Every collision conserves momentum, but not every collision conserves kinetic energy. Day 1 teaches you to classify collisions by what happens to the energy, and tests it on carts. Day 2 predicts what happens with unequal masses, and follows the lost energy into a car crash.
🎯 Goals
- Classify collisions as elastic, inelastic, or perfectly inelastic from the kinetic energy before and after.
- Measure the momentum and kinetic energy of two carts before and after a collision with three kinds of bumper.
- Predict the final velocities of an elastic collision with unequal masses, then test the prediction.
- Find how much kinetic energy a crash loses and explain where it goes.
🧰 Materials
🚗Two dynamics carts or toy cars with free-rolling wheels
🧲Three bumper types: magnets that repel, a rubber-band bumper, and Velcro or putty
🛤️A level track or flat board with a small ramp to release cart A at a steady speed
🪙Loads to add mass (coins or washers) and tape
📏Meter stick and masking tape
📱A phone with slow-motion video (120 or 240 fps)
⚖️A scale that reads in grams
🧮Calculator
📓Physics notebook
DAY 1Classify collisions by their energy
Section 1 of 5
Energy Before and After
1
Read the three types.
Collisions are sorted by what happens to the kinetic energy. Momentum is conserved in all of them.
Elastic: KE_after = KE_before. The objects bounce apart. e = 1
Inelastic: KE_after < KE_before. e is between 0 and 1
Perfectly inelastic: the objects stick, and the most KE is lost. e = 0
Restitution: e = (v_B′ − v_A′) ÷ (v_A − v_B), the speed of separation over the speed of approach
Elastic, B at rest: v_A′ = ((m_A − m_B) ÷ (m_A + m_B)) v_A, and v_B′ = (2m_A ÷ (m_A + m_B)) v_A
2
Warm up with five calculations.
A correct answer is within the tolerance shown by the checker. Keep your work in your notebook.
Energy Warm-Up
Use KE = ½mv² and the rule card.
Section 2 of 5
Bumper Test Lab
3
Set up the track as in Activity 5-1-3.
Use a level track with a collision line, a 0.50 m before zone, and a 0.50 m after zone. Mass both carts, and keep the masses equal for today (about 0.250 kg each). Release cart A from the same ramp height every time, with cart B at rest on the line.
4
Run one collision for each bumper type.
First put repelling magnets on the facing ends, then a rubber-band bumper, then Velcro or putty. Film from the side with the meter stick in view and step through frame by frame. Find cart A’s speed before, and each cart’s speed after (if a cart stops, its speed is 0, and a cart that bounces back has a negative velocity). Speed = 0.50 m ÷ (frames ÷ fps).
5
Calculate the energy and the restitution for each bumper.
For each collision, find KE before = ½m_A v_A² and KE after = ½m_A v_A′² + ½m_B v_B′², then the percent lost. Then e = (v_B′ − v_A′) ÷ v_A. Finally classify each collision.
Sample data (use only if you can’t run the lab)
All carts
0.250 kg, v_A before
0.80 m/s.
Magnets: v_A after
0.02 m/s, v_B after
0.72 m/s.
Rubber band: v_A after
0.12 m/s, v_B after
0.60 m/s.
Velcro: both carts after
0.37 m/s.
What good data looks like
The magnets should come out nearly elastic, with e close to 0.9 and under about 25% of the KE lost. The Velcro should give e near 0 and a loss of 50% or more. Total momentum should be conserved, give or take 5–15%, in all three.
📓 Physics Notebook
Rank your three collisions by kinetic energy lost, and then by e. What pattern do you notice? Was momentum conserved in all three, even the one that lost the most energy? Where did the lost kinetic energy go?
✅ End of Day 1 check: the warm-up is all green, Table A is complete, and you can classify each of your three collisions with a reason.
DAY 2Predict, test, and follow the energy
Section 3 of 5
Predict: Unequal Masses
6
Predict what happens before you test it.
With unequal masses, an elastic collision has a surprising result. Use the B-at-rest formulas to predict the outcome for a heavy cart hitting a light one, and for a light cart hitting a heavy one.
Predict It
Elastic collisions, cart B at rest, right is positive.
Section 4 of 5
Test: Heavy Hits Light, Light Hits Heavy
7
Trial 1: a heavy cart hits a light cart.
Use the magnet bumpers. Tape loads onto cart A so it is heavier than B (for example about 0.450 kg against 0.250 kg). Release A from the usual ramp height, with B at rest. Measure the speed of A before, and the speeds of both carts after.
8
Trial 2: a light cart hits a heavy cart.
Move the loads to cart B so it is the heavy one, and run it again. Cart A should bounce back, so its velocity after is negative.
9
Compare your measurements with the predictions.
Use the Elastic Predictor to get the predicted velocities, then work out the percent error for cart B’s measured velocity.
Sample data (use only if you can’t run the lab)
Trial 1: m_A =
0.450 kg, m_B =
0.250 kg, v_A =
0.80 m/s. After: v_A′ =
0.22 m/s, v_B′ =
0.92 m/s.
Trial 2: m_A =
0.250 kg, m_B =
0.450 kg, v_A =
0.80 m/s. After: v_A′ =
−0.20 m/s, v_B′ =
0.52 m/s.
📓 Physics Notebook
Which cart bounced backward, and why? Did your measured speeds match the elastic predictions? If they were lower, what does that tell you about how elastic your magnet bumpers really are?
Section 5 of 5
Connect It: Where the Energy Goes in a Crash
10
Count the energy lost in a car crash.
A 1,000 kg car at +20 m/s hits an identical car at rest, and the two lock together. This is a perfectly inelastic collision. Find the final velocity and the kinetic energy that disappears.
Crash Budget
Right is positive.
📓 Physics Notebook
Where did the 100,000 J go? Why can’t you tell how fast a car was going from momentum alone after a crash? How might the damage to the cars help an investigator work backward? (You’ll use this idea in Problem 5-3-1.)
Question 1
Using Table A, rank the three collisions by kinetic energy lost and by e. What pattern do you see?
Question 2
Show that momentum was approximately conserved in all three Day 1 collisions, even though kinetic energy wasn’t.
Question 3
Using Table B, explain why a light cart bounces back from a heavy one, but a heavy cart keeps going when it hits a light one.
Question 4
In the crash, 100,000 J of kinetic energy disappeared. Explain where it went, and why that makes a crash an inelastic collision.
📤 Turn In
- Your Energy Warm-Up and Predict It results
- Completed Table A, with the type of each collision and your notebook note on the pattern
- Completed Table B, with your percent errors and your note on which cart bounced back
- Your Crash Budget results and your notebook note on where the energy went
- Written answers to the four Conclusion questions