Physics IA · A · Space, time and motion · topic 3 of 30
Paper cones: what sets the terminal speed? · IB Physics IA idea: guide, sample graph and step-by-step plan
cheap kit, real physics: a good oneDrop a paper cone and it stops speeding up almost at once. Your job is to explain why, and to find what the final speed depends on.
- ✓ you like cheap, hands-on experiments
- ✓ you can film slow-motion on a phone
- ✓ you enjoy testing a formula against reality
The big idea
← prove it's terminal speed!A falling cone speeds up until air resistance balances its weight, then falls at constant terminal speed. For fast-moving light objects drag grows with v², so mg = ½ρC_dAv² and v² = 2mg/(ρC_dA). That predicts v² is proportional to m/A. Test it, and the gradient gives you the drag coefficient, which depends on the cone's shape. A good IA proves the cone has really reached terminal speed before it trusts the number.
Make it yours: pick one twist
Copying a classic won't show your choices. Pick one of these (or invent your own) and your IA becomes yours.
Swipe for more twists →
Cut cones from discs with different sectors removed, keeping the paper area and so the mass the same.
→ The base area changes while the mass stays fixed; your graph is v² against 1/A. But a new angle is a new shape, so the drag coefficient may change too: say how you will tell the two effects apart.Nest one, two, three, four cones together and drop them.
→ Mass changes while shape stays the same, so v² should rise with mass; a neat second test of the same formula.Compare a cone, a flat disc and a cup of the same base area.
→ Drag coefficient becomes your result; the evaluation can discuss why shape matters.Film from a much greater height and plot position against time.
→ The graph shows when the gradient stops changing; you justify the section you time.Track the cone with free video-analysis software against a metre rule.
→ Gives a whole speed-time curve, not a single number; the analysis can fit approach to terminal speed.Parachutes, raindrops or skydivers, scaled down safely.
→ Gives the introduction a purpose; the physics and graph stay the same.Your Physics IA research question: run the check
write it FIRST, then check itWrite your own question first. Then make sure it ticks every box:
- Names one independent variable and its range (cone angle, base area, or number stacked) and how many values.
- Names one dependent variable and how it is found (speed over which stretch, from video or timing).
- Says what stays fixed (mass, drop height, paper, room conditions).
- Says what you compare with (the quadratic-drag prediction, or the effect you expect on terminal speed).
- Is narrow enough for about 10 hours, with at least 5 shapes or areas and repeats.
The set-up
One way to arrange it. Draw yours with the real drop height, ruler position and the stretch you time.
How your Physics IA could be laid out
The usual order for a topic like this, what each part needs to show, and roughly how much of your 3,000 words it takes. The words are all yours.
Your question; where terminal speed matters (parachutes, raindrops); what you expect and why.
Forces on a falling object; why speed levels off; the drag equation and the assumption that drag depends on v²; what the gradient tells you.
Independent, dependent and controlled variables, each with how you set, measure or hold it, and why it matters.
How cones are made identically; drop height and release; how speed is measured over a marked section; how you checked the speed was constant; repeats.
Short: scissors, tidy floor, recycling paper.
One table: cone details, each timing or position reading, units and uncertainties in the headers.
Time and distance to speed, then v²; mass and base area to m/A; propagated uncertainty with one worked example each.
Your chosen graph with error bars and fit; what its gradient means physically; evidence of terminal speed.
Answer with numbers: does v² follow m/A, and what drag coefficient does your gradient imply?
Weaknesses ranked by their effect on your result, each linked to a realistic improvement.
Every source for the drag theory and method.
What your Physics IA graph could look like
Made-up data, to show you the form of a strong graph, not the answer. Yours will look different. example only
- Plotting v² against m/A turns the theory into a straight line through the origin.
- Error bars on every point; the vertical ones are larger because squaring doubles the fractional error in v.
- Two model lines show how sensitive the gradient is to the drag coefficient.
- State how you know the cone reached terminal speed over the section you timed.
- Another graph to consider: position against time for one drop, which should become a straight line once terminal speed is reached.
Which uncertainty matters most?
rank them: don't just list themRank by the effect on your result, the terminal speed. A phone at normal frame rate is often the weak link, and the fix is cheap: slow motion.
Your game plan
Tick steps off as you go. We'll remember on this device.
0 of 11 done
- Read and predictFind the drag equation and how terminal speed follows from it. Predict how v² should change with m/A, and what would break the prediction.
- Trial run (1 lesson)Drop a few cones. Do they fall straight? Is there a draught? Over what stretch does the speed look constant? Fix the problems now.
- Make identical conesUse a template. Decide how you control mass and base area as one changes, and measure both for every cone.
- Decide range, repeats and timingChoose at least 5 shapes or areas, how many drops each, the drop height, and the stretch you time. Write down why.
- Collect the dataFilm every drop square-on against the ruler. Record raw readings in the table with units and resolution; note odd drops.
- ProcessTurn each drop into a speed with an uncertainty, then v². Decide how you treat repeats that disagree.
- Graph and fitPlot v² against m/A with error bars, fit best and worst lines, and read off the gradient. What should it be?
- Compare with theoryFrom the gradient, what drag coefficient do you get? Is it believable for a cone? Does the line pass through the origin?
- EvaluateRank weaknesses by their effect on your result, then make each improvement specific to one of them.
- Write, then cutWrite in the order of the layout and stay within 3,000 words. Tables, graphs and references do not count.
- Check before your teacher's draftRun through the checklist below, then get your RQ or draft checked. Your teacher reads one draft only.
Physics you'll need
Traps to avoid in this Physics IA
- Timing a stretch where the cone is still speeding up, so the "terminal speed" is not terminal.
- Letting the mass change along with the area and not accounting for it.
- Draughts, fans or open windows near the drop.
- Cones that are not identical: ragged cuts, different tape, crumpled paper.
- Reading the cone's position by eye from video frames without a fixed scale.
- Phone filmed at an angle, or not level with the ruler (parallax).
- An evaluation that says "air resistance" without saying how it was controlled.
More Physics IA ideas like this
- Trolley on a ramp: how much energy does friction take?●●○
- Projectile: is the best launch angle really 45°?●●○
- Friction: is the coefficient really a constant?●●○
This guide shows how a topic like this is usually approached. It is not an IA. Your question, choices, data, analysis and words must be your own: change something, tell your teacher where the idea came from, and follow your school's rules on outside help.