Physic- Collisions Lab Report

Abstract :The purpose of the experiment is to explore elastic and inelastic collisions in order to study the conservation of momentum and energy. The guided track, carts, photogates , 250 g weight and picket fences were the primary components used in the procedural part of the experiment. Each experiment involved the use of the photogates and picket fences to measure the initial and final velocities of both carts when they collide. The data was collected and translated to a graphical model for further analysis. The experiment was repeated for elastic and inelastic collisions with varying masses. The calculations state that the percent discrepancies for inelastic collisions were 8.75% and 19.23 % for the equal mass and unequal mass respectively. The percent discrepancies for the equal and unequal mass elastic collisions were 22.07% and 9.78 % respectively. Both of the percent discrepancies for the collisions were close to the 10%-15% range which validates the concept of momentum conservation in inelastic and elastic collisions. In regards to conservation of energy, the calculations state that the percent discrepancies for inelastic collisions were 58.33% and 81.81% for the equal mass and unequal mass respectively. Both of the percent discrepancies were greater than 60% which indicates inelastic collisions are not as inefficient in conserving energy due to a loss in energy. The percent discrepancies for the equal and unequal mass elastic collisions were 36.36% and 56.25 % respectively. Both of the percent discrepancies for the elastic collisions were less than the percent discrepancies in inelastic collisions which validates the concept of energy conservation to be more efficient in elastic collisions.

Introduction
Objective:
The principle of the experiment is to observe elastic and inelastic collisions to study the conservation of momentum and energy.
Materials
• Horizontal dynamics track
• Collision and dynamics carts with picket fences
• 250 g Weight
• Balance
• Photogates connected to the Science Workshop interface

Experimental Procedure
The guided track, carts, photogates , 250 g weight and picket fences were the primary components used in the procedural part of the experiment. Each experiment involved the use of the photogates and picket fences to measure the initial and final velocities of both carts when they collide. The data was collected and translated to a graphical model for further analysis. The experiment was repeated for elastic and inelastic collisions with varying masses. Results: Inelastic collision m1=m2 Inelastic collision m1 ≠m2 Elastic collision m1=m2 Elastic collision m1 < m2
Mass of cart 1 (kg) 0.2646 0.2646 0.2646 0.2646
Mass of cart 2 (kg) 0.2646 0.51678 0.26523 0.51678
Initial velocity of cart 1 (m/s) 0.303 +/- 2.9e-4 0.293 +/- 2.2e-4 0.292 +/- 3.7e-4 0.346 +/- 2.1e-4
Initial velocity of cart 2 (m/s) 0 0 0 0
Final velocity of cart 1 (m/s) 0.143 +/- 4.6e-4 0.0890 +/- 4.4e-4 0.227 +/- 3.1e-4 0.160 +/- 3.0e-4
Final velocity of cart 2 (m/s) 1.34 +/- 4.0e-4 0.0756 +/- 5.2 e-4 0 0

pi Δ p KEi Δ KE
Inelastic collision m1=m2 0.08 -0.007 0.012 -0.007
Inelastic collision m1 ≠m2 0.078 -0.015 0.011 -0.009
Elastic collision m1=m2 0.077 -0.017 0.011 -0.004
Elastic collision m1 < m2 0.092 -0.009 0.016 -0.009

Data Analysis
1. Momentum of cart 1 before collision
• p1i=m1*v1i
2. Momentum of cart 2 before collision
• p2i=m2*v2i
3. Momentum of the system before collision
• pi=p1i + p2i
4. Momentum of cart 1 after collision
• p1f=m1*v1f
5. Momentum of cart 2 after collision
• p2f=m2*v2f
6. Momentum of system after collision
• pf =p1f + p2f
7. Relative Change in total momentum of system
• pf- pi
8. Kinetic energy of cart 1 before the collision- KE1i
• KE1i=(1/2)*(m1)*( v1i)2
9. Kinetic energy of cart 2 before the collision- KE2i
• KE2i=(1/2)*(m2)*( v2i)2
10. Kinetic energy of system before the collision- KEi
• KE1i + KE2i
11. Kinetic energy of cart 1 after the collision- KE1f
• KE1f=(1/2)*(m1)*( v1f)2
12. Kinetic energy of cart 2 after the collision- KE2f
• KE2f=(1/2)*(m2)*( v2f)2
13. Kinetic energy of system after the collision- KEf
• KE1f+ KE2f
14. Relative change in total kinetic energy
• KEf -KEi
Conservation of Momentum
% Discrepancy=( |Δp|/ pi)*100
Inelastic Collision m1=m2
• |-0.007/0.08| *100 = 8.75 %
Inelastic Collision m1 ≠m2
• |-0.015/0.078| *100 = 19.23 %
Elastic Collision m1=m2
• |-0.017/0.077| *100 = 22.07 %
Elastic collision m1 < m2
• |-0.009/0.092| *100 = 9.78 %

