Inelastic Collisions Student Guide.docx

Investigating Inelastic Collisions: From Bounce
to Coefficient of Restitution
Scientific Inquiry with AI
Student Guide
Created by LLNL Summer 2026 STEM Education Research Team
Student Team: Ramina Amino, Jahanvi Chamria, Arya Ferozy, Bryanna Gonzalez, Tai
Le, John Navarra, Joshua Sarabian, Abdurrahman Raza
Faculty Team: Praveen Pathak, David Rakestraw, David Strubbe, Brian Utter
Detailed Instructions & Course Material
Why This Lesson
Drop a ball and it bounces back a little lower each time. It feels obvious, but hidden inside that
fading bounce is a clean, measurable physics story: gravity, the trade between potential and
kinetic energy, and a tiny fraction of energy lost to heat and sound at every impact. This
investigation is about measuring that loss precisely enough to test a model, using nothing but
the sound of the bounces and a high-sampling-rate microphone.
The point is not just to get a number. It is to practice a real research workflow with AI as a
collaborator: you will collect messy experimental data, use AI to graph and process it, and, most
importantly, verify every result against the raw signal before you trust it. AI makes the slow parts
(plotting, smoothing, peak-finding, fitting) fast. The skill that matters is judgment: knowing when
a detected bounce is real, when an algorithm has drifted, and when your model has stopped
describing reality.
Learning Goals
Upon completion of this investigation, students should be able to:
Phenomena:
● Use a model of a ball colliding with a surface to describe the nature of elastic and
inelastic collisional processes.
● Evaluate how collisions between objects with different material properties can
dramatically affect the transfer of energy during a collision and how to characterize the
collisions using the coefficient of restitution.
● Discuss the conservation of mechanical energy and the conversion between kinetic and
potential energy for an object in free fall.
Experimental Practices:
Scientific Inquiry with AI • Investigating Inelastic Collisions • Student Guide Page 1

● Use indirect measurement techniques (detection of sound waves using high sampling
rate microphone) to infer the timing of physical events (collision of ball with surface).
● Identify and evaluate the precision of different digital signal processing methods
including strategies that involve rapid initial analysis followed by more computationally
intensive refinement.
● Apply equations of motion for constant acceleration to calculate the position and velocity
of an object in free fall given the time.
Habits of Mind:
● Use a series of graphs to quantitatively describe the phenomena through the variation of
different variables as a function of time, bounce number, and velocity.
● Describe how the high precision that results from careful experimental design and
computational analysis enables more detailed testing of models and provides a deeper
understanding of the phenomena.
● Use simulations of phenomena to extend understanding and predict how material
properties impact energy transfer of collisions.
What You Will Need
• The three balls from your prelab: a happy ball, a sad ball, and a ping pong ball.
• A device that records audio at a high sampling rate (your phone voice recorder is
usually fine), and a hard, flat surface.
• Your AI model with data-analysis / code execution enabled, so it can plot and process
your audio file.
• Your prelab materials: the technical data sheet on the happy and sad balls and the
completed Collision Analysis review sheet.
The Core Idea
• When a ball bounces, the ratio of its speed leaving the surface to its speed arriving is the
coefficient of restitution (COR). A perfectly elastic bounce has COR = 1; a dead bounce
has COR = 0.
• Because each bounce is a free fall, the time between successive bounces shrinks in a
predictable way. The ratio of successive bounce-intervals is the COR, so you can extract
the physics from timing alone, without ever measuring height directly.
• You can hear each impact. A microphone recording turns the experiment into a long sound
file where every bounce is a spike, so the whole investigation becomes: find the precise
time of each spike, then look at how those times change.
Scientific Inquiry with AI • Investigating Inelastic Collisions • Student Guide Page 2

