Climb the Stairs — Same Work, Your Choice of Time
A stairwell with the stopwatch built in. One flight of sixteen steps, a vertical rise of 3.20 m, and a climber whose mass is fixed at 60.0 kg on the scale at the foot of the stairs. Tap to take a step; tap faster and you climb faster. The clock starts on your first step and stops on your last, and the row that lands in the table afterwards has three numbers in it — two of which never change.
How to use this simulation
- Tap to take a step — the single control. One tap is one riser; a stride has to land before the next tap counts, so sixteen taps in a millisecond will not give you an impossible time.
- Reaching the top records the climb and offers to put you back at the bottom for another run.
- Drag anywhere on the scene to orbit the stairwell.
What to look for
- The Work column reads 1.88 kJ on every row. Only the Time and W/t columns move.
- Climb it slowly once and quickly once, and the ratio of the two powers is exactly the inverse ratio of the two times.
- The purple dimension marks the 3.20 m of vertical rise; the grey one marks the 5.50 m you actually walk. Only the first goes into mgh.
- Push for the fastest climb you can and watch how few tenths of a second separate your attempts — which is why a real measurement times each ascent twice and averages.
The physics behind it
The work you do lifting yourself is W = mgh = 60.0 × 9.8 × 3.20 = 1881.6 J ≈ 1.88 kJ. The h in that expression is the height you gained, not the distance you walked: the stairs measure 5.50 m along the slope and only 3.20 m vertically, and it is the 3.20 m that counts. So every climb you make costs the same 1.88 kJ. Divide it by the time you took and you get the average power, W/t, in watts — and that is the only number in the table that responds to how you climb. A relaxed ascent of a flight sits around 150 W; a hard one can pass 800 W briefly. One point about measuring matters too: your reaction time on the stopwatch is worth a couple of tenths of a second, which is a far larger percentage of a fast climb than of a slow one.