When a coaster car finally rolls to a stop, its energy hasn’t vanished. Day 1 measures how much work friction turns into heat and practices the energy budget. Day 2 uses that budget to predict how high a marble can climb, and then asks why no machine is ever 100% efficient.
🎯 Goals
- Measure how much work friction turns into thermal energy, using E_heat = F_f × d.
- Balance an energy budget: starting energy = ending energy + thermal energy.
- Use the fraction of height a track returns to predict the lowest release height that clears a hill.
- Calculate efficiency and explain why no real machine can be 100% efficient.
🧰 Materials
🧱Day 1: a wooden block with a string loop, and a spring scale (10 N or 20 N)
📄Day 1: three surfaces to drag it on, such as the bare table, sandpaper, and felt or cloth
🧊Day 2: two pieces of foam pipe insulation, split lengthwise, about 1.2 m long each
🔵Day 2: a marble or small steel ball, and a scale that reads in grams
📚Books or boxes to prop up the ends, masking tape, and a catch box for stray marbles
📏Meter sticks (one stood upright for heights)
🧮Calculator
📓Physics notebook
DAY 1Friction turns work into heat
Section 1 of 5
Drag and Measure
1
Mass the block and set up your surfaces.
Find the block’s mass in kilograms. Tie a string loop to it and hook on the spring scale. Lay out a 1.00 m track on each surface you’ll test, such as the bare table, sandpaper, and felt or cloth.
2
Drag the block 1.00 m at a slow, steady speed on each surface.
Pull parallel to the surface and read the scale while the block is moving steadily. At a steady speed your pull equals the friction force, so that reading is F_f. Do each surface twice and use the steadiest reading.
3
Calculate the thermal energy friction produced.
Your pull did work on the block, but the block’s speed never changed, so that work went into thermal energy: E_heat = F_f × d.
E_start = E_end + E_thermal
Energy is never destroyed. When friction acts, some of the mechanical energy (PE + KE) becomes thermal energy, and the amount is F_f × d.
📓 Physics Notebook
Which surface turned the most work into thermal energy over the same 1.00 m? Rub your hands together for ten seconds and notice what happens. How is that the same thing the block was doing? What would be true about its speed if you stopped pulling?
Section 2 of 5
Energy Budget Practice
4
Balance the budget on four situations.
Use starting energy = ending energy + thermal energy, with PE = mgh and KE = ½mv². Use g = 9.8 N/kg. A correct answer is within 3%.
Budget Practice
Find the thermal energy produced in each case.
✅ End of Day 1 check: friction table complete and all four Budget Practice rows green. Tomorrow you’ll use this to predict something.
DAY 2Budget the energy and predict the climb
5
Build a valley.
Tape two foam half-pipes together at the bottom to make a smooth U shape, with no bump or kink where they meet. Prop each end on books so that each side rises to about 0.40 m above the bottom. Stand a meter stick upright beside the right-hand side.
6
Mass the marble.
Mass it in grams, then divide by 1000 to get kilograms. A typical glass marble is about 0.005 kg.
7
Release the marble from rest at three heights: 0.10 m, 0.20 m, and 0.30 m.
Measure each height straight up from the bottom of the valley. Let go without a push. Mark where the marble stops rising on the far side and measure that peak height h₂ above the valley bottom. Do three runs per height and average h₂.
⚠️ Marbles roll off tables. Keep a catch box at the ends and pick up strays right away.
8
Calculate how much height and energy the marble lost.
At both turning points the marble is momentarily at rest, so all of its energy is PE. Any drop in PE is thermal energy: E_thermal = mg(h₁ − h₂). The percent returned is h₂ ÷ h₁ × 100.
What good data looks like
Most valleys return about 70–95% of the release height. If your peak is higher than your release, recheck that both heights were measured from the bottom of the valley.
📓 Physics Notebook
Look at your three release heights. Does the percent returned change much, or stay about the same? Why might that make sense? (Think about what happens to both the starting energy and the friction as you release from higher up.)
Section 4 of 5
Predict It: Beat the Hill
9
Practice the prediction.
If a valley returns a fraction f of its release height, then to reach a hill of height H you need to release from h₁ = H ÷ f. Try two practice cases first.
Predict Practice
Use the fraction as a decimal.
10
Predict your own release height.
Tape a marker on the right-hand side at 0.15 m. Use your averaged f from your Valley Run table to predict the lowest release height that gets the marble to the marker. Then do the same for a 0.20 m hill. Write your predictions before you test anything.
11
Test your predictions.
Release the marble from your predicted height, and again 2 cm lower. Record whether it reached the marker each time, and find the lowest release height that actually worked.
📓 Physics Notebook
How close was your prediction to the lowest height that worked? If it missed, which assumption didn’t hold? (Was f really the same at every height, and did your measurements have much scatter?)
Section 5 of 5
Efficiency: Why No Machine Is 100%
12
Calculate efficiency.
The efficiency of a machine is the useful energy it delivers divided by the total energy put in: η = E_out ÷ E_in × 100%. The rest is wasted, mostly as thermal energy.
Efficiency Practice
Use g = 9.8 N/kg where needed.
📓 Physics Notebook
Every real machine has friction, air resistance, or some other way of turning organized motion into thermal energy. Use your valley and your efficiency answers to explain why no machine can be 100% efficient.
Question 1
Using your Day 1 table, which surface produced the most thermal energy over 1.00 m, and what does that tell you about a sliding object that has to stop on that surface?
Question 2
What percent of your marble’s starting energy was returned as height in the valley? Where did the rest go, and how do you know it wasn’t destroyed?
Question 3
Explain how you predicted your release height for the hill, and compare your prediction with what worked. What would you change to predict better?
Question 4
A coaster designer says, “Make the second hill the same height as the first, and the car will clear it.” Use what you learned to explain why that wouldn’t work, and what the designer should do instead.
📤 Turn In
- Completed Day 1 friction table, with your notebook note on which surface made the most heat
- Your Budget Practice and Efficiency Practice results
- Completed Valley Run table with your note on how the percent returned changes
- Your hill predictions, test results, and the comparison between them
- Written answers to the four Conclusion questions