• AI can graph, smooth, and detect peaks far faster than you could by hand, but it can also
confidently mislabel noise as a bounce or miss faint late bounces. Treat every AI-detected
bounce time as a claim to verify against the raw waveform, not a fact.
• The driving question is real research: does the percentage of energy lost per collision stay
constant across velocities, or does it change? You are looking for consensus across the
whole group's measurements.
Part 1 — Pre-Class Preparation 1.5 - 2 hours
A. Exposure to the Phenomena (~5 minutes)
Explore the properties of the two solid balls. You will be asked about your observations during
the Socratic tutoring session.
B. Socratic AI Tutoring Session (~30 minutes)
Upload prelab tutor document into a chatbot and thoughtfully engage with the AI. The
discussion will prepare you with the knowledge necessary for conducting the in class
investigation.
C. Happy and Sad Balls Reading (~10 minutes)
Read a short document describing the materials used to make the two balls and a short
explanation of the observed behavior. This will reinforce the discussion from the Socratic tutor.
D. Collision Analysis (~45 minutes)
Read the Collision Analysis Guide which provides a summary of the equations and analysis
methods used to analyze the experimental data. Once you complete reviewing the guide,
complete the self-check review sheet and submit it to an AI for self-assessment.
E. Review In-Class Investigation (~10 minutes)
Review Phase 2 of this guide to prepare for the in-class investigation.
Part 2 — In-Class Investigation 1.5 - 2 hours
The Investigation, Stage by Stage
Scientific Inquiry with AI • Investigating Inelastic Collisions • Student Guide Page 3

Below is a summary of in-class workflow condensed into ten stages. Your instructor will lead the
group through these together, so this guide gives you the why and the what to look for at each
stage rather than every keystroke.
Stage 1 — Record and visualize your data
Drop your ping pong ball a couple of centimeters and let it bounce until it stops, recording the
audio on your smartphone. Upload the audio file to your AI along with a short description of the
experiment (ball type, surface, precise drop height) and ask it to plot the full waveform —
amplitude versus time.
Look for: a series of “spikes” that get closer together and shrink over time. That overall shape is
the entire experiment in one picture. Compare it with a peer's — where are they similar, where
do they differ?
Stage 2 — Check your sampling rate and trim the file
Ask the AI for a table of the time and amplitude for the first 10 data points, and have it calculate
the sampling rate from the spacing.
Why it matters: the sampling rate sets the best timing precision you can possibly achieve. This
becomes more and more important as the time between bounces becomes smaller.
Stage 3 — Zoom in on a single bounce
Pick one clear bounce and have the AI zoom in on it. You will probably not see a single clean
spike — you will see a complicated, messy waveform.
Ask the AI: why does one bounce produce such a complex sound wave pattern? This is exactly
why picking the exact bounce time is harder than it looks. Since we care about the relative time
between bounces, do we need to know the exact time of the bounce, or can we identify a
repeatable feature?
Stage 4 — Compare early, middle, and late bounces
Have the AI show you bounces from the beginning, middle, and end of the recording. Does the
pattern of the sound amplitude change significantly as the bounces get weaker? Does the
amplitude alone look like a reliable measure of energy?
Decide: you are testing whether amplitude or timing is the better handle on the physics. Spoiler
from the workflow: timing wins — but see the reasoning for yourself before you accept it.
Stage 5 — Smooth the signal with RMS
A raw waveform swings rapidly above and below zero, which makes peak-finding fragile. Ask
the AI to compute a running RMS (root-mean-square) of the signal, which turns each messy
burst into a single smooth hump. Graph the RMS for the whole file and for early, middle, and
late bounces.
Judgment call: how wide should the RMS window be? Too wide and two late bounces blur
together; too narrow and the hump stays jagged. Try a couple of widths and reason about the
shortest time between bounces you need to resolve.
Scientific Inquiry with AI • Investigating Inelastic Collisions • Student Guide Page 4

