Bumper Cars Conservation: Analyzing Momentum in Action

NGSS Performance Expectation: HS-PS2-2 Science and Engineering Practice: Using Mathematics and Computational Thinking Disciplinary Core Idea: PS2.A: Forces and Motion Crosscutting Concept: Systems and System Models

Phenomenon

Have you ever ridden bumper cars at an amusement park? Sometimes when you hit another car, you bounce right off each other. Other times, the two cars might seem to get stuck and travel together for a moment, or you might hit a stationary car and send it flying while your car comes to a near stop. Despite all these different types of collisions, there is a hidden rule governing exactly how the cars behave before and after they crash. In this activity, you will use a simulation to explore this rule by acting as an accident investigator for a new amusement park ride.

Simulation Link

Conservation of Momentum Simulation

Instructions

You are investigating the safety and physics of a new bumper car attraction. The bumper cars can be equipped with different types of bumpers—some are very bouncy (elastic), while others are designed to crumple or stick together (inelastic). Your task is to use the simulation to model these collisions and track the momentum of the system.

Part 1: Bouncy Bumpers (Elastic Collisions)

First, let’s test the “bouncy” bumpers. These bumpers are designed to bounce off each other without losing any energy.

1. Open the simulation and set the Elasticity (e) to 1.0. This represents a perfectly elastic collision.
2. Set the following initial conditions for two bumper cars:
   • Car 1 (Left): Mass = 2.0 kg, Initial Velocity = 3.0 m/s
   • Car 2 (Right): Mass = 1.5 kg, Initial Velocity = -2.0 m/s (moving towards Car 1)
3. Before pressing Start, calculate the initial momentum for each car and the total momentum of the system. Show your work.
   • Initial Momentum of Car 1 (p_1i = m₁ × v_1i): ____ kg·m/s
   • Initial Momentum of Car 2 (p_2i = m₂ × v_2i): ____ kg·m/s
   • Total Initial Momentum (P_total,i = p_1i + p_2i): ____ kg·m/s
4. Press Start and observe the collision. Use the simulation output or the data log table to find the final velocities.
   • Final Velocity of Car 1 (v_1f): ____ m/s
   • Final Velocity of Car 2 (v_2f): ____ m/s
5. Calculate the final momentum for each car and the total final momentum of the system.
   • Final Momentum of Car 1 (p_1f = m₁ × v_1f): ____ kg·m/s
   • Final Momentum of Car 2 (p_2f = m₂ × v_2f): ____ kg·m/s
   • Total Final Momentum (P_total,f = p_1f + p_2f): ____ kg·m/s
6. Compare the Total Initial Momentum and the Total Final Momentum. What do you notice?

Part 2: Sticky Bumpers (Inelastic Collisions)

Now let’s test the “sticky” bumpers. These bumpers have Velcro and are designed to stick together upon impact.

1. Press Reset.
2. Set the Elasticity (e) to 0.0. This represents a perfectly inelastic collision where the objects stick together.
3. Set the following initial conditions for the two bumper cars:
   • Car 1 (Left): Mass = 3.0 kg, Initial Velocity = 4.0 m/s
   • Car 2 (Right): Mass = 2.0 kg, Initial Velocity = 0.0 m/s (stationary)
4. Calculate the initial momentum for each car and the total momentum of the system.
   • Total Initial Momentum (P_total,i): ____ kg·m/s
5. Press Start and observe the collision. What happens to the two cars after they collide?
6. Use the simulation output to find the final velocity of the combined cars.
   • Final Velocity (v_f): ____ m/s
7. Since the cars are stuck together, their combined mass is m₁ + m₂. Calculate the total final momentum using the combined mass and the final velocity.
   • Total Final Momentum (P_total,f = (m₁ + m₂) × v_f): ____ kg·m/s
8. Compare the Total Initial Momentum and the Total Final Momentum for this sticky collision. How does this result compare to what you observed in Part 1?

Part 3: Investigating Kinetic Energy

The simulation also tracks Kinetic Energy (KE = ½ m × v²).

1. Look back at the data log table for the elastic collision (Part 1). What happened to the total kinetic energy of the system before and after the collision?
2. Look at the data log table for the inelastic collision (Part 2). What happened to the total kinetic energy of the system before and after the collision?
3. Based on your observations, write a brief explanation describing the difference between an elastic and an inelastic collision in terms of momentum and kinetic energy.

Part 4: Conclusion & Application

1. Write a mathematical claim about the total momentum of a system of objects before and after a collision.
2. Use the data you collected in Parts 1 and 2 as evidence to support your claim.
3. If a small child in a 1.0 kg bumper car moving at 2.0 m/s collides head-on with an adult in a 3.0 kg bumper car moving at -2.0 m/s, which car will experience a greater change in velocity? Explain your reasoning using the concept of conservation of momentum.