Interactive practical

Terminal speed

Drop stacks of paper cake cases from 2 m, time the falls by hand three times each, and see how the terminal speed depends on the mass.

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GCSE Physics

Investigating terminal speed

WJEC 3420QS — matched to your course.

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Practical focus

Use lightweight falling objects to investigate how terminal speed depends on mass.

Practical method

Aim

Investigate how the terminal speed of falling paper cake cases depends on their mass.

Variables

Independent variable: mass (number of stacked cake cases)
Dependent variable: terminal speed
Control variables: shape and size of the cases; drop height; timed distance in the lower part of the fall.

Apparatus

Paper cake cases
Metre rule or tape measure
Stopwatch or video camera
Balance

Method

Hold one cake case 2.0 m above the floor and mark a timing zone from 1.0 m above the floor down to the floor.
Release the case and time it through the lower 1.0 m, where it has reached terminal speed.
Calculate speed = 1.00 m ÷ time. Repeat three times and use the mean time.
Stack 2, 3, 4 and 5 cases together and repeat.
Plot terminal speed against mass (number of cases).

Sample results

Cake cases dropped from 2.0 m, timed over the lower 1.00 m.

Number of cases	Mean time / s	Terminal speed / m/s
1	0.95	1.05
2	0.68	1.47
3	0.56	1.79
4	0.48	2.08
5	0.42	2.38

Analysis

Terminal speed increases with mass, but less than in proportion: 1 case gives 1.05 m/s and 4 cases give 2.08 m/s (about double). A heavier stack has more weight, so air resistance must be larger before it balances the weight; air resistance increases with speed, so the terminal speed is higher.

Errors and improvements

Problem	Effect	Improvement
Cases still accelerating in the timing zone	Speed too low	Start the timing zone further below the release point; check that times over the top and bottom halves match
Reaction time over short times	Large timing uncertainty	Film the fall against a scale and use frame times
Draughts	Cases drift	Close windows and doors

Risk assessment

Hazard	Risk	Control measure
Standing on a chair to release	Falling	Use a stable step and have someone hold it
Low risk overall	-	Keep the floor clear

Common mistakes

Timing the whole fall including the acceleration phase.
Saying air resistance disappears at terminal speed.
Changing the shape of the cases when stacking.

Worked analysis

Two stacked cases take 0.68 s to fall the last 1.00 m. Terminal speed = 1.00 ÷ 0.68 = 1.47 m/s.

Common misconception

At terminal speed the forces are balanced; the object keeps moving at constant speed. It does not mean there is no air resistance.

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