Stage 6 — Find a first estimate of each bounce time
Using the smoothed RMS, have the AI detect the peak of each hump and mark the bounce
times. Ask it to make a graph with the detected times marked on the first ~50 bounces, and a
second zoomed graph near the end where bounces crowd together.
Verify, do not trust: this is the most important habit in the lab. Look at every marked peak. Did
it catch a real bounce, invent one from background noise, or miss a faint late one? A panel of
small graphs with each peak labeled is the best way to check. Adjust the algorithm until the
marks match what your eyes see.
Stage 7 — Refine the times using the raw signal
RMS gives you good approximate times, but it smears the exact moment of impact. Now center
a short window (about 10 ms) of the original raw data on each RMS time and look for a sharp,
repeatable feature you can use as a consistent marker. Ask the AI for ideas on refining the
times, then pick one approach and apply it.
Key insight: you do not need the true instant of impact — you only need the time between
bounces measured consistently. Measuring change in time between bounces is what we need
for our analysis, not the absolute value of the bounce time.
Stage 8 — Plot time-between-bounces and extract the COR
Have the AI plot the time between successive bounces against bounce number, then plot the
log of that time against bounce number. The early bounces should fall on a straight line. Fit the
first ~40 linear-looking bounces and use the slope to calculate the coefficient of restitution.
This is the payoff: a single number, COR, pulled from timing alone. Roughly check the
calculation manually to confirm the AI analysis — do not accept the conversion blindly.
Stage 9 — Turn timing into velocity, energy, and COR vs. velocity
From the bounce intervals, have the AI calculate the velocity at each bounce, then the COR as
a function of bounce number, and finally the percent of energy lost as a function of velocity.
Graph each one.
Return to the driving question: does the percent energy lost per collision stay flat across
velocities, or trend with speed? This graph is your answer, and the one you will compare against
the rest of the group.
Stage 10 — Check consistency and spread
Finally, look at reliability. Graph height versus bounce number for the full run and for the final 20
bounces, build an overlay graph of the first ~60 bounces, and plot the mean and spread of your
measurements.
Scientific Inquiry with AI • Investigating Inelastic Collisions • Student Guide Page 5

Ask yourself: how tight are your measurements, and where does the scatter grow? The spread
tells you how far to trust your COR, and sets up the reflection on where the technique starts to
fail.
Reflect: where does it break down?
Close the investigation by stepping back. In a line each: When does the measurement
technique begin to fail — where do overlapping sound waves or background noise make
bounces impossible to separate? Are there conditions where our model might begin to fail —
what happens if the initial drop is very high, or when the contact time becomes significant
compared to the flight time? What surprised you, and where did you struggle most? You are not
expected to have clean answers; noticing the edges of your method is important to understand
for any investigation.
Part 3— After Class 1.5 - 2 hours
A. Generate Your Report
Ask the AI to produce a report based on your analysis. You write the prompt: specify exactly
which text and which graphs you want included. Then read the report critically and assure it
captured the graphs and analysis as you desired — the report is only as trustworthy as your
verification of it.
B. Expand Your Investigation of Different Collision Pairs and Conditions
We focused on the detailed measurement of a specific ball dropped on a specific surface from a
short distance where drag was insignificant. Once we understand the model, we can build a
simulation to extend our exploration. Use the simulation provided to look at the results for
different ball-and-surface pairs, the effect of drag force, and the impact of gravity. For 5 of the
different scenarios you investigated with the simulation, summarize your findings.
C. Retrieval Practice (~30 min)
Spend about 30 minutes with the AI-enhanced retrieval tool, which spaces and interleaves
material across the whole course — an adaptive alternative to flashcards.
Everything You Turn In
• Your completed self-check worksheet.
• Your AI generated report, which you have carefully curated, including the key graphs we
built together in class.
• Your summary report from the simulation.
Scientific Inquiry with AI • Investigating Inelastic Collisions • Student Guide Page 6

• Your short reflection on the key findings from the investigation and the limitations of our
model and approach. Include how you might improve the experimental design and
analysis approach.
Scientific Inquiry with AI • Investigating Inelastic Collisions • Student Guide Page 7