Collision+Lab

=1D Cart Collisions Lab= September 23, 2009


 * Participants**: Sean Hamilton and Niko Pearson
 * Purpose**: The purpose of this lab is to confirm the law of conservation of momentum.
 * Lab Documents**: [[file:1D Collsions.doc]]

For this experiment we used the software Logger Pro to analyze prerecorded videos of two carts on a track colliding in various versions and ways. We first imported the movie Collision 1 Version 1 into Logger Pro and created a scale for meters by using the meter stick that was in the video. Once we set up the origin directly on the track, we plotted points from the blue carts initial place, to when it started to collide with the red cart. By doing this right on the video, we were able to form a data table and chart as to what the velocity was of the cart and where it was on the x axis. After they collided, we created a second set of points then calculated the red carts initial and final velocity. We used a linear fit, and determined the slope of each line and found that they were roughly the same. Then we calculated the average of all the velocities and the cart's masses and found both of their momentum. Once we figured out what we needed to calculate, we spilled up and each took two versions of collisions and collected the data.
 * Brief Description of Experiment**:

media type="file" key="Collision 1 small.wmv" width="210" height="210" media type="file" key="Collision 2 small.wmv" width="210" height="210" media type="file" key="Collision 3 small.wmv" width="210" height="210"

media type="file" key="Collision 5 small.wmv" width="210" height="210" align="left"

Video 4 Unavailable


 * Data**: Data Tables and also the Graphs are shown for each of the five experiments.

Collision 1 Version 1 Data Table Collision 1 Version 1 Graph
 * Carts || Mass (kg) || Initial Velocity (m/s) || Final Velocity (m/s) || Average Velocity (m/s) || Slope (m/s) || Momentum (kg m/s) ||
 * Blue || 0.256 || 0.585 || 0.359 || 0.537 || 0.5546 || 0.138 ||
 * Red || 0.254 || 0.477 || 0.5 || 0.505 || 0.5095 || 0.129 ||

Collision 2 Version 1 Data Table Collision 2 Version 1 Graph
 * Carts || Mass (kg) || Initial Velocity (m/s) || Final Velocity (m/s) || Average Velocity (m/s) || Slope (m/s) || Momentum (kg m/s) ||
 * Blue || 0.774 || 0.452 || 0.111 || 0.329 || 0.4343 || 0.256 ||
 * Red || 0.255 || 0.522 || 0.51 || 0.545 || 0.5537 || 0.138 ||

Collision 3 Version 1 Data Table Collision 3 Version 1 Graph
 * Carts || Mass (kg) || Initial Velocity (m/s) || Final Velocity (m/s) || Average Velocity (m/s) || Slope (m/s) || Momentum (kg m/s) ||
 * Blue || 1.29137 || 0.522 || 0.26 || 0.3996 || 0.5122 || 0.52 ||
 * Red || 0.255 || 0.622 || 0.739 || 0.7599 || 0.7776 || 0.194 ||

Collision 4 Version 1 Data Table Collision 4 Version 1 Graph
 * Carts || Mass (kg) || Initial Velocity (m/s) || Final Velocity (m/s) || Average Velocity (m/s) || Slope (m/s) || Momentum (kg m/s) ||
 * Blue || 0.256 || 0.564 || 0.521 || 0.546 || 0.5491 || 0.14 ||
 * Red || 0.515 || 0.261 || 0.12 || 0.195 || 0.1827 || 0.101 ||

Collision 5 Version 1 Data Table Collision 5 Version 1 momentum= mass x velocity p = m x v ex. Collision 1. p = (0.537)(0.256) = 0.138kg m/s || KE= ½mv² || F **·** Δt = m **·** Δv || F **·** d = ΔKE ||
 * Carts || Mass (kg) || Initial Velocity (m/s) || Final Velocity (m/s) || Average Velocity (m/s) || Slope (m/s) || Momentum (kg m/s) ||
 * Blue || 0.256 || 0.673 || 0.621 || 0.512 || 0.6551 || 0.131 ||
 * Red || 0.254 || 0.338 || 0.207 || 0.271 || 0.2686 || 0.069 ||
 * Calculations:** The formulas that we used throughout this lab are:
 * //Momentum// || The momentum in kilograms per meter per second is calculated by taking the average velocity in meters per second and multiplying it by the mass in kilograms.
 * //Kinetic Energy// || Kinetic energy is calculated by taking half of the mass multiplying velocity squared.
 * //Impulse// || Impulse is change in momentum.
 * //Work// || Work is the change in kinetic energy.


