Build a marble coaster from foam tubing and predict, before the marble ever rolls the whole course, how high it will climb the final hill. You’ll measure how much height your tubing costs per meter, budget the energy along your track, and then see how close the budget came.
🎯 Goals
- Calibrate foam tubing by measuring how much height a marble loses per meter of track.
- Design and build a coaster with a drop, a curve, and a final climbing hill.
- Predict how high the marble will climb the hill from an energy budget, before testing.
- Compare your prediction with the real result, calculate your percent error, and explain the gap.
🧰 Materials
🧊Foam pipe insulation, split lengthwise (about 5 m per team in total; your teacher cuts it)
🔵One marble or small steel ball, and a scale that reads in grams
📚Books, boxes, and cardboard to hold the track up, plus plenty of masking tape
🧵String (about 4 m) for measuring the length of curved track
📏Two meter sticks and a tape measure
📦A catch box for stray marbles
🧮Calculator
📓Physics notebook
📏 Constraints
- The track is foam pipe insulation only. Books, boxes, cardboard, and tape may be used to hold it up.
- Release the marble from rest at h₀ = 0.50 m above the base of the final hill. No pushing.
- The track before the hill must be 2.0 to 3.5 m long (measured along the tube) and include at least one drop and one curve of 90° or more.
- The final hill must have a straight, even slope between 15° and 30°, marked every 5 cm of height, and be at least 10 cm taller than your predicted climb.
- The marble must stay in the tubing for the whole run: no jumps and no loops.
- Write your prediction down before you measure any climb.
- Show every calculation with units: heights and lengths in meters, energy in millijoules (mJ).
- Safety: your teacher handles any blades. Pick up stray marbles right away, because they’re a slipping hazard.
1
Prepare your tubing and mass your marble.
Your teacher cuts the foam tubes lengthwise. Mass the marble in grams, then divide by 1000 to get kilograms. Use this same marble for every run.
⚠️ Your teacher handles any blades. Students shouldn’t cut the tubing.
2
Build a calibration valley.
Tape two foam half-pipes about 1.2 m long into a smooth U, with no bump or gap at the bottom. Prop each end so each side rises about 0.40 m. Stand a meter stick upright beside it.
3
Release the marble from rest at h₁ = 0.30 m and measure how high it rises on the far side.
Measure both heights straight up from the bottom of the valley. Do three runs and average the peak height h₂.
4
Measure the path length the marble traveled.
Lay a string along the inside of the tube from the release point, down to the bottom, and up to the average peak. Mark the string at both ends and measure it. That total length is s.
5
Calculate λ, the height lost per meter of track.
For each run, λ = (h₁ − h₂) ÷ s. The energy lost per meter is mgλ. Average your λ values. You’ll use this number to predict your coaster.
λ = (h₁ − h₂) ÷ s
λ is the height the marble loses for every meter of track it rolls. A smaller λ means a smoother, lower-friction track.
What good data looks like
Most foam valleys give a λ between about 0.01 and 0.05 m per m. If your three λ values are very different from each other, look for a kink or a gap and fix it before you move on.
📓 Physics Notebook
In Activity 4-2-2 you used the fraction of height returned. Why wouldn’t that single fraction work for a longer, curvier coaster? Explain why a per-meter number like λ is better.
6
Warm up with the budget formulas.
Read the Deep Dive first if any of these are new. These four are the calculations you’ll use for the rest of the project.
Warm-Up
Check each calculation before you use it on your own data.
7
Sketch your coaster.
Draw a side view with the release point at 0.50 m, at least one drop, at least one curve of 90° or more, and a final hill with a straight, even slope. Estimate the track length before the hill and check it against the constraints (2.0 to 3.5 m).
8
Build your coaster.
Follow your sketch. Check that the marble stays in the tubing the whole way with a quick test, but don’t measure the climb yet. Keep joints smooth, with no gaps or bumps where tubes meet.
9
Measure the track length before the hill.
Lay your string along the inside of the tube from the release point to the base of the final hill. Mark and measure it. That is s for your prediction.
10
Build and measure the hill.
Make the hill a straight, even slope between 15° and 30°. Mark it every 5 cm of height. Measure the length of track along the hill up to the 0.20 m mark. The slope factor is k = track length ÷ rise, so k = length ÷ 0.20 m.
11
Predict the climb before any test.
Use h = (h₀ − λs) ÷ (1 + λk) with h₀ = 0.50 m and your λ, s, and k. Write your prediction in your notebook and show it to your teacher before you roll the marble up the hill.
h = (h₀ − λ s) ÷ (1 + λ k)
h₀ is the release height, s is the track length before the hill, and k is the hill’s track length per meter of rise. The λk term accounts for the friction on the climb itself.
12
Fill in your predicted energy budget.
Show where the energy is at three moments, in millijoules. At the hill base the height is zero, so PE is zero. At the peak the marble is at rest, so KE is zero. Thermal energy is whatever is missing, so every row should total the starting energy.
📓 Physics Notebook
Which part of your coaster do you expect to cost the most energy: the straight sections, the curves, or the climb? Write down your guess and your reason. You’ll check it on Day 3.
13
Test your coaster three times.
Release the marble from rest at 0.50 m. Read the highest mark it reaches on the hill each time. Record all three and average them to get your actual climb.
14
Calculate your percent error.
Percent error compares your prediction with what really happened: |actual − predicted| ÷ actual × 100.
15
Diagnose any gap and make a second prediction.
If your error is more than about 10%, find out why. Re-measure s and k. Check for kinks and gaps. If your coaster has tight curves, build a short curved calibration track, measure a new λ, and make a second prediction with it. Test again.
Common causes of a gap
A kink or gap at a joint. A track length measured too short. A λ measured on a straight valley when the coaster has tight curves. A hill whose slope isn’t even. The marble catching on a tape seam.
16
Work out the actual energy budget.
Using your measured average climb, calculate the actual thermal energy: E_thermal = mg(h₀ − h_actual). Compare it with the thermal energy you predicted, and explain the difference.
📓 Physics Notebook
Write a claim, evidence, and reasoning paragraph. Claim: how well did your energy budget predict your coaster’s climb? Evidence: your predicted and actual heights, your percent error, and your thermal energy numbers. Reasoning: what caused any gap, and what would you change?
Question 1
State your predicted climb, your actual climb, and your percent error. Was your prediction too high or too low, and what does that suggest about your track?
Question 2
Using your actual budget, what percent of the marble’s starting energy became thermal energy by the top of the climb? Where did it go?
Question 3
Which part of your coaster cost the most energy per meter: straights, curves, or the climb? Use your data as evidence, and compare it with your Day 2 guess.
Question 4
Your hill needs to be 5 cm higher than your actual climb. Use the budget formula to say what you would change (release height, track length, or curves) and by how much.
📤 Turn In
- Your built coaster, shown working (or a photo or video of a run)
- Calibration table with your λ, and your sketch
- Your predicted vs. actual climb, with percent error for each attempt
- Your energy budget, both predicted and actual, with every calculation shown
- Claim–evidence–reasoning explanation and answers to the four Conclusion questions