Choose an example at the top: 🏃 who is the most powerful on the stairs? · 🚗 a car driving up a hill · 🛗 a lift motor.
Pick a preset (class demo, slide examples, cards, exit questions) or set the values yourself. Type a value in the box next to a
slider and press Enter.
Press ▶ Start. ◂ / ▸ (or the ← → keys) step through the motion and pause.
The middle column shows the free-body diagram and a Sankey diagram of the energy transferred so far.
Graphs: the Tangent tool on an energy–time graph gives the power; the Area tool under P–t gives the
energy transferred.
● Record saves a trial; the Data tab plots P against 1/t (stairs) or P against v (car, lift).
Work through the Tasks tab. Write explanations on your worksheet.
The physics
P = ΔW/Δt (1 W = 1 J s⁻¹) · P = Fv
Power is the rate of doing work (transferring energy). Stairs: useful power = mgh/t.
P = Fv comes from W = Fs divided by t. F is the driving force at speed v.
At constant speed the resultant force is zero: driving force = resistive forces (+ mg sin θ up a hill).
At full power the driving force P/v gets smaller as the car speeds up; the top speed is reached when P/v = the forces
against the motion.
For scale: human sprint ≈ 1–2 kW · 1 horsepower = 746 W · car engine ≈ 100 kW. Muscle efficiency ≈ 25 %: most of the chemical energy
becomes thermal energy (that is why you get hot).
Model: g = 9.81 N kg⁻¹. The stair climber moves up at a steady speed. The car's resistive force is constant (as in the slide
problems); at full power the driving force is limited by the tyres' grip (0.8 × mg cos θ). The lift speeds up and slows down with the same
acceleration; tension T = m(g + a).