Conservation of Momentum Lab Report PDF

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professor Olugbenga Adeyemi Olunloyo ...

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Physics 221 Section 009 Olugbenga Adeyemi Olunloyo Experiment Performed: 10 October 2017 Report Handed In: 17 October 2017

Conservation of Momentum Introduction The scientific purposes of this experiment are to understand the law of conservation of momentum, to learn the definition of momentum and how to analyze it as a vector quantity, to learn the difference between elastic and inelastic collisions, and to verify the law of conservation of momentum for both collisions. Momentum is calculated by multiplying the mass of an object times the velocity of the same object. In this experiment we calculated the total initial momentum, the total final momentum, and the percent difference. The total initial momentum is calculated by M1V1i+M2V2i (where M1V1i is the first mass times its initial velocity, and M2V2i is the second mass times its initial velocity) . The equation for total final momentum for this experiment was M1 V1f+M2V2f (where M1 V1f is the first mass times its final velocity, and M2 V2f is the second mass times its final velocity) . Percent difference was then calculated by (initial momentum - final momentum) divided by the initial momentum multiplied by 100 to get a percent. These calculations were then used to prove that the total initial momentum is equal to the total final momentum. Procedure The materials used for this lab are the apparatus shown in Figure 1 that consists of: a Pasco two meter air track, gliders with flags, glider weights, inelastic collision pin and putty receptacle, bumpers, air blowers, two photogates, Pasco 850 Universal Interface, computer, and Pasco Capstone software. For each type of collision (inelastic collision with one mass at rest, elastic collision with one mass at rest, and elastic with both masses moving), three different masses were measured. The inelastic collision with one mass at rest was done using the inelastic collision pin and putty receptacle attached to the front of each glider. The second glider was placed between the two photogates, the first glider was then pushed down the track to hit and stick to the second glider. The initial and final velocities were found through the two photogates for each glider and were then multiplied to the mass and added together to get the initial and final momentums. The same process is done for the elastic collision, but bumpers were attached to the front of the gliders instead of the inelastic collision pin. For the elastic collision with both masses moving, the two gliders were put at different ends of the air track and were then pushed towards the center, allowed to hit one another and bounce off. Once again the initial and final velocities were found in order to calculate the initial and final momentums. Percent difference was then used in order to compare all of the values to one another.

Data See attached. Analysis In this experiment, the distance between leading edges of the flag (change in x) was measured with a ruler, the masses were found using a digital scale, and initial velocity was measured by Capstone software configured with the Pasco data acquisition system. The initial and final momentum, as well as percent error, were calculated using Microsoft Excel. Initial and final momentum were calculated for run 1, an inelastic collision, as follows: Initial momentum = pi = (m1v1i + m2v2i) = (0.2123kg x 1.75 m/s) + (0.2142kg x 0m/s) = 0.372 kg x m/s Final momentum = pf = (m1+m2)vf = (0.2123kg + 0.2142 kg)(0.57m/s) = 0.243 kg x m/s Initial and final momentum were calculated for run 6, an elastic collision, as follows: Initial momentum = pi = (m1v1i + m2v2i) = (0.3143 kg x 0.97 m/s) + (0.2147kg x 0m/s) = 0.305 kg x m/s Final momentum = pf = (m1 v1i + m2 v2f  ) = (0.3143 kg x 0.1m/s) + (0.2147kg x 1.01 m/s) = 0.248 kg x m/s Percent error values for all of the runs and a sample calculation are shown below. Please note that run 8 was excluded from the calculation of average percent error for reasons described below. Run Number

Percent Error

1

34.68%

2

54.57%

3

25.82%

4

45.71%

5

49.87%

6

18.60%

7

0%

8

900%*

9

14.71%

Average

30.50%

Table I: Percent Error Sample Calculation: percent errortrial 1 = |(initial momentum - final momentum)|/initial momentum] x 100% = |(0.372 kg x m/s - 0.243 kg x m/s)|/0.372 kg x m/s| x 100% = 34.68% *The percent error value for run 8 has been excluded from the average percent error calculation since it is an outlier. Referencing the data sheet, it can be seen that this is due to the initial momentum values both being extremely small, negative numbers, that are both very close to zero. Due to how small the numbers are, any slight variation results in a large calculated percent error. The experiment demonstrates that in both elastic and inelastic collisions, momentum is conserved. This is supported by the fairly small average percent error value of 30.50%. In the runs where the percent error value was larger, the final momentum was smaller than the initial momentum. This likely indicates that some of the energy was lost to friction, as it is difficult to maintain a perfectly frictionless surface. Additionally, the gliders occasionally made sounds when they collided, indicating some of the collisions were not perfectly elastic or inelastic. In these instances, some energy was lost to sound or friction. A loss in energy results in a lower measured final velocity, and therefore a lower calculated final momentum. This source of error was random, as it did not remain constant between trials. Overall, however, the data supports the law of conservation of momentum, with the initial and final momentums being extremely similar, particularly when the slight presence of friction is taken into account. Conclusions The prediction that momentum would be conserved in both elastic and inelastic collisions was confirmed by this experiment. The low percent error values indicate the conservation of momentum in each run, with slight variations likely due to the presence of friction or collisions that were not perfectly elastic or inelastic. The experiment can thus be considered successful. This lab taught the concepts of conservation of momentum, analyzing momentum as a vector quantity, and the differences between elastic and inelastic collisions. Though the results indicate the conservation of momentum, they also demonstrate that it is extremely difficult to maintain ideal conditions in an undergraduate laboratory setting. To improve the experiment in the future, it would be useful to have an air track with a stronger and more constant air blower that could more reliably maintain a frictionless surface over the course of the experiment....