When objects collide or push apart, the total momentum of the system before equals the total after. Today you’ll use that rule to predict outcomes, test it on real carts, and settle the question of which vehicle feels the bigger force in a truck-versus-car crash.
🎯 Goals
Use conservation of momentum to find the final velocity in sticking and push-apart situations.
Measure the momentum of two carts before and after a collision, and calculate how well it was conserved.
Show that kinetic energy is not conserved when objects stick together.
Explain why the truck and the car in a collision get equal and opposite changes in momentum.
🧰 Materials
🚗Two dynamics carts or toy cars with free-rolling wheels
🧲Velcro strips, magnets, or a ball of putty so the carts stick together
🛤️A level track or long flat board, and 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), or photogates if available
⚖️A scale that reads in grams
🧮Calculator
📓Physics notebook
Section 1 of 3
Before and After: Warm-Up
1
Read the rule.
If no net outside force acts on a system of objects, the total momentum before an interaction equals the total after it. Take right as positive, and give each velocity its sign.
p_before = p_after Objects that collide and stick together: m₁v₁ + m₂v₂ = (m₁ + m₂)v_f Objects that push apart from rest: 0 = m₁v₁′ + m₂v₂′
2
Solve four before-and-after problems.
Enter each final velocity with its sign. A correct answer is within 2%.
Before and After
Right is positive.
A 2.0 kg cart moving at +3.0 m/s collides with and sticks to a 1.0 kg cart at rest. What is their final velocity?m₁v₁ + m₂v₂ = (m₁ + m₂)v_f
A 1.0 kg cart at +4.0 m/s and a 3.0 kg cart at −2.0 m/s collide head-on and stick. What is their final velocity?
A 60 kg skater and a 40 kg skater, both at rest, push apart. The 40 kg skater glides away at +3.0 m/s. What is the 60 kg skater’s velocity?Total momentum starts at 0, so it must end at 0
A 10,000 kg freight car at +2.0 m/s couples to a 30,000 kg car at rest. What is their final velocity?
Section 2 of 3
Cart Collision Lab
3
Set up the track.
Put a level track or flat board on the table and check that a cart placed on it doesn’t roll. Tape a collision line. Tape two marks 0.50 m apart so the “before zone” ends at the line, and two more 0.50 m apart so the “after zone” starts at the line. Put Velcro or putty on the carts’ bumpers so they stick when they meet. Set up a small ramp so cart A is released from the same height every time.
⚠️ Keep the track well back from the table edge and put a catch block past the after zone.
4
Run Trial 1 with equal masses.
Mass both carts. Place cart B at rest on the collision line. Release cart A from the ramp so it crosses the before zone and hits B. Film from the side with the meter stick in view, and step through the video frame by frame to time each zone. Speed = 0.50 m ÷ (frames ÷ fps). Record cart A’s speed before and the stuck-together speed after.
5
Run Trials 2 and 3 with different mass ratios.
In Trial 2, tape a load onto cart A so it’s heavier than B. In Trial 3, take the load off A and tape one onto B so it’s heavier. Release A from the same height each time and re-mass the carts.
6
Calculate the momentum before and after.
Before: p = m_A × v_A (cart B is at rest). After: p = (m_A + m_B) × v. Then find the percent difference: (p_after − p_before) ÷ p_before × 100.
Sample data (use only if you can’t run the lab)
Trial 1: m_A = 0.250 kg, m_B = 0.250 kg, v_A = 0.80 m/s, v after = 0.37 m/s. Trial 2: m_A = 0.350 kg, m_B = 0.250 kg, v_A = 0.78 m/s, v after = 0.44 m/s. Trial 3: m_A = 0.250 kg, m_B = 0.350 kg, v_A = 0.80 m/s, v after = 0.32 m/s.
Trial
m_A (kg)
m_B (kg)
v_A before (m/s)
p before = m_A·v_A (kg·m/s)
v after, stuck (m/s)
p after = (m_A+m_B)·v (kg·m/s)
% difference
Collision Checker
Work a row by hand first. Then enter it here to check your momentum, the predicted final speed, and the kinetic energy.
What good data looks like
Most groups find that the momentum after is the same as before, give or take about 5–15% lower. A little is lost to friction in the wheels and to timing error. It should never come out clearly bigger.
📓 Physics Notebook
How well was momentum conserved in each trial? Use the Collision Checker to look at the kinetic energy too. Was kinetic energy conserved? Where could the missing kinetic energy have gone? (Think about the Velcro, the sound of the collision, and what you learned about thermal energy in Unit 4.)
Section 3 of 3
Connect It: The Semi and the Compact Car
7
Settle the unit’s big question.
A 20,000 kg semi truck at +10 m/s hits a 1,000 kg compact car at rest, and they stick together. Find the final velocity, the change in each vehicle’s momentum, and the average force if the collision lasts 0.10 s.
Semi vs. Compact Car
Right is positive.
A 20,000 kg semi at +10 m/s hits a 1,000 kg car at rest, and they stick together. What is their final velocity?
What is the change in the car’s momentum?Δp = m(v_f − v_i)
What is the change in the semi’s momentum?
The collision lasts 0.10 s. What is the average force on the car?F = Δp ÷ Δt
📓 Physics Notebook
Which vehicle experiences the bigger force? Which one experiences the bigger change in velocity? Use F·Δt = Δp to explain why the people in the car are in far more danger even though the forces are equal.
Question 1
Using your three trials, how closely was momentum conserved? Give the percent differences and one reason for any gap.
Question 2
Two equal-mass carts stick together, and one starts at rest. Predict the final speed as a fraction of the moving cart’s initial speed, then compare it with your Trial 1 result.
Question 3
Your carts lost kinetic energy even though momentum was conserved. Explain where the energy went, using ideas from Unit 4.
Question 4
In the semi-and-car crash, which vehicle feels the larger force and which has the larger change in velocity? Explain using Δp.
📤 Turn In
Your Before and After results
Completed collision table, with the percent difference for each trial
Your notebook note on where the missing kinetic energy went