Marissa,+Stephanie,+and+Ryan+(loser)+Collision+Lab

=​1D Cart Collisions Lab= Date of Publication (Date of Most Recent Edits)


 * Participants**: Marissa, Stephanie, and Ryan.
 * Purpose**: The purpose of this lab is to confirm the law of conservation of momentum.
 * Lab Documents**: [[file:1D Collsions.doc]]

First, the group utilized logger pro in order to view the various collisions of the red and blue car that were designed prior to this lab. We took measurements of each frame (at spesific times that were vital like a few frames before the colllision, the collision, and a few frames following the collision for example - but prior to the collision, we would skip one or two frames in order to speed up the process) by plotting points for each car in order to get an accumulation of the overall velocity from start to finish. As we collected this data through the whole cart collision, it was recorded onto a graph and a chart. In turn, we recorded the mass of the carts given in each video and we were able to determine the velocities by looking at the slope for the initial and final velocities of both the red and blue cart. As a result, we then knew the mass and the velocity and we could then calculate the initial and final momentums. From the gathered velocities and the mass of each car we were able to calcualte the momentum.
 * Brief Description of Experiment**:


 * Data**:

Cart collision video number two, version one: media type="file" key="Collision 2 small.wmv" width="300" height="300"

Here is an example of video number two (version one) where we had our chart, our graph, and the slopes of each initial and final cart collision (velocity). This lead us into the calculation process of the momentum for each cart.


 * Sample Calculations:**

__Momentum Formula__: For each video, we calcualted the momentum for both the initial and final speeds of the blue and red car. The momentum is calculated by taking the mass (in kilograms) and multiplying it by the velocity of the cart (which is expressed in distance in cm per time in seconds). As a result, the answer will be in kilograms per centimeters per second. P = M * V

__Example - Video # 2 (version 1):__ Blue Initial: 0.5 kg * 42.13 cm/s = 21.065 kg cm/s Blue Final: 0.5 kg * 9.08 cm/s = 9.54 kg cm/s Red Initial: 0.25 kg * 0 cm/s = 0 kg cm/s Red Final: 0.25 kg * 56.73 cm/s = 14.1825 kg cm/s

__Kinetic Energy Formula__: The kinetic energy is calculated by multiplying one half times the mass in kilograms and velocity (expressed in centimeters per second) squared. The answer will result in joules. We calcualted the kinetic energy in order to compare the final results for each collision to the final momentums. KE = 1/2 mv² __Example - Video #2 (version 1):__ Blue Initial: (1/2) (0.5 kg) (42.13cm/s) ² = 443.73 j Blue Final: (1/2) (0.5 kg) (19.08 cm/s) ² = 91.01 j Red Initial: (1/2) (0.25 kg) (0 cm/s) ² = 0 j Red Final: (1/2) (0.25 kg) (23.65 cm/s) ² = 69.92 j

__Percent Difference__: The percent difference is calculated by first calcualting the difference by subtracting the final total number of the momentum or kinetic energy from the initial total number of the momentum or kinetic energy for the red and blue cart. Then, the difference must be divided by the old value by dividing the difference result by the initial total number of the momentum or kinetic energy. The next step is to convert the percentage by mulitplying that quotient by 100. This is depicted in the lab questions below.

Describe the major result of the experiment and how you arrived at this result. Typically, this will refer back to the purpose. For example, if the purpose was to find the coefficient of friction, you would write: The coefficient of static friction was determined to be 0.45. This was calculated from a measured angle using Newton's first law as described in the calculations.
 * Results **:

- In the result of the experiment, we found that momentum and kinetic energy is conserved in collisions. We know this because of conservation laws and observations. W saw that some collisions are elastic and some are inelastic. Elestic collisions are when kinetic energy is completely/mostly transfered from cart a to cart b.


 * Lab Questions **:

1. Momentum is a vector quantity (it has a direction associated with it). This is relevant for some of the collisions you analyzed. Which ones and why?

