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)

-A means of enacting a force on the balls to achieve a constant velocity (ex. remote- controlled cars that can push the balls) -A second person (Teammate) -A camera capable of taking video on a tripod (both must have same diameter; the diameter of the balls used was 0.3m) Procedure: 1-The surface was set up and the camera was pointed towards the area that was intended to be used in the experiment 2-The two basketballs were placed on the surface with negligible friction one meter away from each other measured from their center, with the measuring tape visible to the camera. 3-The remote-controlled cars were set up behind the balls facing each other and the videorecording with the camera was started. 4-As the stopwatch was started, the second person set the remote-controlled cars in motion, applying a constant, but varying in magnitude, force on both balls (in order for the balls to achieve different, constant speeds). 5-Just before the balls collided, the remote-controlled cars were slowed and directed out of the way from the line of collision. 6-A lap time was recorded with the stopwatch as the collision between the two balls occurred and then the time was stopped 2 seconds later. 7-The camera was stopped and the lap and final times were recorded.

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: