Method

Analyze the data to verify that momentum remains conserved while kinetic energy is not conserved in inelastic collisions.

Following these steps, you can perform a detailed inelastic collision experiment, gather data, and analyze the results using ImageJ and Excel.

Step 2: Set Initial Conditions for Ball 1:

1. • For Ball 1, configure the following initial velocity:

     • Vx=0.5 m/s

     • Vy=0.5 m/s

   • This means that Ball 1 will move at an angle of 45 degrees from the x-axis.

   • Set its initial position to:

     • X=0 m

     • Y=0 m

   • This places Ball 1 at the simulation space's origin (0, 0).

   • Make sure to apply these velocity and position settings for Ball 1 correctly.

Step 3: Set Initial Conditions for Ball 2:

1. • For Ball 2, configure its velocity:

     • Vx=0 m/s

     • Vy=0 m/s

   • This indicates that Ball 2 will remain stationary at the start.

   • Set the initial position for Ball 2:

     • X=0.5 m

     • Y=0.5 m

   • This places Ball 2 at coordinates (0.5, 0.5) on the simulation grid.

   • Ensure the velocity and position values for Ball 2 are properly entered.

Step 4: Set the Masses for the Balls:

1. • Assign masses to the two balls as follows:

     • Ball 1 mass = 0.5 kg

     • Ball 2 mass = 1.5 kg

   • Double-check that these mass values are correctly set in the simulation.

Step 5: Configure the Simulation Setup:

1. • Arrange the experiment as shown in the provided figure (if available). Ensure that all parameters—velocities, positions, and masses—are accurately set according to the instructions.

   • Confirm that all settings match the experimental requirements before starting the simulation.

Step 6: Run and Record the Simulation:

1. • Start the simulation and record the experiment using a screen capture tool.

   • After recording, convert the video file into a format compatible with ImageJ for further analysis.

Step 7: Track the Motion Using ImageJ:

1. • Load the recorded video into ImageJ and use the tracking feature to follow the movement of both Ball 1 and Ball 2 during the collision.

   • Track both balls' spatial positions (x, y coordinates) at each time step to gather data for analysis.

Step 8: Analyze the Data in Excel:

1. • Export the position data from ImageJ and import it into Excel for further analysis.

   • Calculate the velocities, momentum, and kinetic energy before and after the collision.

   • Use the following conservation laws to analyze the elastic collision:

     • Momentum Conservation: Check momentum conservation in the x- and y-directions.

     • Kinetic Energy Conservation: Verify that the total kinetic energy before and after the collision remains the same, confirming an elastic collision.

 Following these steps, you can conduct a two-dimensional elastic collision experiment, collect data from the simulation, and analyze the results using ImageJ and Excel.

   Step 2: Set Initial the  for Ball 1:

1. • For Ball 1, configure the initial velocity as follows:

     • Vx=0.5 m/s

     • Vy=0.5 m/s

   • This ensures Ball 1 moves diagonally at a 45-degree angle to the x-axis.

   • Set the initial position for Ball 1:

     • X=0 m

     • Y=0 m

   • This places Ball 1 at the simulation grid's origin (0, 0).

   • Ensure these values are correctly entered for Ball 1.

Step 3: Set Initial Conditions for Ball 2:

1. • For Ball 2, set its initial velocity:

     • Vx=0 m/s

     • Vy=0 m/s

   • This means Ball 2 will remain stationary at the start of the experiment.

   • Set the initial position for Ball 2:

     • X=0.5 mX

     • Y=0.5 m

   • This places Ball 2 at coordinates (0.5, 0.5) in the simulation.

   • Confirm that the velocity and position for Ball 2 are correctly set.

Step 4: Set the Masses for the Balls:

1. • Assign the following masses to the two balls:

     • Ball 1 mass = 0.5 kg

     • Ball 2 mass = 1.5 kg

   • Verify that the mass values are correctly entered into the simulation settings.

Step 5: Configure the Inelastic Collision Setup:

1. • Adjust the settings in the simulation to simulate an inelastic collision. In an inelastic collision, the two balls will stick together after the collision. If available, enable the inelastic collision option in the settings.

   • Ensure that all other parameters—velocities, positions, and masses—are configured accurately before running the simulation.

Step 6: Run and Record the Simulation:

1. • Start the simulation and observe how the two balls collide and then move together as a single mass after the collision.

   • Record the screen using a screen capture tool to document the entire collision process.

   • After recording, convert the video to a format compatible with ImageJ for further analysis.

Step 7: Track the Motion Using ImageJ:

1. • Import the recorded video into ImageJ and use the tracking tool to monitor the motion of both balls before the collision and the combined mass after the collision.

   • Track the x- and y-coordinates of the balls frame by frame to gather data on their positions over time.

Step 8: Analyze the Data in Excel:

1. • Export the position data from ImageJ and import it into Excel for analysis.

   • Use the position data to calculate the velocities and momentum of the two balls before the collision and their combined velocity after they stick together.

   • Apply the following equation for momentum conservation in two-dimensional inelastic collisions:

     • In the x-direction

1. • • In the y-direction

1. • where vfx and vfy​ are the x and y components of the final velocity after the collision.

   • Analyze the data to confirm that momentum is conserved while kinetic energy is not conserved (as it is converted to other forms of energy).

By following these steps, you will successfully simulate and analyze a two-dimensional inelastic collision using PhET, ImageJ, and Excel. This process will help you verify momentum conservation while demonstrating the energy loss typical of inelastic collisions.