Day 1 stretches conservation of momentum to harder problems: both objects moving, an unknown quantity, a system that splits. Day 2 uses it to identify a hidden mass, and then works backward from a skid mark to the speed before a crash.
🎯 Goals
- Solve before-and-after problems when both objects are moving, using signs for direction.
- Find an unknown mass or velocity from conservation of momentum, and use it to identify a hidden mass.
- Handle a system that splits apart while already moving.
- Use momentum for a collision and work-energy for the skid afterward to work backward to a pre-crash speed.
🧰 Materials
🚗Two carts or toy cars with free-rolling wheels. One is the “mystery” cart, prepared by your teacher
🎁A sealed or covered mystery cart with a hidden load, and Velcro or putty to make the carts stick
🛤️A level track or flat board, with a small ramp to release cart A at a steady speed
📏Meter stick and masking tape
📱A phone with slow-motion video (120 or 240 fps)
⚖️A scale that reads in grams, for the reveal at the end
🧮Calculator
📓Physics notebook
DAY 1Harder before-and-after problems
Section 1 of 4
Both Objects Moving
1
Read the method.
Pick a positive direction. Write the momentum of each object before and after, with signs. Set the total before equal to the total after. If the collision is elastic, add the equation that the relative velocity reverses.
Total momentum: m_A v_A + m_B v_B = m_A v_A′ + m_B v_B′
Stick together: m_A v_A + m_B v_B = (m_A + m_B) v_f
Elastic: also v_A − v_B = −(v_A′ − v_B′)
Skid to a stop: v = √(2μgd), from F_f × d = ½mv² with F_f = μmg
2
Solve five problems where both carts move.
The last two need two equations: conservation of momentum and the reversal of relative velocity. Enter each answer with its sign.
Both Moving
Right is positive.
Section 2 of 4
Solving for the Unknown
3
Solve for a missing mass or velocity.
The same equation works backward. Put the numbers you know into the conservation equation and solve for the one you don’t. The last problem starts with a moving system that splits, so the momentum before is not zero.
Find the Unknown
Right is positive.
✅ End of Day 1 check: Both Moving and Find the Unknown are all green, and you can explain in a sentence how you picked your positive direction.
DAY 2A mystery mass and a skid mark
Section 3 of 4
Mystery Mass Lab
4
Get your mystery cart and mass cart A.
Your teacher gives you a sealed cart with a hidden load. Do not open it and do not put it on the scale. Mass your known cart, A, and write it down.
5
Collide A into the mystery cart and measure the speeds.
Set up the track with a 0.50 m before zone and a 0.50 m after zone, as in Activity 5-1-3. Put the mystery cart, B, at rest on the collision line with Velcro or putty so the carts stick. Release A from the same ramp height each time. Film from the side and step through frame by frame. Find A’s speed before and the stuck-together speed after. Do three runs.
6
Work out the hidden mass from each run.
Momentum is conserved, so m_A v_A = (m_A + m_B) v. Solving for the unknown gives m_B = m_A (v_A − v) ÷ v. Calculate m_B for each run and average.
7
Reveal the answer.
Only after you’ve written your estimate, put the mystery cart on the scale and find its actual mass. Calculate the percent error.
Sample data (use only if you can’t run the lab)
Cart A
0.250 kg. Run 1: v_A =
0.80, v =
0.35. Run 2:
0.78,
0.34. Run 3:
0.81,
0.36 (all in m/s). After the reveal, the mystery cart’s mass is
0.300 kg.
What good data looks like
Most groups land within about 5–15% of the true mass. A small final speed makes the estimate more sensitive to timing error, since the same one-frame mistake is a bigger fraction of a slow speed.
📓 Physics Notebook
How close was your estimate? Which measurement had the biggest effect on the answer, and why? How could you have made the estimate more reliable?
Section 4 of 4
Collide, Then Skid
8
Reconstruct a crash from its skid mark.
Two cars lock together and skid to a stop. You can’t measure their speed before the crash, but you can measure the skid. Work in two stages. After the collision, friction takes all of the kinetic energy, so v = √(2μgd). Across the collision, momentum is conserved, so you can work back to the speed before.
Crash Reconstruction
Use g = 9.8 N/kg. Dry asphalt has μ = 0.70 and wet asphalt has μ = 0.40.
📓 Physics Notebook
Why can you use conservation of momentum across the collision but not across the skid? What force acts during the skid that is not part of the collision? Why do real investigators report a range of speeds instead of a single number?
Question 1
Show your calculation for the mystery mass and compare it with the actual mass. Which measurement had the biggest effect on your uncertainty, and why?
Question 2
Explain why momentum can be used across the collision but not across the skid. What changes about the forces on the cars?
Question 3
On a wet road, the same 12 m skid means a slower pre-crash speed. Explain why the friction assumption matters, and why investigators give a range.
Question 4
A cart rolling at +1.0 m/s splits into two 1.0 kg halves, and one half moves at +3.0 m/s. Where does the other half go, and where did the extra kinetic energy come from?
📤 Turn In
- Your Both Moving and Find the Unknown results
- Completed mystery-mass tables, with your estimate, the actual mass, and the percent error
- Your Crash Reconstruction results and your notebook note on why investigators give a range
- Written answers to the four Conclusion questions