# Intro but if all external forces do not equal

Intro to momentum: Linear momentum, also known as just momentum, is basically the vector quantity of an object that is in motion. The momentum of any object in motion can be calculated by multiplying the mass of the object with its velocity. Due to velocity being a vector, momentum is a vector as well. Its direction is the same direction as the direction of the velocity. During collisions, there are questions that arise regarding momentum, such as: Is momentum conserved? The law of conservation of momentum states that momentum will always be conserved if and only if no external forces(forces outside of the system) act upon the system. According to newton’s third law, all of the internal forces will equal zero but if all external forces do not equal zero, momentum will not be conserved. Therefore, it can be concluded that the total momentum prior to a collision is equal to the total momentum after the collisions, Pi=Pf, if no external forces play a role. There are two types of collisions, inelastic and elastic. In both these collisions, momentum is expected to be conserved, however kinetic energy is not.Objective:The main objective of this lab is to test the law of conservation of momentum.This law will be put to the test through the use of an air track, which minimizes friction. The minimization of friction allows for the momentum to be conserved and prevent momentum from changing. However, the air track does not completely reduce friction, thus forming a small margin of error. However, if we consider friction to be part of the system, and an internal force, the momentum should still be conserved because both objects face the same amount of friction. Therefore, the total momentum in this experiment should be conserved throughout all trials. In this experiment, we will analyze the momentum in multiple collisions, with varying velocities, and determine if the total momentum was, in fact, conserved.Material List:Air track systemTwo glidersWeights for glidersMotion sensor Datahub setiPadProcedure: Two gliders, weights, a motion sensor box, datahub box, an iPad, and air track system was collected. The air track system was set up and the weights were put onto the gliders.The mass of both gliders was measured, both weighed the same.Then, the datahub was setup and connected with the iPad. Afterwards, the motion sensor was taken out of the blocks and set up. One glider was placed in the center of the airtrack and held at rest. The second glider was placed on the far left side with the motion sensor behind it, to measure its initial and final velocity. The second glider was then released with some force as it collides with the first glider. The first glider, which was held by a hand, was released prior to the collision. However, the air gave the glider some initial velocity, thus not making it at “rest”. The collision part of the experiment was reenacted multiple times to receive a substantial amount of evidence. Data:Collision 1Collision 2Collision 3Data analysis: Through the data gained by the trials, the initial and final momentum were able to be calculated. Using the initial and final velocity of the second glider, while knowing that the initial velocity of glider 1 = final velocity of glider 2, the final velocity of the second glider can be solved using the equation below. m1v1+m2v2= m1fv1f+m2fv2fm1v1- initial velocity and mass of glider 1m2v2= initial velocity and mass of glider 2m1fv1f= final velocity and mass of glider 1m2fv2f= final velocity and mass of glider 2Through substitution, the final velocity of glider 2 was calculated in all 3 collisions. Then, the initial momentum and final momentum was calculated through equation below.Total Momentum =P= P1+P2 P1is the momentum for glider 1P2is the momentum for glider 2Calculating the initial and final momentum, the calculations show how momentum was conserved with a small margin of error. Due to the same amount of air “pushing” both gliders, it is safe to assume that the initial velocity of glider 1 is equal to the final velocity of glider 2. However, another way to approach this is that the same amount of velocity is affecting both gliders, thus canceling itself through the math. Therefore, through calculations, it is shown that momentum is conserved throughout all three collisions. Also, the transferring of velocity determines that all collisions were elastic.Uncertainty and Error: Human errors in this experiment were: hands holding the motion sensor. With hands holding the motion sensor, a slight shake could have affected the readings. Also, the motion sensor did not stay in place as the person did move his hands, thus causing the motion sensor to read other things and not get an accurate reading of the glider’s velocity. An experimental error is the motion sensor. The motion sensor picks up nearly everything. That said, the motion sensor could have picked up the velocity of someone walking by the experiment and leading to an incorrect velocity reading of glider 2. Also, the air track could have been pushing out more air on one side of the track, which would have affected that glider more, but we do not know for sure. Conclusion: The data gained by the experiment helps support the hypothesis, that momentum will always be conserved in elastic collisions.  Based on the classification of our system, there were no external forces, thus resulting in momentum being conserved in each collision.Question:In each collision, most of the momentum was conserved with a small margin of error, we assumed the initial velocity of glider 1 was equal to the final velocity of glider 2(since that is what happens in an elastic collision). However, if we include the air released from the air track, this would end up canceling the effect of the air, thus resulting in momentum being conserved. If the air track was tilted.The momentum would be the same, but in the opposite direction. The forward momentum becomes the backward momentum. Depending on the system, momentum can be conserved if the air track was tilted. Assuming the earth as the system, momentum will be conserved. Gravity would be an equal effect on both gliders, thus causing its effect to cancel, and momentum would still be conserved. Newton’s third law concludes that the sum of all the internal forces equal zero thus not affecting the momentum. If the isolated system was just the two objects colliding, then gravity would be the external force, thus causing momentum to not be conserved.  In our experiment, we classified the entire earth as our system, thus eliminating all external forces, such as friction and gravity, as a factor of disrupting momentum.