Terminal velocity by video analysis
The question
How does terminal velocity depend on the mass of a falling object, and is drag proportional to speed or to speed squared?
Meteorites in dark flight fall at their terminal velocity, which depends on their mass, size and shape. Knowing the drag lets scientists predict where they will land.
Equipment
- Paper cake cases (stacking 1 to 6 changes the mass but not the shape)
- A phone camera that records at 60 frames per second or more
- A metre rule fixed vertically behind the drop as a scale
- Free video analysis or a frame-by-frame player, and a spreadsheet
Method
- Drop 1 cake case from about 2 m in front of the metre rule and film it.
- Step through the video frame by frame to find its position every few frames and work out its speed once it stops speeding up.
- Repeat for 2, 3, 4, 5 and 6 stacked cases, three times each.
- At terminal velocity, drag equals weight. Plot weight against terminal velocity and against terminal velocity squared.
- What to measure
- Terminal velocity for each mass, and which graph gives the straighter line.
- How to present it
- Graphs and a conclusion about whether drag is proportional to v or v², with uncertainties and a link to meteorite dark flight.
- Take it further
- Estimate the terminal velocity of a 100 g stony meteorite using the drag equation, and compare it with the values scientists use for dark flight.
Safety
Drop from a stable stair landing or balcony with a rail, with an adult; never stand on furniture.