 * Results**: The results for this lab were fairly divided. The majority of the collisions ( 2, 3, and 5) did not conserve momentum, while only two (1 and 4) did conserve momentum. This conclusion was reached by determining and comparing the percent differences between the initial momentum and the final momentum for each collision.

//1. Momentum is a vector quantity (it has a direction associated with it.) This is relevent for some of the collisions you analyzed. Which ones and why?// According to our data, the direction of the cart was irrelevent because all of our experiments went to the right and had a positive momentum whereas if we had a negative momentum, the cart would have gone to the left.
 * Lab Questions**:

//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?// Collision 1: (0.129 - 0.138) / 0.138= -0.0652x100= **6.52 %diff.** Collision 2: (0.138 - 0.256) / 0.256= -0.4609x100= **46.09 %diff.** __Collision 3: (0.194 - 0.52) / 0.52= -0.627x100= **62.7 %diff.**__ Collision 4: (0.101 - 0.14) / 0.14= -0.279x100= **27.9 %diff.** Collision 5: (0.069 - 0.131) / 0.131= -0.4733x100= **47.33 %diff.** Collision 3 had the largest percent change in momentum.

//3. If you ad 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.// Even though our data would not be exactly the same as if we actually did the experiment, all the numbers on the charts would correspond with each other and still proved the result of conservation of momentum.

//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 used and one immediately before the collision. Which would be better to use to evaluate your prediction and why?// It would be better to use the velocity of the cart just before the collision as opposed to its velocity just after being pushed, and that is because the velocity of the cart just before the collision is the velocity at which it interacts with the second cart. Because we are measuring whether or not momentum is being conserved during the collision, when the momentum is transferred from one cart to the other, this is should be the more valued velocity.

//5.Calculate the percent difference between the initial total kinetic energy and the final toal kinetic energy for each collision. Which collisions had large percent changed in kinetic energy?// Collision 1: Initial KE= 0.0370 Final KE= 0.0325 (0.0325 - 0.0370) / 0.0370= -0.1216x100= **12.16 %diff.** Collision 2: Initial KE= 0.0419 Final KE= 0.0379 (0.0379 - 0.0419) / 0.0419= -0.0954x100= **9.55 %diff.** Collision 3: Initial KE= 0.1031 Final KE= 0.0736 (0.0736 - 0.1031) / 0.1031= -0.2861x100= **28.62 %diff.** __Collision 4: Initial KE= 0.0381 Final KE= 0.00979 (0.00979 - 0.0381) / 0.0381= -0.7430x100= **74.30 %diff.**__ Collision 5: Initial KE= 0.03355 Final KE= 0.00933 (0.00933 - 0.03355) / 0.03355= -0.7219x100= **72.19 %diff.** Collision 4 had the largest percent change in Kinetic Energy.

//6. Examine the groups' analysis to see how each collision was characterized (as elastic or inelastic). How cab you tell if a collision will be inelastic?// Collisions 1,2, and 3 were elastic and collisions 4 and 5 were not elastic. With the data that we have collected, there isn't a solid way to predict the elasticity of a collision.

The results produced from this lab are valid and reproducible, however, the results concerning the law of conservation of momentum seemed a bit of track. For example, the fact that only two collisions (collisions 1 and 4) seemed to conserve momentum. Something else that seemed offset from what they should have been were the percent difference values for both the changes in momentum and the changes in kinetic energy. They appeared to express the right answers and were all proportional to each other, but were just too high in value. A big reason that our experimental results differ from any expected results is human error (ie: miscalculating data). Another could be that we (the class) are overlooking certain variables that may affect the carts' movements (ie: air resistance). A suggestion to improve the experiment would be to further incorporate impulse and work calculations into the lab. Putting a little more attention impulse and work calculations for each collision could make results more accurate.
 * Conclusion**:

//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.//
 * Reflection:**