Digital Photogate Free-Fall Lab

Dropped Object

Mass 0.20 kg

Drag coefficient × area 0.004

Gate 1→2 separation 1.20 m

Photogate Timer

Gate 1: — s Gate 2: — s Δt: —

Instant speed

0.00 m/s

Experimental g

— m/s²

Terminal velocity

— m/s

Drops logged

How it works

The object falls under gravity while air drag opposes its motion. Its equation of motion is integrated numerically each frame:

m·(dv/dt) = m·g − k·v²      (k = drag coefficient × area)
v(t+dt) = v(t) + (g − (k/m)·v²)·dt
y(t+dt) = y(t) − v(t+dt)·dt

Two virtual photogates sit a fixed distance apart. Each one records the exact simulated time the falling object's leading edge crosses its light beam — exactly like the digital timers used in a real classroom free-fall lab. From those two timestamps the app computes:

Δt — the measured time between the gates.
Instant speed at gate 2, from Δt and the gate separation.
Experimental g, back-solved from the two gate speeds and Δt using v₂ = v₁ + g·Δt (only accurate with negligible drag — a heavy compact object like the steel ball gives you close to 9.8 m/s²; increase drag/area to see the estimate degrade).
Terminal velocity v_t = √(m·g / k) — the speed at which drag exactly balances gravity, shown once the object is falling fast enough to approach it.

This is the core mechanic behind classroom "smart lab" kits: replacing a stopwatch and human reaction time with digital photogates removes timing error, turning a free-fall drop into a precise, repeatable measurement of g and of how air resistance changes with an object's shape and mass.

Gate 1: — Gate 2: — Status: ready

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