Collisions

1 Collisions Assignment Zaryan Syed Physics (SPH4U) Mrs. Kennedy Feb 1, 2023

2 Testable Question How does a change in elasticity affect the momentum of two objects involved in a collision? Independent Variable Elasticity Dependent Variable Momentum Control Variable Mass Hypothesis If the elasticity of two objects changes and their velocity is constant, the momentum of the objects will be conserved regardless of how elastic an object is. In an elastic collision, momentum and kinetic energy are conserved before and after (HyperPhysics, 2019). Elastic means that no energy is converted into heat during the collision so kinetic energy before and after the collision remains constant (Khan Academy, n.d.). In an inelastic collision, momentum will be conserved before and after the collision, but kinetic energy is lost after the collision (HyperPhysics, 2019). In both scenarios, momentum is conserved due to the law of conservation of momentum which says that; in an isolated system the total momentum of two or more bodies acting upon each other remains constant unless an external force is applied (Byjus, n.d.). Therefore, in both elastic and inelastic collisions, momentum is always conserved. Materials  A meter stick or measuring tape  Stopwatch  Two 1kg hard balls (ex. Billiard Ball)

4 Vector Diagrams:

5 Results Table 1 - Initial vs Final Distances and Times of Two Objects in Collision Ball 1 Ball 2 Type of Collision (Elasticity) Mass (kg) Initial Distance Travelled (m) Initial Time (s) Final Distance Travelled (m) Final Time (s) Mass (kg) Initial Distance Travelled (m) Initial Time (s) Final Distance Travelled (m) Final Time (s) Basketball vs Basketball (100%) 1.00 1.42 1.42 0.00 2.00 1.00 0.00 1.42 0.58 2.00 Basketball vs Billiard Ball (50%) 1.00 1.42 1.42 0.23 2.00 1.00 0.00 1.42 0.75 2.00 Billiard Ball vs Billiard Ball (0%) 1.00 1.42 1.42 0.09 2.00 1.00 0.00 1.42 0.29 2.00 Sample calculations: Initial Velocity Initial Velocity (Ball 1) (100%): V 1i = d/t V 1i = 1.42m / 1.42s V 1i = 1.00 m/s Initial Velocity (Ball 2) (100%): V 2i = d/t V 2i = 0m / 1.42s V 2i = 0 m/s Final Velocity Final Velocity (Ball 1) (100%): V 1f = (m 1 – m 2 / m 1 + m 2 ) v 1i V 1f = (0.50kg - 0.50kg / 2.00kg) (1.00 m/s) V 1f = (0) (1.00m/s) V 1f = 0 m/s Final Velocity (Ball 2) (100%): V 2f = (2m 1 / m 1 + m 2 ) v 1i V 2f = (2(1kg) / 2.00 kg) (1.00m/s) V 2f = (1kg) (1.00m /s) V 2f = 1.00 m/s

7 Sample calculations: Total initial momentum (50%) P Ti = P 1i + P 2i P Ti = 1.00 kg m/s + 0.00 kg m/s P Ti = 1.00 kg m/s Total final momentum (50%) P Tf = P 1f + P 2f P Tf = 0.25 kg m/s + 0.75 kg m/s P Tf = 1.00 kg m/s Table 3 - Total Momentum Before and After Collision Elasticity of Collision Total Initial Momentum (kg ⋅ m/s) Total Final Momentum (kg ⋅ m/s) Basketball vs Basketball (100%) 1.00 1.00 Basketball vs Weight Ball (75%) 1.00 1.00 Weight Ball vs Weight Ball (50%) 1.00 1.00

8 0 50 100 0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00 1.00 1.00 1.00 1.00 1.00 1.00 Elasticity vs Momentum Total Initial Momentum Total Final Momentum Elasticity (%) Momentum (kg m/s) Discussion: The momentum of an object is calculated based on its mass and velocity. When this object collides with another stationary object, its momentum is conserved within the system (Khan Academy, 2018). An elastic collision conserves the system's overall momentum and kinetic energy. As a result, overall momentum and kinetic energy remain constant before and after elastic contact. In contrast, an inelastic collision conserves the system's momentum but loses its kinetic energy. This can be caused by a variety of variables, including friction and item deformation. The elasticity of a collision is a measurement of an object's capacity to return to its original shape following a collision. A fully elastic collision transfers all momentum to the stationary item, leaving it with a final momentum of zero. Momentum is only partially transferred between two objects in any collision where the elasticity of the objects is less than 100%; nevertheless, because the momentum of the system must be conserved, the total momentum of the two objects prior to the collision equals the total momentum of the two objects following the collision. The purpose of the lab was to see how elasticity affects the momentum of two objects involved in a collision. Based on the results, the experimental data had a pattern that was consistent throughout the experiment; as elasticity decreased, the transfer in individual

1 0 Conclusion: In conclusion, the experiment aimed to find out how elasticity affects the momentum of two objects involved in a collision. Through the results, while the change in elasticity shifted the momentum of the two objects in collision, the overall combined momentum of the objects remained the same due to the law of conservation of energy, which supports the hypothesis being that momentum is always conserved regardless of elasticity.

1 1 References Conservation of Momentum - Definition, formula, examples, applications, video and FAQs . (n.d.). BYJUS. https://byjus.com/physics/derivation-of-law-of-conservation-of-momentum/ #:~:text=Law%20of%20conservation%20of%20momentum%20states%20that,neither %20be%20created%20nor%20destroyed. HyperPhysics. (2019). Elastic and Inelastic Collisions. Gsu.edu. http://hyperphysics.phyastr.gsu.edu/hbase/elacol.html Khan Academy. (n.d.). Elastic and inelastic collisions . Khan Academy. https://www.khanacademy.org/science/physics/linear-momentum/elastic-and-inelastic- collisions/v/elastic-and-inelastic-collisions#:~:text=Elastic%20means%20that%20no %20energy,collisions%2C%20momentum%20is%20always%20conserved.