4/22/15: Collisions In Two Dimensions Lab 15

Purpose: Determine if momentum and energy are conserved by looking at a two-dimensional collision.

Experiment / Procedure: 

This lab consisted of setting up two elastic collisions using a steel ball paired with another steel ball and a steel ball paired with an aluminum ball. We used a smooth glass table with a camera mounted on it to give a birds eye view of each collision. The camera captured the data needed to determine if momentum and energy were conserved.

Part 1: Steel Ball and Steel Ball Collision

We used the video capture software on logger pro to plot the position of each ball before, during, and after the collision. To actually do the calculations, all we needed was the mass of the balls and the graphs generated by Logger Pro. M steel ball = 66.8 g

As the points are being plotted for each ball, Logger pro will generate graphs for the x and y motion of each. The graphs can be used to determine the initial and final x and y components of velocity for each ball.

Below is the position vs time graph of the ball that is initially rolling and by taking the slope of the graph, the initial velocity can be determined. The initial speed of the rolling ball before the collision Vo1 = 188.3 and the final velocity of the x component V1f,x = 104.5

  

Next, we can look at the y components of velocity for the ball that is initially rolling

Below shows the y component of the final velocity. V1f,y = 56.09 and the initial velocity of the first rolling ball in the y direction is 0. Taking the slope of the position vs. time graph will yield the velocity.

Next we examined the ball that was initially at rest. The initial x and y components will both be 0. (Ball is initially at rest). Again, by taking the slope of the position vs. time graph will give the velocity. 

The final y component of velocity V2f,y = 58.98

Below shows the the final x component of velocity V2f,x = 75.85

Now that we have all of our required values, we can see if momentum and energy were conserved. The equations necessary for this step are shown below as well as the actual calculations. 

Conservation of momentum and conservation of energy. 

Calculations

Below, the finals values are not exact, but we can see that momentum in the x and y directions should be conserved. 

Below shows that energy was lost. It could have been lost due to heat and sound when the collision occurred.

Part 2: Steel Ball and Marble Collision

The same set up is used as in part 1 except we will be replacing one of the steel balls with a marble. We plotted points again and analyzed the motion of our graphs, took the slope to determine the velocity, and used the necessary equations to see if momentum and energy were conserved. Mass of marble = 20.7 g and mass of steel ball = 66.8 g

Below are the calculations. The graphs are almost identical to the ones from part 1, only the slopes have changed. Note that M = steel ball and m = marble

Conservation of Momentum

Again it was observed that momentum should be conserved in both the x and y directions. 

Conservation of Energy

Below the calculations show that some energy was lost and again most likely due to heat and sound. 

Conclusion: Our main objective was to see if momentum and energy were conserved for two elastic collisions. Once we had determined the velocities of each ball in the x and y directions and substituting those values into the proper equations, we were able to see that in both situations, momentum was conserved, but energy was not. In a perfectly elastic collision, no kinetic energy should be lost. In part 1, the difference in energy is somewhat significant, and in part 2 the final and initial kinetic energies are a little bit closer. Again, the energy loss is most likely due to heat, sound, or improper analysis of the video. Another source of error could have been from not choosing the exact same point on the ball when we plotted it frame by frame, as it should have been done from the center of the ball.