Verifying the Law of Conservation of Momentum. Jeremy Vosen Lili Lackner. Mrs. Rudstrom


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1 Verifying the Law of Conservation of Momentum Jeremy Vosen Lili Lackner Mrs. Rudstrom January 26, 2012
2 Introduction The Law of Conservation of Momentum lab was performed using an air track that minimized friction, allowing us to test or hypotheses. Our first hypothesis is momentum is conserved in elastic and inelastic equations, so pi=pf. Our second hypothesis is kinetic energy is conserved in elastic collisions but not in perfectly inelastic collisions. Our first collisions consisted of air gliders crashing into each other and bouncing back separately, while our second collisions involved crashing two air gliders together that stuck together and moved as one. While the air track did allow us to minimize friction, it did not completely remove it. Air track Two air gliders Two photogates Masses Clay Materials Method While doing to lab, it is a good idea to have one person performing the collisions while the other person collects data using LoggerPro. 1. The masses of both air gliders were recorded in columns m1 and m2. 2. The air track was prepared for an elastic collision. One air glider was set on the far left and the other air glider was placed between the two photogates. 3. The collect was pushed, and air glider one hit air glider two in an eleastic collision. The velocities were recorded in the table. 4. Steps 2 and 3 were repeated, with air glider two having 100 grams of extra mass.
3 5. The air trach was prepared for a perfectly inelastic collision. A piece of clay was placed on air glider two and the glider was put it between the photo gates. The air glider one was placed at the far left. One note card was removed from the air gliders. 6. Hit collect and push air glider one into air glider two. The initial velocity and combined final velocity were recorded in the data table. 7. Steps 5 and 6 were repeated with air glider two having 100 grams of extra mass. Data Column1 Column2 Column3 p,i p,f Collision kg*m/s kg*m/s Collision kg*m/s kg*m/s Collision kg*m/s kg*m/s Collision kg*m/s kg*m/s Momentum Column1 Column2 Column3 Column4 KEi KEf % Lost Collision J J 14% Collision J J 6% Collision J J 65% Collision J J 90%
4 Kinetic Energy Column1 Column2 Column3 Column4 Column5 Column6 Column7 m1 V1,i V1,f m2 V2,i V2,f Collision kg m/s 0 m/s kg 0 m/s m/s Collision kg m/s Neg m/s kg 0 m/s m/s Collision kg m/s m/s kg 0 m/s m/s Collision kg m/s m/s kg 0 m/s m/s Column1 Column2 Column3 Column4 Column5 Column6 Column7 m1 V1,i V1,f m2 V2,i V2,f Collision kg m/s 0 m/s kg 0 m/s m/s Collision kg m/s Neg m/s kg 0 m/s m/s Collision kg m/s m/s kg 0 m/s m/s Collision kg m/s m/s kg 0 m/s m/s Results and Discussion Using the data obtained through our air track trials, we then calculated exactly how much initial momentum and kinetic energy; final momentum and kinetic energy; and how much percent of kinetic energy was lost through these collisions. To calculate momentum we used the equation pi=pf which expands to m1v1,i+m2v2,i=m1v1,f+m2v2,f. We substituted our numbers obtained through the experiment into the left side of the equation to get our pi and the right side to get our pf. Since these two values are very close (for example, Collision 1: pi=0.078 kg*m/s & pf= kg*m/s), we can say that our first hypothesis was accepted. Collisions 3 and 4 showed significant loss in momentum which probably ensued from the use of clay. Had we used Velcro I believe the two values would have been very close. Next we used the equations KEi=1/2m1v1 2 and KEf= 1/2m2v2 2 to find the KEi, KEf, and the % lost. We substituted our numbers obtained through the experiment into the equations and found out that KE is conserved in elastic equations but not in perfectly inelastic equations (65% and 90 % decrease in KE in an inelastic, compared to 6% and 14% in an elastic collision), supporting our second hypothesis. We
5 noticed, however, that there were still small amounts of KE lost during the elastic collisions. This is most likely due to friction, because the air track did not completely remove it. There could also have been some calculation errors which would lead to inaccurate data as well. Conclusion Through this experiment we were able to successfully prove our two hypotheses: that momentum is conserved, and that kinetic energy is only conserved in elastic collisions. Again, there were some slight discrepancies which happened due to small amounts of friction and the use of clay instead of Velcro. There could have been miscalculations also. Doing experiments like this could have valuable applications in places like the auto industry, in which they need this data to test for safety. Although not used in this lab, the impulse equation could be used to better enhance the safety of vehicles. The more time during the collision, the less force felt on the passengers. This experiment gave me a greater understanding of collisions and facilitated performing these calculations.
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