Conservation of Energy
% Discrepancy= (|ΔKE|/ KEi)*100
Inelastic Collision m1=m2
• |-0.007/0.012| *100 = 58.33 %
Inelastic Collision m1 ≠m2
• |-0.009/0.011| *100 = 81.81 %
Elastic Collision m1=m2
• |-0.004/0.011| *100 = 36.36 %
Elastic collision m1 < m2
• |-0.009/0.016| *100 = 56.25 %

Discussion
The purpose of the experiment was to investigate elastic and inelastic collisions to study the conservation of momentum and energy. The graphs generated in class demonstrate the relationship between position vs time which was used to measure the initial and final velocities of the collisions to later calculate momentum and kinetic energy. In regards to conservation of momentum, the percent discrepancy was calculated by dividing the change in momentum by the initial momentum of the system (|Δ p|/ pi*100). The calculations state that the percent discrepancies for inelastic collisions were 8.75% and 19.23 % for the equal mass and unequal mass respectively. Both of the percent discrepancies were close to the 10%-15% which indicates that the conservation of momentum is valid even with varying weights . The percent discrepancies for the equal and unequal mass elastic collisions were 22.07% and 9.78 % respectively. Both of the percent discrepancies for the elastic collisions were close to the 10%-15% range which validates the concept of momentum conservation in elastic collisions.
In regards to conservation of energy, the percent discrepancy was calculated by dividing the change in energy by the initial energy of the system (|Δ KE|/ KEi*100). The calculations state that the percent discrepancies for inelastic collisions were 58.33% and 81.81% for the equal mass and mass respectively. Both of the percent discrepancies were greater than 60% which indicates inelastic collisions are not as inefficient in conserving energy. The percent discrepancies for the equal and unequal mass elastic collisions were 36.36% and 56.25 % respectively. Both of the percent discrepancies for the elastic collisions were less than the percent discrepancies in elastic collisions which validates the concept of energy conservation to be more efficient in elastic collisions.
There can definitely be more room for improvement in the experiment. The experiment can have higher quality validation of results if multiple trials were performed or if the class data were to be compared and averaged. Performing the experiments under a vacuum and frictionless setting would remove external variables that affect the data leading to more precise numbers. More accurate percent discrepancies illustrating laws of conservation can be achieved by adding more trials and including more sophisticated measuring tools. These techniques would lead to more accurate results to reduce any experimental errors and to better validate the concepts of energy and momentum conservation.

Conclusion
The purpose of the experiment was to investigate simple elastic and inelastic collisions to study the conservation of momentum and energy concepts. The objective of the lab was met since the validity of the Law of Conservation of Momentum was confirmed by determining the relationship of energy and momentum conservation between inelastic and elastic collisions by utilizing percent discrepancy calculations. The calculations state that the percent discrepancies for inelastic collisions were 8.75% and 19.23 % for the equal mass and unequal mass respectively. The percent discrepancies for the equal and unequal mass elastic collisions were 22.07% and 9.78 % respectively. Both of the percent discrepancies for the elastic collisions were close to the 10%-15% range which validates the concept of momentum conservation in inelastic elastic collisions. In regards to conservation of energy, the calculations state that the percent discrepancies for inelastic collisions were 58.33% and 81.81% for the equal mass and mass respectively. Both of the percent discrepancies were greater than 60% which indicates inelastic collisions are not as inefficient in conserving energy. The percent discrepancies for the equal and unequal mass elastic collisions were 36.36% and 56.25 % respectively. Both of the percent discrepancies for the elastic collisions were less than the percent discrepancies in elastic collisions which validates the concept of energy conservation to be more efficient in elastic collisions. The data validates that the Law of Conservation of Mechanical Energy hold true in all types of collisions.