Drew+Jill+Collision+Lab

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


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


 * Brief Description of Experiment**: To collect the data we needed for this lab. First we opened up one of the collision videos in logger pro. We then set a scale for each video using the 61cm level on the table in each video as a reference. Next we started the video until the blue cart was in sight. Once the cart was in in sight, we plotted point on the front of the cart every few frames of the video. Once the cart came close to colliding with the red cart, we plotted many more points to be able to see where momentum was transferred and give us the velocity at that moment. We plotted another set of points for the red cart as soon as it was hit by the blue cart. (We put these points on the back of the red cart so at one point the blue and red points would overlap representing the collision and transfer of momentum). To find the initial and final velocity of the carts we used our data to guess at which points (one point before and one after the collision) would prove the law of conservation of momentum correct. We found this method not very accurate so for the last two trials we instead used our graphs to find velocities. To do that, we had to find the slope of the points for the blue cart before the collision (initial) and after (final). The numbers we got from the slope = our velocities. The initial velocity of the red cart was always zero because the cart wasn’t moving to begin with; to find it's final velocity we found the slope of the red carts points after the collision.


 * Data**:
 * Note: Bold letters are the blue and red initial momentums or blue and red final momentums added together.

//*Note this is an example of our group using the slope to find a more accurate velocity, this is collions 5 version 1.//




 * Sample Calculations: To see if momentum was conserved, we multiplied the mass of the cart by its initial velocity and then mass times its final velocity. We did the same thing for the second cart. Then we added the initial velocity of the first cart and initial velocity of the second cart together, followed by the final velocity of the first cart and final velocity of the second cart together. If those two numbers came out the same, then the law of conservation of momentum was proven correct. **


 * //Initial/Final Momentum

Total Momentum//

//% Difference

Kinetic energy// || Blue cart mass*Blue cart initial velocity= Initial momentum 1. Blue cart mass*Blue cart final velocity=Final momentum 1

Red cart mass*Red cart initial velocity= Initial momentum 2. Red cart mass*Red cart final velocity=Final momentum 2 Initial momentum 1+2= total momentum before collision. Final momentum 1+2= total momentum after collision

(Initial - Final)/ Initial * 100

KE=1/2(mass)(velocity)^2 ||
 * Results**: The purpose of the lab was to prove that the law of conservation of momentum is correct. From the data we collected from this lab this law seems true. The two momentum values (before and after collision) that we collected experimentally were generally close together in value; however, most lost about .03 kg*m/s of momentum. This is only a slight difference overall, and the numbers may not be exactly the same before and after the collision, because of the way we collected our data. Our data might be slightly inaccurate causing the results to be slightly skewed, as well.

In the collsions that momentum being a vector quantity is relevant, it can be seen that as the red car moves to the left the velocity is negative and as the blue car moves to the right the velocity is positive which means if the two cars are moving at the same speed heading toward each other, the momentum will cancel out and the two cars will become motionless. This can be seen in collision number 7.
 * 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?**

1. 2.81 % 2. 20% Collision 2 version 1 had the greatest percent difference. 3. 5.38% 4. 18.5% 5. 0.48%
 * 2. Calculate the percent difference between the initial total momentum and the final total momentum for each collision. Which collision had the largest percent change in momentum? **

**3. ** **If you had not correctly scaled the video (the scale line was drawn incorrectly, 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.** The reason the scale line would not affect the conservation of momentum is because the conservation of momentum is determined by whether or not the initial and final totals are almost the same after the collision and the scale line only gives velocity the correct units.

**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 would be better to use to evaluate your prediction and why?** The velocity that should be measured is the one right before the collision because the cart has had time for friction to take some control of its speed as it moves accross the ramp. When the cart has just been pushed, the velocity will be greater because friction hasn't had an affect on the cart and slowed it down. Therefore, if that the velocity at the push it wouldn't be accurate because it slows down right before the collision, so then our data would be inaccurate.

1. 7.04% 2. 26.64% 3. 17.53% 4. 69.07% 5. 50.84% Number 4 and 5 had the largest percent changes in kinetic energy.
 * 5. Calculate the percent difference between the initial total kinetic engery and the final total kinetic energy for each collision. Which collisions had large percent changes in kinetic energy?**

Our group characterized collison 4 and 5 as inelastic because the percent change in kinetic change were very high. you can tell if a collsion will be inelastic if colliding objects such as the blus and red cars become tangled or couple together. This can be seen in collison 4 and 5.
 * 6. Examine the groups analysis to see how each collision was characterized (as elastic of inelastic). How can you tell if a collision will be inelastic?**

The experiment produced a valid and reproducible result depending on the type of collision. For example: Collision 1: Version 1, the blue car completely transeferred its' momentum to the red car causing the blue car to stop and the red car to continue on. If all collisions transferred the momentum directly from one car to the other then we would know that the car [initially moving] would stop. The reason why momentum may not have been conserved is because of human error in reading the charts and graphs. Also, because it lost it in heat and sound, as well as escaping into the air and track. A suggestion for the improvement of the experiment would be to have detailed notes of how each collision was performed. Also, in the beginning of doing the calculations for this lab, we were just reading the velocity from the chart and then we were told to use the slope for more accurate results. It would have been nice if we had not had to be told to use the slope from the beginning to get more accurate results. Another issue was trying to figure out where to place the points in LoggerPro so you could analyze the brief momentum conservation right before and right after the collsion.
 * Conclusion**:
 * A statement about whether you think that the experiment produced a valid and reproducible result and reasoning supporting your statement.
 * A suggestion as to why your experimental results differ from any accepted value or your expected result (if appropriate).
 * A suggestion for a simple improvement to the experiment. Think about what caused problems, measurement inaccuracies, or inappropriate simplifying assumptions and propose a change. A sketch may be helpful.