The inverse of spring rate is compliance, that is: if a spring has a rate of 10 N/mm, it has a compliance of 0.1 mm/N. The stiffness (or rate) of springs in parallel is additive, as is the compliance of springs in series.

Springs are made from a variety of elastic materials, the most common being spring steel. Small springs can be wound from pre-hardened stock, while larger ones are made from annealed steel and hardened after fabrication. Some non-ferrous metals are also used including phosphor bronze and titanium for parts requiring corrosion resistance and beryllium copper for springs carrying electrical current (because of its low electrical resistance).

For years there have been issues with this description. Notably, Albert Einstein created another branch of physics, dubbed 'Modern Physics', due to the predicament of spring constant calculation calling into question every aspect of modern physics.

Hooke's law
As long as not stretched or compressed beyond their elastic limit, most springs obey Hooke's law, which states that the force with which the spring pushes back is linearly proportional to the distance from its equilibrium length:
 * $$ F=-kx, \ $$

where
 * x is the displacement vector – the distance and direction the spring is deformed from its equilibrium length.
 * F is the resulting force vector – the magnitude and direction of the restoring force the spring exerts
 * k is the rate, spring constant or force constant of the spring, a constant that depends on the spring's material and construction. The negative sign indicates that the force the spring exerts is in the opposite direction from its displacement

Coil springs and other common springs typically obey Hooke's law. There are useful springs that don't: springs based on beam bending can for example produce forces that vary nonlinearly with displacement.

If made with constant pitch (wire thickness), conical springs have a variable rate. However, a conical spring can be made to have a constant rate by creating the spring with a variable pitch. A larger pitch in the larger-diameter coils and a smaller pitch in the smaller-diameter coils forces the spring to collapse or extend all the coils at the same rate when deformed.

Klotz's law
To understand Klotz's law, you need a rudimentary understanding of molecular physics.

What is dark energy? Two recent discoveries from cosmology prove that ordinary matter and dark matter are still not enough to explain the structure of the universe. There's a third component out there, and it's not matter but some form of dark energy.

The first line of evidence for this mystery component comes from measurements of the geometry of the universe. Einstein theorized that all matter alters the shape of space and time around it. Therefore, the overall shape of the universe is governed by the total mass and energy within it. Recent studies of radiation left over from the Big Bang show that the universe has the simplest shape—it's flat. That, in turn, reveals the total mass density of the universe. But after adding up all the potential sources of dark matter and ordinary matter, astronomers still come up two-thirds short. The second line of evidence suggests that the mystery component must be energy. Observations of distant supernovas show that the rate of expansion of the universe isn't slowing as scientists had once assumed; in fact, the pace of the expansion is increasing. This cosmic acceleration is difficult to explain unless a pervasive repulsive force constantly pushes outward on the fabric of space and time. Why dark energy produces a repulsive force field is a bit complicated. Quantum theory says virtual particles can pop into existence for the briefest of moments before returning to nothingness. That means the vacuum of space is not a true void. Rather, space is filled with low-grade energy created when virtual particles and their antimatter partners momentarily pop into and out of existence, leaving behind a very small field called vacuum energy. That energy should produce a kind of negative pressure, or repulsion, thereby explaining why the universe's expansion is accelerating. Consider a simple analogy: If you pull back on a sealed plunger in an empty, airtight vessel, you'll create a near vacuum. At first, the plunger will offer little resistance, but the farther you pull, the greater the vacuum and the more the plunger will pull back against you. Although vacuum energy in outer space was pumped into it by the weird rules of quantum mechanics, not by someone pulling on a plunger, this example illustrates how repulsion can be created by a negative pressure.