• Terminara – Terminal Velocity Physics Sticker

Indexतरंगें, अराजकता और पदार्थSticker

Terminara

Terminal Velocity Physics

\[m\frac{dv}{dt} = mg - \tfrac12\rho C_d A\,v^2\]
$4.99 USD
$4.99 USD
सेल बिक चुका
Size
Surface

Why does a skydiver stop speeding up? Air drag grows with the square of the speed. When drag balances weight, the net force is zero and the fall settles at terminal velocity, v_t = √(2mg/ρC_dA). For an 80 kg skydiver falling belly-down in sea-level air, that is about 53 m/s, roughly 190 km/h. A 3" pixel-art sticker; equation, symbols and sources in the physics panel below.

Shipping calculated at checkout by destinationMade to order, ships in 2–5 business days

Details

Size3″ × 3″

3″ × 3″ kiss-cut sticker.

Shipping

Shipping calculated at checkout by destination. Printed to order for you.

Delivery times & where we ship

Returns & replacements21 days

Every item is printed to order, so we can’t accept returns or exchanges for change of mind, or if you ordered the wrong size or colour.

Print defect, misprint, damage or the wrong item? We’ll send a free replacement, or a refund if you prefer. Report it within 21 days of delivery with a photo; no need to send it back.

Full refund & replacement policy

The physics

A falling object speeds up until air drag, which grows with the square of speed, balances its weight. From then on it falls at a steady terminal velocity, approaching it along a tanh curve.

Terminara has stopped speeding up. She is still falling, just not any faster.

Air pushes back on a falling body with a drag force ½ρC_dA v² that grows with the square of the speed. When drag equals weight, the net force is zero and the speed stops changing. That speed is the terminal velocity, v_t = √(2mg/ρC_dA).

With the illustrative values in the art, an 80 kg skydiver lying belly-down (C_dA = 0.45 m²) in sea-level air, v_t is 53.4 m/s, about 192 km/h. Falling from rest the speed follows v = v_t tanh(gt/v_t) and reaches 99 % of v_t after about 14 s. The graph on her sticker is that curve, checked against a numerical solution.

Real skydivers change v_t by changing shape: tucking in shrinks C_dA and they fall faster.

I stopped speeding up.

Equations

\[m\frac{dv}{dt} = mg - \tfrac12\rho C_d A\,v^2\]
\[v_t = \sqrt{\frac{2mg}{\rho C_d A}}\]
\[v(t) = v_t\tanh\!\left(\frac{g t}{v_t}\right)\]
SymbolMeaningUnit
\(m\) mass of the skydiver (here 80 kg) \(\mathrm{kg}\)
\(v\) falling speed \(\mathrm{m/s}\)
\(t\) time since leaving the plane, falling from rest \(\mathrm{s}\)
\(g\) gravitational acceleration \(\mathrm{m/s^2}\)
\(\rho\) air density (here 1.225 kg/m^3, sea-level standard) \(\mathrm{kg/m^3}\)
\(C_d A\) drag coefficient times frontal area (here 0.45 m^2, belly-down) \(\mathrm{m^2}\)
\(v_t\) terminal velocity (here 53.4 m/s, about 192 km/h) \(\mathrm{m/s}\)

Sources

  1. NASA Glenn Research Center, Beginner’s Guide to Aeronautics: Terminal Velocity
  2. Taylor, Classical Mechanics (2005), Sec. 2.4: Quadratic air resistance

Source Newton, I. (1687). Philosophiæ Naturalis Principia Mathematica, Book II, Section II (motion of bodies resisted in the duplicate ratio of their velocities). London: Royal Society (J. Streater).

Field notes

सभी देखें
1 3
सभी देखें