Roller Coaster Physics — Energy Lab

Set the hills, the car’s mass and the track friction. Release the car, time it through the photogates, and work out where its energy went. The simulation reports only what an instrument could measure — every energy value is yours to calculate.

1 · Build the ride

Predict first — will the egg survive?

2 · Run it

AT THE TOP
0.000 s
Height gridlines are exactly 0.25 m apart · g = 9.8 m/s²
0.000 s

3 · Read the instruments

  1. Slide the two photogates along the flat run-out to where you want to measure.
  2. Release the car. Each gate stamps the clock as the car passes.
  3. Everything below is a direct reading — a height, a mass, a distance, two clock times. Nothing else.
Release height  h₁
— m
Mass of the car  m
— kg
Gate separation  d
— m
Gravity  g
9.8 m/s²
Clock at gate A  tA
— s
Clock at gate B  tB
— s

The run-out is level, so the car has no height between the gates — every joule it still has is kinetic. Two gates give you an average speed across the gap, so keep them close together if you want the speed at a particular spot.

4 · Do the maths yourself

5 · Check your work against the energy graph

The energy graph stays hidden until you have finished all five calculations for this run. Work them out first — then compare.

6 · Your runs

Speed at the gates against release height — one dot per saved run
No runs saved yet — finish the five calculations, then press Save this run.
The track is 14 m long end to end and the run-out is level. Friction acts along the whole path, so a longer route costs more energy even when the drop is the same.

How to use this simulation

  1. Grab any of the three blue dots on the hill crests in the scene and drag it up or down — or use the Hill height sliders in Build the ride — to shape the track, then set the car's mass and the track friction.
  2. Predict whether the egg will survive, then press Release the car to run it. Use ⟲ Reset simulation at the top any time to put the hills, mass, friction, and gates back to their starting values.
  3. Drag the two photogates onto the flat run-out where you want to measure, and use the transport buttons or the scrubber under the scene to step through the run frame by frame.
  4. Work through the five calculations in Do the maths yourself using only the instrument readings — height, mass, gate positions, and the two clock times. Type an answer and press Check.
  5. Once all five are correct, the energy graph in section 5 unlocks so you can compare your worked values against the car's real kinetic, potential, and total energy over time.
  6. Press Save this run to add it to the table and the speed-vs-height graph in Your runs, so you can compare several hill and friction setups side by side.
  7. Press Back to the top to replay the same setup, or Start over in the worksheet to clear your answers without changing the track.