Tag: physics

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The Symbiotic Relationship Between Physics and Mathematics

Physics created mathematics, or was it mathematics that created physics? Back in ancient times, it is evident that gravity gave rise to what we now call a 90-degree angle, a symbol of perpendicularity in two or three dimensions. This marked our hominid ancestors’ first concrete encounter with mathematics. Other rediscoveries followed, as mathematics is, at its core, a constant RE-discovery of the hidden facets of the world around us. In the natural world, physics shaped the mathematical instincts of countless builders, from bees constructing their hives to spiders weaving their webs, both sensing forces and symmetry with innate precision.
Today, however, the realms of the infinitely small and the infinitely large can only be understood through mathematics. Our senses and intuition fall short when faced with these new dimensions. Concepts such as the EPR effect, gauge invariance, and spin would remain invisible to us without the crutches provided by mathematics.

· EPR effect: A quantum phenomenon where two particles become instantaneously linked, regardless of distance.
· Gauge invariance: A principle that certain physical properties remain unchanged under specific transformations.
· Spin: A fundamental quantum property of particles that represents intrinsic angular momentum.

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Bullets vs. Water: The Physics of Drag Force in Action

Ever wondered what happens when you shoot a bullet in water?
The deeper the water, the faster the bullet slows down. Water’s higher density causes much more resistance than air, rapidly draining the bullet’s kinetic energy. In just a few meters, the bullet can come to a complete stop!
Why? Water creates a drag force that decelerates the bullet. The formula behind this?
Drag Force (Fₑ) = ½ * Cₔ * ρ * A * v²
Where:
Cₔ​ = Drag coefficient (depends on the bullet shape)
ρ = Water’s density (about 1000 kg/m³)
A = Bullet’s cross-sectional area
v = Bullet’s velocity

As the bullet travels, drag slows it down and uses up its energy quickly. In just a few meters, the bullet is stopped dead in its tracks!

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Walking on Water—No Miracle Needed!

Paper wasps (Polyistes dominula) stand on the water’s surface while drinking. The ‘surface tension‘ of the water, a property that causes water molecules to stick together, acts like an elastic sheet, supporting the wasp’s weight. The wasp’s six legs create depressions in the surface, forming lens-like curvatures that cast tiny shadows beneath the water. Surface tension is crucial for many organisms, as it creates a habitat for various life forms on the water’s surface.

surface-tension-formula

In this formula, surface tension (γ) represents the force across an imaginary line divided by twice the length of that line. The factor of 2 is essential because, when splitting the surface of a bubble, we’re actually pulling apart molecules on two surfaces—the inner and the outer.

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The Doppler Effect: A Mathematical Symphony

Imagine a siren on a fire truck…
· When the truck is approaching you: The siren’s sound waves are compressed, making it sound higher pitched. It’s like the truck is “pushing” the waves together.
· When the truck is moving away from you: The siren’s sound waves are stretched out, making it sound lower pitched. It’s like the truck is “pulling” the waves apart.
This is the Doppler effect: the change in pitch of a sound wave due to the relative motion between the source of the sound and the observer.
The same concept applies to light waves, with objects moving toward us appearing bluer and those moving away appearing redder.

⇨ Further reading.