Physics · Unit 4: Work, Energy & Power ·  Project 4-2-3

Foam Coaster Energy Budget

Build a marble coaster out of foam tubing, then predict how high your marble will climb the last hill before it ever rolls, by budgeting every joule friction takes on the way  ·  3 class days

Starringmgh₀ = mgh + E_friction% error = |actual − predicted| ÷ actual
Unit 4: Work, Energy & Power

🔁 Review the Concepts

This project builds on three activities. If you’re short on time, start with 4-2-2, then skim whichever other one feels shaky.

Activity 4-1-1
Work & the Work-Energy Theorem
Friction does negative work: W = F × d. That’s the energy friction takes from your marble.
Review activity →Deep dive →
Activity 4-1-3
Gravitational Potential Energy
PE = mgh, and choosing a zero level. Every height in this project is measured from one.
Review activity →Deep dive →
Activity 4-2-2
Conservation of Energy With Friction Losses
The energy budget, thermal energy, and predicting a climb from the fraction of height returned. Start here.
Review activity →Deep dive →

🧭 Plot Summary

Every coaster is an energy budget. The lift hill buys height, the track spends that height as speed, and friction quietly takes a cut along every meter of the way. In Activity 4-2-2 you budgeted a climb using a fraction. A real coaster is longer and more twisted than a valley, so friction’s cut depends on how much track the car actually travels.

You’ll start by measuring how much height your foam tubing eats per meter. Then you’ll design a coaster, predict how high the marble will climb the final hill before you roll it, and test. The goal isn’t a perfect prediction. It’s a prediction you can explain, check, and improve.

What you will do in this project

  • Calibrate your foam tubing: measure how much height a marble loses for every meter of track it travels.
  • Design a coaster with a drop, a curve, and a final climbing hill, within the project’s constraints.
  • Measure your track length and the slope of the hill, then predict the climb with an energy budget, before the first real test.
  • Test your coaster, calculate your percent error, and work out what caused any gap.
  • Use the budget to explain how you’d redesign the track to reach a higher hill.

Why it matters

Engineers predict before they build, because a wrong guess in steel costs far more than a wrong guess in foam. Budgeting energy by the meter is the same skill you’ll need for the emergency slide in Problem 4-3-1.

✅ Self-Check Before You Roll On

Check off each item as you get there. These are not grades — they are your own signal.