Examples
The examples are ready-made scenes and Python scripts for classic problems and machines, published in the marketplace by Ordinate 2D (with a verified tick): in the studio, Home → Marketplace, first section. Most open in Research with graphs and a table of the run, and many with the theory curve to compare. Click one below to open it in the studio.
Motion and projectiles
- Projectile Motion Research
A ball launched at 14 m/s and 40°: x runs at a constant speed, y under g. Range R = v₀² sin 2θ / g and the height against its theory curve. - Terminal Velocity Research
Three 2 kg blocks fall: in a vacuum, as a skydiver (F = −kv²) and with a parachute. v approaches √(mg/k) and the weight is balanced by the drag. - Four Models of Air Resistance Research
Four balls dropped in air: no drag, F = −bv, F = −kv² and the shape model ½ρC_dAv². Compare their speeds and the energy they lose. - The Monkey and the Hunter Research
A dart is aimed straight at a monkey that lets go at the instant of the shot. Both fall by ½gt², so the dart hits whatever its speed: the distance between them shrinks at exactly v₀.
Forces and friction
- Inclined Plane
28° ramp. Friction is below tan θ, so the block slides. - Sliding to a Stop Research
A block slides across a floor with μ = 0.1: the speed falls linearly at μg and it stops after s = v²/(2μg). - Crate on a Slope Held by a Rope Research
A 50 kg crate on a smooth 20° slope: the rope carries T = mg sin θ = 168 N. Its free-body diagram is drawn. - Hooke's Law: Three Masses on Springs Research
1, 2 and 3 kg hang on identical 40 N/m springs: the extension is mg/k, so twice the mass stretches the spring twice as far.
Energy, momentum and collisions
- Newton's Cradle
Five balls. Pull the end ball back and let it go. - Bouncing Ball: Energy Research
A ball dropped from 5 m: PE becomes KE (v = √(2gh)), and each bounce keeps e² of the energy. - Disc Rolling in a V-Track Research
A disc rolls down one ramp and up the other: potential energy, kinetic energy of the motion and of the spin, and a constant total. - Elastic Collision Research
1 kg at 3 m/s hits 2 kg at rest: the velocities after are −1 and +2 m/s; momentum and kinetic energy are both conserved.
Oscillations and waves
- Pendulum
A bob on a rigid rod, released from 38°. - Double Pendulum
Two rods, chaotic for almost any release angle. - Mass in a Slot Research
A mass in a slot with hatched channel walls, tied to the slot end by a spring (k, c). Labels, dimension x, frame I. - Pendulum on a Trolley Research
A pendulum hanging from a trolley that runs in a rail and is tied to its end by a spring. Angle arc θ, length ℓ, frame I.
Circular motion, rotation, gravitation
- Disk on a Cart Research
A disk rolling without slipping on a spring-tied cart. Dimensions x and R. - Whirling Mass Research
A ball on a rod in zero gravity at 3 m/s: the rod's pull is the centripetal force mv²/r and the acceleration is v²/r. - Vertical Circle Research
A ball swung in a vertical circle: the rod pulls hardest at the bottom (mg + mv²/r) and least at the top, while the energy stays constant. - Rolling Race: Slider, Discs and a Hoop Research
Four ramps: with no friction nothing spins and the slider wins at g sin θ; a disc turns I = ½mr² and runs at g sin θ / 1.5, small or big, light or heavy; a hoop (a ring, I = ½m(R² + r²), nearly mr²) comes last at g sin θ / 1.9.
Pulleys, ropes and chains
- Atwood Machine
Two masses over an ideal pulley. a = (m₁ − m₂)g / (m₁ + m₂). - Atwood, Massive Pulley
The pulley grips the rope, so its rotational inertia slows the fall. - Movable Pulley
A 2:1 tackle. The counterweight moves twice as far as the moving pulley. - Heavy Chain off a Table
A 1 kg/m chain pulls a block across a smooth table; the hanging part grows, and so does the pull: (m₁ + m₂ + ρL) ÿ = (m₂ + ρy) g.
Statics and structures
- Seesaw: Moments Research
4 kg at 0.75 m balances 3 kg at 1.0 m: the moments about the pivot cancel. Change a mass or a distance (m₂, d₂) and watch the plank tip. - Ladder against a Wall Research
A ladder on a smooth wall stands only if the floor friction is at least ½cot θ (0.29 at 60°). Set the floor friction to 0.2 and it slips. - Bracket: Strut and Tie Research
A strut and a tie hold a 4 kg load: the tie pulls mg√(L²+h²)/h, the strut pushes mgL/h. Analyze → Member Forces lists them. - Weight on Two Cables Research
A 5 kg weight hangs from two cables at different slopes: the sine rule gives both tensions, and the free-body diagram closes.
Machines, drives and control
- Rack and Pinion
A driven pinion moves a rack in a guide: v = ω r. The rack lets go when it runs out of teeth. - Planetary Gear Set
Driven sun, fixed ring, planets on a carrier: the carrier turns at ω_S · Z_S / (Z_S + Z_R). - Belt Drive Research
Two wheels joined by a belt: the rims move at the same speed, so the small wheel turns r₁/r₂ = 2 times faster. - Gear Train with an Idler Research
16 → 24 → 32 teeth: the idler reverses the direction and drops out of the ratio, ω_C = ω_A·Z_A/Z_C = ω_A / 2.
Complex mechanisms
- V-Twin Engine Research
Two pistons 90° apart on one crank pin: each stroke follows s = r cos δ + √(l² − r² sin² δ), and the momentum of the moving parts turns in a nearly steady circle. - Warren Truss Bridge Research
Fifteen rods and nine pins carry a 30 kg load: the method of joints gives every member force, which the rods confirm. Analyze → Member Forces lists them. - Warren Truss: forces under a changing load Research
The truss with Analyze → Member Forces switched on, tension red and compression blue, while an extra load rises from 0 to 600 N and back every 6 s: each of the fifteen members follows the method of joints as the load changes, and the truss does not move. - Peaucellier–Lipkin Straight-Line Linkage Research
Seven bars turn a to-and-fro swing of the crank into a perfectly straight line at the far corner of the rhombus: its distance from the pivot is inverted, |OP||OQ| = ℓ² − s².
Sandbox and play
- Wrecking Ball
A 20 kg ball on an arm released from 58° swings into a wall of bricks. - Lever Catapult
A weight dropped on one end of a lever throws the small ball on the other end. - Dominoes
Fourteen dominoes and a rolling ball. A chain of falls: try moving one to change the spacing. - Drop Zone: Cut the Chain
A 25 kg weight hangs on a chain over a pyramid of crates. Pick the Slice tool (Build → Modify) and drag across the chain to cut it.