Choose an example at the top: 🎢 a cart on a ramp or a track (Smart Cart demo, roller coaster, half-pipe) · 🎳 the pendulum to the nose ·
🌀 the flying spring practical · ⬇️ a falling ball.
Pick a preset or set the values yourself (type a value in the box next to a slider and press Enter). Switch friction or air
resistance on and off.
Press ▶ Start. ◂ / ▸ (or the ← → keys) step through the motion and pause.
The middle column shows the free-body diagram and the energy stores as bars — or, with Energy chart: Sankey, a Sankey
diagram of where the starting energy has gone so far.
Graphs: E–t and E–h show the energy moving between the stores; the dashed total line stays flat.
The Tangent tool on E–t gives the rate of energy transfer (power).
● Record saves a trial; the Data tab plots v² against h (gradient 2g), or h against x² for the
spring (gradient k/2mg).
Work through the Tasks tab. Write explanations on your worksheet.
The physics
Ek = ½mv² = p²/2m · ΔEp = mgΔh · EH = ½kΔx²
Conservation of energy: Estart + Wapplied = Eend + Edissipated.
Without friction or air resistance the mechanical energy (Ek + Ep + EH) stays the same.
From rest: mgh = ½mv² ⇒ v = √(2gh). The mass cancels, and the path does not matter (no friction).
With friction or air resistance the total energy is still conserved: the "lost" mechanical energy becomes thermal energy.
Average friction force = energy lost ÷ distance.
Flying spring: ½kx² = mgh ⇒ h = (k/2mg) x², so h against x² is a straight line.
Model: g = 9.81 N kg⁻¹; heights are measured from the lowest point (track, pendulum, drop) or from the release level (spring).
Track friction Ff = μFN; air resistance Fd = ½ρCdAv² (ρ = 1.2 kg m⁻³, Cd = 0.47). The Smart Cart ramp
is fitted to the PASCO lab 06 sample data (0.500 kg, 6°, 1.00 m: GPE 0.513 J, KE at the bottom 0.483 J). The spring is released in
about 0.03 s, so gravity during the launch is ignored; "energy lost on release" models the spring's vibration and sound.