How to Use the Conservation of Momentum Simulator
 

Top Bar

• Use the play button in the top right corner to run the interaction and the reset button to return the carts to their starting positions.

• The moon icon switches between light and dark mode, and the fullscreen icon gives the canvas more room.
   

Cart A (Blue) & Cart B (Orange)

• Set the Mass and Initial Velocity of each cart with the sliders or by typing a value.

• The positive direction is to the right, so a negative velocity means the cart is moving left.
   

Interaction Type

• Perfectly Elastic: the carts bounce apart and kinetic energy is conserved (e = 1).

• Inelastic: the carts bounce apart but some kinetic energy is lost to heat or sound. Choose a coefficient of restitution (e) of 0.2, 0.6, or 0.9, or set your own.

• Perfectly Inelastic: the carts stick together and move as one, losing the most kinetic energy possible (e = 0).

• Explosion: the carts start joined and push apart. Set their Initial Common Velocity and the Energy Added (ΔK).

• The final velocities of both carts (vAf and vBf) are shown below the interaction type.
  Note for teachers: Run the same masses and velocities through all four interaction types. The total momentum is identical every time, while the kinetic energy changes. This is the clearest way to separate the two ideas for students.
   

Speed

• Slow the interaction down to 0.25× or 0.5× to watch the collision more closely.
   

Display

• Velocity Arrows draws each cart's velocity.

• Center of Mass Dot marks the center of mass of the two-cart system.

• ΔK Badge shows how much kinetic energy was gained or lost in the interaction.

• Show Grid adds a grid to the track.
  Mastery tip: Turn on the Center of Mass Dot and run each interaction type. Watch how the dot moves before, during, and after the interaction, and explain what that tells you about the system's total momentum.
   

Graphs

• Choose from x-t (Position), v-t (Velocity), p-t (Momentum), and a Momentum Bar Chart.

• Use the p-t graph or the Momentum Bar Chart to compare each cart's momentum before and after the interaction. The individual momenta change, but add them together and the total stays the same.
  Note for teachers: The v-t graph shows that both carts change velocity over the same short time interval. Paired with the p-t graph, it is a good lead-in to impulse and Newton's third law.
   

Challenge Mode (Test your understanding!)

• Difficulty: Easy, Medium, or Hard.

• Choose a challenge type:

  • Vel. Prediction: you're given Cart A's final velocity and asked to predict Cart B's final velocity (vBf).

  • Mystery Mass: Cart B's mass is hidden. Click Play Interaction, then use the v-t graph and conservation of momentum to find it.

• Enter your answer and click Check. Use Reset to try again.
  Mastery tip: Keep track of signs. Write the total momentum before the interaction, set it equal to the total after, and let a negative answer mean the cart moves left.