Assignment_Collisions

Testable question: How does a change in elasticity affect the momentum of two objects involved in a collision? Hypothesis: If the elasticity of two objects colliding changes and their velocity remains constant, the final momentum of the objects will be directly proportional to the collision's elasticity because while the system's total momentum is conserved in all collisions regardless of how elastic the objects are, the individual final momentums will vary (Peter Urone & Hinrichs, 2022).In this experiment, the independent variable is the elasticity, the dependent variable is momentum, and the control variable is the mass. The formula used to show the relationship between a system's momentum before and after a collision is: p i = p f Where: p = mv p object 1 final =( 100% elasticity ) . p system initial .m object 1 When the individual momentums of the two objects are taken into account, the equation becomes: And from there since p 1 = p f , object 2's final momentum can be solved using: p object 1 initial + p pobject 2 initial = p object 1 final + p object 2 final Or:

m 1 initial .v 1 initial + m 2 initial .v 2 initial = m 1 final .v 2 final + m 2 final . v 2 final However, this equation does not take into consideration the effect of elasticity on the final individual momentums. The collision's elasticity is not accounted for because of the conservation of momentum principle; the momentum of all objects before the collision equals the momentum of all objects after the collision (Khan Academy, 2018). To solve for the final momentum of the first object while considering the elasticity of the collision, one must multiply the percent elasticity by total initial momentum of the system and the object's mass. The Equation for object 1 looks like: p object 1 final =( 100% elasticity ) . p system initial .m object 1 And from there since p 1 = p f , object 2's final momentum can be solved using: p object 2 final = p system initial − p object 1 final The fundamental principle of an isolated system containing two colliding objects is that the loss of momentum in one object is equivalent to the gain of momentum in the other object, as represented by these two equations (The Physics Classroom Website, n.d.). This last concept reveals the immediate impact of elasticity on the ultimate velocities of two objects that undergo a 1-D collision. Materials: A meter stick or measuring tape -A stopwatch that can time laps -Surface with negligible friction (ex. Ice or an air hockey table) -2 500g hard balls (ex. basketballs) -2 500g soft balls (ex. weight balls)

8-Steps 2 through 7 were repeated using the combination of one tennis ball colliding with one billiard ball, and two tennis balls colliding with each other. 9-After all times were recorded, the footage from the camera was analyzed to determine and record the displacement of the balls during each iteration of the experiment. Observations: -The total initial momentum was equal to the total final momentum of both balls throughout the entirety of the experiment. -A perfectly elastic collision at 100% had a complete transfer of momentum from before and after the collision, but as the elasticity decreased, the transfer in momentum decreased (Ball 1 of trial 2 and 3 remained in motion). Vectors diagram: Basketball - Basketball (100%) Before: After:

Basketball -Weight ball (75%): Before: After: Weight ball - Weight ball (50 %) Before: After: Results: Table 1: Initial and final distances and times of two objects in collision.

( m / s ) collision ( kg.m / s ) ( m / s ) collision ( kg.m / s ) collision ( kg.m / s ) Basketball vs Basketball (%100) 1.00 0.50 0.00 0.00 0.50 Basketball vs Weight ball (%75) 1.00 0.50 0.00 0.00 0.50 Weight ball vs Weight ball (%50) 1.00 0.50 0.00 0.00 0.50 Table 3: Elasticity and Velocity vs Momentum of Two Objects After Collision. Elasticity of collision Velocity of ball 1 before collision Momentum of ball 1 before Velocity of ball 2 before collision Momentum of ball 2 before Total system momentum before the

( m / s ) collision ( kg.m / s ) ( m / s ) collision ( kg.m / s ) collision ( kg.m / s ) Basketball vs Basketball (%100) 0.00 0.00 1.00 0.50 0.50 Basketball vs Weight ball (%75) 0.13 0.06 0.88 0.44 0.50 Weight ball vs Weight ball (%50) 0.25 0.13 0.75 0.38 0.50 Calculations: Initial velocity (Ball1): V = d t

V 2 f = ( 2 ( 0.50 ) 1 ) ( 1 ) V 2 f = 1 m / s Initial momentum (Ball 1): p = m.v p =( 0.50 ) . ( 1 ) p = 0.50 kg.m / s Final momentum (Ball 1): p = m.v p =( 0.50 ) . ( 0 ) p = 0.00 kg.m / s Initial momentum (Ball 2): p = m.v p = ( 0.50 ) . ( 0 ) p = 0.00 kg.m / s Final momentum (Ball 2): p = m.v p = ( 0.50 ) . ( 1 ) p = 0.50 kg.m / s

Graph: Discussion: The momentum of an object is calculated based on its mass and velocity. When this object then collides with another stationary object, its momentum is conserved within the system (Khan Academy, 2018). In a perfectly elastic collision, the momentum is transferred entirely to the stationary object and is left with a final momentum of zero. In any other collision (inelastic), where the elasticity of the objects is less than 100%, the momentum is

transfer of momentum between the two balls in visually showing the shift from a 100% transfer of momentum, down to 75% and 50% transfers. Error analysis: Although the laboratory work was carried out using a simulation, which prevented any outside factors from affecting the experiment, the same experiment conducted in a less controlled setting could be impacted by external factors like gravity, friction, and air resistance, leading to a certain degree of inaccuracy. To prevent such influences, additional steps would need to be taken, such as using a vacuum chamber to eliminate air resistance and minimize the effects of friction and gravity. Conclusion: In conclusion, a change in elasticity shifted the individual momentums of two objects involved in a collision; however, due to the conservation of momentum, the total combined momentum of the system remained the same. References -Khan Academy. (2018). What are elastic and inelastic collisions? Khan Academy Retrieved from: https://www.khanacademy.org/science/physics/linear-momentum/elastic-and- inelastic-collisions/a/what-are-elastic-and-inelastic-collisions

-Collisions Peter Urone, P., & Hinrichs, R. (2022, March 26).8.3 Elastic and Inelastic Collisions - Physics.Openstax.org; OpenStax. Retrieved from: https://openstax.org/books/physics/pages/8-3-elastic-and-inelastic-collisions -Todd, J. T., & Warren, W. H. (1982, June 1). Visual perception of relative mass in dynamic events - sage journals. Sage Journals. Retrieved June 17, 2022, from: https://journals.sagepub.com/doi/10.1068/p110325