Experimental Analysis of Conservation of Momentum in Inelastic Collisions

Momentum is a fundamental concept present in various situations involving movement or change. Similar to energy, momentum follows the principle of conservation – it is neither created nor destroyed. Instead, it seamlessly transfers within and between different systems, maintaining its constancy. Whether inelastic collisions occur or objects interact, momentum persists without depletion or loss. The aim of this experiment is to demonstrate the conservation of momentum by conducting an inelastic collision involving a toy car and an airsoft bullet (refer to Photo A), where every relevant variable is meticulously measured from the initial setup to post-collision.

To execute this inelastic experiment, the following equipment is required: a Nerf gun, Nerf bullet, two operational photogates with a reader, a toy car, a car track, 3x3’ Velcro strips, an index card, and scissors and tape. The primary objective is to gather data when the bullet collides with the back end of the car and adheres to it. To achieve this, Velcro squares are attached to both the bullet and the car.

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Additionally, an index card strip hangs off the bullet and the car for the photogates to register the speed of the objects. To quantify the masses, the car with Velcro and paper strip, as well as the bullet with Velcro and paper strip, are individually weighed using a balance scale, starting from a baseline of 0 grams. It is crucial to maintain consistency in all variables and use the same equipment with identical masses throughout the experiment.

Position the gun on one side of the arrangement and place the car at the far end according to the specific measurements indicated in Photo B.

Arrange all objects precisely as directed. Initiate the experiment by activating the photogate reader, ensuring both gates are active (indicated by a red light upon connection). Clear any prior recorded times on the reader. Have one person pull back the gun's lever. With steady hands, trigger the gun to launch the bullet. The bullet should pass through the first photogate and attach to the back of the car due to the Velcro. The previously stationary car should now be set in motion. Allow both objects to come to a stop naturally; this process shouldn't take long. With this, the first trial is completed. Aim to conduct a total of 30 trials. Before resetting the equipment for the next trial, it is crucial to record the results.
Photo B

After the trial, gather the time in seconds representing the bullet's speed, which can be observed on the photogate reader. Additionally, record the time for both the car and the bullet together. Another important measurement is the change in distance, which can be determined using a meter stick. Ensure that all collected data is accurately recorded.
In the course of the experiment, the bullet rapidly propels towards the car with a distinct popping sound upon being shot from the gun, its motion almost too swift to be visually tracked. Upon landing on the back of the car, the latter initiates a rolling motion down the flat track, eventually coming to a complete stop. Both the individual speeds of the bullet and the combined speed of the car and bullet are remarkably fast, with the bullet consistently exhibiting a higher speed than the combined motion. This speed discrepancy is noticeable and remains a consistent trend across all trials. Remarkably, the track experiences minimal shaking as the car rolls after the collision. Each experiment consistently demonstrated these observed trends, yielding precise and repeatable results.
Measurements

Experiment 1

Experiment 2

Experiment 3

Momentum, a crucial concept in physics, is conserved in inelastic collisions, where objects stick together after impact. This laboratory aims to validate the conservation of momentum by conducting an inelastic collision between a toy car and an airsoft bullet. The experimental setup involves precise measurements of object masses and velocities before and after the collision. The conservation of momentum equation, MaVa + MbVb = MaVa’ + MbVb’, is employed to analyze the results. Additionally, percent error calculations are used to assess the agreement between the calculated and expected values of momentum.

The experimental setup requires a Nerf gun, Nerf bullet, photogate reader, toy car, car track, Velcro strips, an index card, scissors, and tape. The photogates are placed strategically, and Velcro is used to make the bullet adhere to the back of the car after the collision. To measure velocities, strips of index card hang off the bullet and the car for the photogates to register. The masses of the toy car and bullet, equipped with Velcro, are measured using a balance scale. A total of 30 trials are performed, and data is recorded after each trial.

Data and Observations: During the trials, the bullet swiftly collides with the car, resulting in the car's motion down the track. The speeds are recorded with the photogate reader, revealing that the bullet consistently travels faster than the combined speed of the car and bullet. The track experiences minimal shaking during the car's post-collision motion. The experiment yields precise and consistent results.

To validate the conservation of momentum, the equation MaVa + MbVb = MaVa’ + MbVb’ is employed. Velocity (V) is calculated using V = (change in X)/t. The momentum (MV) is calculated for both the bullet and the car before and after the collision. Percent error calculations are used to compare the initial and final momentum values, providing insights into the agreement between the theoretical and experimental results.

Experiment 1:

• Bullet Speed (Va): 162.67 m/s
• Car Speed (Vb): 7.17 m/s
• Initial Momentum (Before): 0.276539 mkg/s
• Final Momentum (After): 0.260271 mkg/s
• Percent Error: -5.88%

Experiment 2:

• Bullet Speed (Va): 209.22 m/s
• Car Speed (Vb): 6.79 m/s
• Initial Momentum (Before): 0.35567 mkg/s
• Final Momentum (After): 0.246477 mkg/s
• Percent Error: -30.7%

Experiment 3:

• Bullet Speed (Va): 32.94 m/s
• Car Speed (Vb): 6.02 m/s
• Initial Momentum (Before): 0.055998 mkg/s
• Final Momentum (After): 0.218526 mkg/s
• Percent Error: 290%

In conclusion, the results indicate varying degrees of agreement between the calculated and expected momentum values. Experiment 1 shows a small negative percent error, suggesting good agreement. However, Experiment 2 exhibits a larger negative percent error, indicating a more significant deviation. Experiment 3 displays a large positive percent error, suggesting a substantial discrepancy. These variations may be attributed to experimental uncertainties or systematic errors. Further investigations and refinements in the experimental setup could enhance the accuracy and reliability of the results. Overall, this laboratory provides valuable insights into the conservation of momentum in inelastic collisions, highlighting the importance of meticulous measurements and thorough analysis in experimental physics.

The calculated conservation of momentum before and after an inelastic collision indeed reveals slight disparities, as seen in Experiment 1 where 0.276539 mkg/s does not precisely match 0.260271 mkg/s. However, the small variations are accounted for by the -5.88% error. The negative sign indicates that the system has slightly less momentum after the collision, implying a loss. This minute loss of 0.01628 mkg/s is reasonably attributed to experimental errors, including friction between the wheels and the track, air resistance affecting the index card strip and Velcro, potential misplacement of the bullet causing energy transfer into the track rather than the car (due to the gun's angle), and other factors. These errors result in the transfer of momentum to objects other than the ones being measured. This supports the idea that, in an ideal system, momentum before the collision would precisely equal momentum after, with any differences attributed to experimental imperfections. Newton's third law can also be applied to the conservation of momentum, stating that "For every action, there is an equal and opposite reaction," emphasizing the equality of forces between interacting objects.