Quick answer: Terminal velocity is the steady speed at which a resistive force balances the weight, so the net force is zero. This AP Physics C lab on terminal velocity gives the aim, the equipment, the safety points, a step-by-step method, sample results and 7 analysis questions; the answers are on a separate page and the lab sheet is a free printable PDF.
A stack of paper cupcake cases falls fast but not freely, because air drag is quadratic at these speeds. By timing the last metre of the fall for different masses, you test whether terminal speed squared is proportional to mass, as vt = √(mg/c) predicts.
Level: AP Physics C (Mechanics and E&M, calculus-based) · Curriculum: AP PC:M Unit 2
Aim
Find how the terminal speed of a falling object depends on its mass when drag is quadratic, and estimate the drag constant c.
Equipment
- Paper cupcake cases, all identical (5 or more)
- Balance reading to 0.01 g
- Metre rule and tape, fixed vertically
- Phone with slow-motion video
- Stopwatch app or frame-by-frame viewer
Safety
Work at floor level or from a low, stable step only. Clear the floor of bags, and tell others where you are dropping things so nobody trips or looks up into the falling cases.
Method
- Weigh one case, then nest 1, 2, 3, 4 and 5 cases together so they fall as one open cup. Record the masses.
- Mark two lines on the wall: one 1.00 m above the floor and one at the floor, as shown below.
- Release the stack, open end up, from 2.5 m above the floor, so it has 1.5 m to reach a steady speed before the timed section.
- Film the fall and find the time to cross the 1.00 m section. Repeat three times for each stack.
- Calculate the mean time, then v = 1.00 m divided by the mean time.
Results
| Cases n | Mass m (g) | t₁ (s) | t₂ (s) | t₃ (s) | Mean t (s) |
|---|---|---|---|---|---|
| 1 | 0.80 | 0.68 | 0.66 | 0.67 | 0.67 |
| 2 | 1.60 | 0.47 | 0.48 | 0.46 | 0.47 |
| 3 | 2.40 | 0.39 | 0.37 | 0.38 | 0.38 |
| 4 | 3.20 | 0.33 | 0.34 | 0.32 | 0.33 |
| 5 | 4.00 | 0.30 | 0.31 | 0.29 | 0.30 |
Analysis questions
Question 1 Speeds and squares
Calculate v = 1.00/t using each mean time, then v². Complete a table of n, m, v and v².Question 2 Graph
Plot v² (vertical) against m in kg (horizontal). Draw the best-fit line through the origin and find its gradient.Question 3 Drag constant
Use vt² = (g/c) m to find c from the gradient.Question 4 Why the last metre?
Explain why the time is measured over the last metre instead of the whole fall.Question 5 Uncertainty
The time for the 5-case stack is 0.30 s with an uncertainty of ±0.02 s. Calculate the percentage uncertainty in v and in v².Question 6 Conclusion
State what the straight-line graph shows about the relation between vt and m.Question 7 Improvements
Propose two modifications to the drop that would make your value of c more reliable.