- Yes, vector quantities are relevant to some of out collisions. In collision number four (version one), the mass of the red car was greater than the blue and when they collided, the blue car would ricochet back in the direction that it initially started from. As a result, the final velocity of the blue car was negative. For the collision number eight (version one), the opposite effect occurred where the red car weighed less than the blue and when they collided, the red car would ricochet off of the blue one and would travel back into the direction it initially started in. However, it started out coming towards the blue car rather than staying stagnant like collisions two and six and when thy hit it traveled back the way it came. Finally, for collision number ten (version one) the blue car weighed less than the red car. They were both traveling towards each other (blue’s initial velocity was positive and red’s initial velocity was negative as a result) and when they hit, they both traveled back the way they came. Thus, the blue car’s final velocity turned out to be negative and the red can’t final velocity turned out to be positive. Overall, the main idea is that some velocities were negative due to the direction they traveled on the track. This is the vector quantity of momentum.

2. Calculate the percent difference between the initial total of momentum and the final total of momentum for each collision. Which collision had the largest percent change in momentum?

Video #2 (version 1): 12.6% percent change Video #4 (version 1): 57.7% percent change Video #6 (version 1): 11.96% percent change Video #8 (version 1): -102% percent change Video #10 (version 1): -2186.85% percent change

- Video number 10, version one had the largest percent change. It was concluded that this unusually high percent change was due to the firing off of a spring during the collison adding extra energy to the impact.

3. If you had not correctly scaled the video (the scale line was drawn incorreclty, for instance) it would have no effect on your data's ability to support or refute the law of conservation of momentum. Explain why this is so.

- Our data on the conservation of momentum completely relies on the scale drawn in the video. The data is based on position measurements taken over time. If the scale is drawn incorrectly then all of the measurements would be false and our calculated velocities would also be incorrect. Therefor the law of conservation of momentum would not be supported or fefuted by our video.

4. You may have observed the carts slowing down as they moved across the track before the collision. Suppose you have two velocities for a cart; one just after it was pushed and one immediately before the collision. Which one would be better to evaluate your prediction and why?

- We feel that it would be best to evaluate the velocity right before the collision. This is due to the fact that it would be more accurate in light of the collision because the velocity right after the car is released is not exactly the same as the velocity right before impact. Also, as the cart slows down, the speed that it is traveling at right before the collision is what has the greatest impact on the post collision result of the other cart. What is transferred from one cart to another is the main focus here and how they are affected and travel after the collision. Overall, the pre and post collisions can be compared more accurately.

5. Calculate the percent difference between the initial total kinetic energy and the final total kinetic energy for each collision. Which collisions had large percent changes in kinetic energy?

Percent Difference In Kinetic Energy of Collision Videos: Video 2 (version 1) = 60% Video 4 (version 1) = 40% Video 6 (version 1) = 10% Video 8 (version 1) = 80% Video 10 (version 1) = 180%

- Our results (shown above) show that collisions 2, 8, and 10 had large percent changes in kinetic energy. This means that these collisions were most likely inelastic because the kinetic energy was not conserved upon collision.

6. Examine the group's analysis to see how each collision was characterized (as elastic or inelastic). How can you tell if a collision will be inelastic?

- One can tell if a collision will be inelastic by calculating the kinetic energy before and after the collision. If the result is different before and after, then it will be considered elastic. Elastic collisions have been known to conserve both momentum and the kinetic energy. In addition, one can also determine if the objects decrease in total energy or if they stick together. If they do either of the two, then they will be considered inelastic. Inelastic collisions tend to conserve momentum but not kinetic energy.


 * Conclusion **:

We think that the experiment did produce a valid and reprodible result because the video will always stay the same and there is a very low level of possible human error that could be associated with this lab. Though the human error level is low, it is still there so it is possible to get experimental results that will differ from the expected values. The possible human error margin could include a calculation error or when plotting the data, not putting the dots exactly on the same part of the cart in the video. Well, there could be a set number of decimal point places everyone will stop at to avoid different types of simplifying and approximating when doing calculations. This would provide more accurate data if everyone used the same simplifying technique.

//Don't forget to link to your lab report from the lab reports page and to include a link to your lab report in your reflection.//