Roll carts into each other, measure their velocities before and after, and test whether the total momentum was conserved. Real data never matches exactly, so your job is to decide whether the gap is within your measurement uncertainty, and to explain it if it isn’t.
🎯 Goals
- Build and level a collision track, and measure how much friction alone slows a cart.
- Measure every speed from slow-motion video, with an uncertainty on each.
- Calculate the momentum before and after each collision, and test whether the two agree within their uncertainty.
- Find and explain any systematic error, then write a verification you could defend to a skeptic.
🧰 Materials
🚗Two dynamics carts or toy cars with free-rolling wheels
🧲Three bumper types: repelling magnets, a rubber-band bumper, and Velcro or putty
🛤️A level track or long flat board, with a small ramp to release cart A
🪙Loads to add mass (coins or washers) and tape
🔵A marble, for checking that the track is level
📏Meter stick and masking tape
📱A phone with slow-motion video (120 or 240 fps), or photogates if available
⚖️A scale that reads to the nearest gram
🧮Calculator
📓Physics notebook
📏 Constraints
- Release cart A from the same ramp height for every run. The track must be level: a marble set on it should not roll.
- The timing zones are 0.50 m long (to within 2 mm), directly before and directly after the collision line.
- Use slow-motion video at 120 fps or faster, or photogates. Record the raw frame counts, not just the speeds.
- Run at least five settings: equal masses stuck together, heavy hitting light stuck together, light hitting heavy stuck together, equal masses bouncing (magnets), and one setting of your choice. Both carts moving is a good choice.
- Do three runs of every setting. Keep every run. If you drop one, write down why.
- Mass the carts, with any loads, for every setting. Treat the mass uncertainty as ±0.001 kg.
- Give every momentum an uncertainty, and state every conclusion in terms of that uncertainty.
- Safety: keep the track well back from the table edge, put a catch block past the end, and keep magnets away from phones.
DAY 1Build, Level & Calibrate 1
Build and level the track.
Set the track on the table and place a marble on it. If the marble drifts, shim one end with folded paper until it stays put. A tilted track adds or removes momentum on its own, so this step matters.
2
Mark the collision line and the two timing zones.
Tape a collision line. Tape the before zone so it ends at the line, 0.50 m long, and the after zone so it starts at the line, also 0.50 m. Check both lengths against the meter stick to within 2 mm.
3
Mass every cart and loaded combination.
Use the scale to the nearest gram. Label each cart, and write down the mass of every loaded version you plan to use.
4
Run a coast test.
Release cart A from the ramp with no collision and let it roll through the before zone and then the after zone. Film it and find its speed in each zone. The speed lost between the zones is how much friction slows the cart on its own. This is your baseline.
Sample data (use only if you can’t run the tests)
Coast test:
0.80 m/s in zone 1 and
0.78 m/s in zone 2.
5
Practice measuring, and estimate your uncertainty.
Film a practice run and step through it frame by frame until two people count the same number of frames. Then work through the warm-up. It sets up the uncertainty you’ll attach to every number.
Uncertainty Warm-Up
A correct answer is within the tolerance shown by the checker.
6
Plan your settings.
Fill in the plan table with at least five settings that follow the constraints. Decide the order, and plan three runs of each. Read the Deep Dive first if you aren’t sure what to expect.
7
Run every setting three times.
Release A from the same ramp height each time, with B at rest on the line (unless your own setting says otherwise). For each run, film from the side and record the raw frame counts: A before, A after, and B after. Note anything odd, such as a cart that twisted or a bumper that didn’t catch.
8
Convert to speeds and log each setting’s averages.
For each run, v = 0.50 m ÷ (frames ÷ fps). Average the three runs. Then calculate p before = m_A v_A and p after = m_A v_A′ + m_B v_B′, with signs, and the percent difference. A cart that stops has a speed of 0, and one that bounces back has a negative velocity.
Sample data (use only if you can’t run the lab)
Equal masses, stuck: m_A = m_B =
0.250 kg, v_A =
0.80, after (both)
0.38 m/s.
Equal masses, magnets: m_A = m_B =
0.250 kg, v_A =
0.80, v_A after
0.02, v_B after
0.74 m/s.
What good data looks like
The three runs of a setting should agree to within a few percent. If one run is far off, find out why before you average it in. Don’t just throw it away. Expect the momentum after to come out a little low, since friction acts on the carts between your two zones.
9
Attach uncertainties and test every setting.
For each setting, find δp before and after (percent uncertainties add: mass plus speed). Then compare: if |gap| ≤ δ_before + δ_after, the totals agree within uncertainty. Use the Collision Verifier to check your hand work.
Speed: v = 0.50 ÷ (frames ÷ fps), with a percent uncertainty of 1 ÷ frames + 0.002 ÷ 0.50
Momentum: δp = p × (mass % + speed %)
Test: conserved within uncertainty if |p_after − p_before| ≤ δ_before + δ_after
10
Look for a systematic error.
Look down your “% difference” column. If it’s negative for every setting, that isn’t random scatter. It’s systematic. Compare it with your coast test. Then correct each setting back to the collision line using the friction deceleration, and see whether the totals now agree.
📓 Physics Notebook
Are your differences all the same sign? What is the likely cause, and how does your coast test support it? After the friction correction, which settings agree within uncertainty, and which still don’t? What might explain the ones that don’t?
11
Extension: check the energy.
For each setting, find the kinetic energy before and after, and the percent lost. Classify each as nearly elastic, inelastic, or perfectly inelastic, as in Activity 5-2-1. Does your classification match the bumper you used?
12
Write your verification.
Write a claim, evidence, and reasoning paragraph. Claim: was momentum conserved? Evidence: your before-and-after totals with uncertainties, your coast test, and the corrected values. Reasoning: what “conserved” means for real data, and what the systematic error was. Then list two changes that would make the experiment better.
Question 1
For each of your settings, was momentum conserved within uncertainty? Summarize the result in a sentence, with numbers.
Question 2
If your momentum after was consistently lower, what is the likely cause, and how does your coast test support that explanation?
Question 3
Which setting had the largest uncertainty, and why? What would you change to reduce it?
Question 4
In Problem 5-3-1 you’ll use conservation of momentum on a real crash. Based on this lab, how much agreement would you want before trusting it, and what could go wrong?
📤 Turn In
- Your plan table, your coast-test result, and your raw frame counts for every run
- Your before/after velocity table with momentum totals
- Your uncertainty table, with a yes/no for each setting, plus your friction-corrected values
- Your claim–evidence–reasoning verification, with two proposed improvements
- Written answers to the four Conclusion questions